The wave of downsizing is generally thought to have originated in the merger boom of the late 1980s and the subsequent recession of the early 1990s. This study attempts to quantify the exact impacts of a downsizing on the return to a stock. Specifically, how does the news of a downsizing affect the stock price, which is the investor's expectation of discounted future cash flows? For the purposes of this study, a company will be included in the data set if it meets the following criteria:

1. The company is public, and listed either on the New York Stock Exchange or the NASDAQ at the time of the downsizing.
2. The company was not in bankruptcy or reorganization at the time of the downsizing.
3. The firm's principal offices are located in the US or Canada.
4. The downsizing was reported by Bloomberg News Service, Reuters, CNN, or CNBC the day of the downsizing (when applicable).
5. The downsizing was mentioned in at least five of the following newspapers the day following the announcement:

1. The New York Times
2. The Los Angeles Times
3. The San Francisco Chronicle
4. The Boston Globe
5. The Chicago Tribune
6. The Atlanta Journal-Constitution
7. The Washington Post

These criteria ensure that the measurement of the change in equity value is quantifiable, and that the downsizing is large enough not only to be considered "news" that investors should take seriously, but also "news" for the general labor market.

For the purposes of the study, the following types of labor decisions are considered downsizing; all other kinds of changes in employment are simply considered "layoffs," as they do not meet the specialized criteria for a downsizing.

1. The company eliminates either at least 2,000 jobs if it has more than 20,000 employees.
2. The company eliminates at least 10% of its workforce if it has less than 20,000 on its payroll.
3. Terminated employees who work in a unit that the parent company is planning to divest are not included.
4. Employees whose positions are terminated, but are relocated to another business area of the company are not included.
5. Workers to be eliminated as a result of a merger are included. If the downsizing relates to a merger, the employees eliminated by the target company are regressed against the target company's stock price only. The same applies to a company eliminating jobs as the result of its acquisition of another company.
6. Eliminated positions are included regardless of the severance package involved.
7. The actual amount of workers eventually terminated is not relevant; only the announcement of how many workers will be eliminated is included.
8. The downsizing announcement occurred between January 1990 and December 1997.
9. The downsizing occurs at least six months after the company's last downsizing.

As a result of these criteria, 38 such downsizings occurred between 1990 and 1997. 34 companies were involved in massive downsizings. Three companies: BankAmerica Corp., Boeing, and Digital Equipment Corp. (DEC) had more than one downsizing that meet all of the criteria above. For example, the Bank of America cut jobs in 1992 related to a merger, and it cut jobs in 1996 to reduce costs. The following companies made headlines with the announcement of massive job cuts.

The announcement of a downsizing can be viewed as a rare event, in that the company's decision to lay off workers is generally uncommon. The closing prices for the 102 days prior to and including a downsizing announcement were obtained from Datastream and adjusted for stock splits, but not for dividends. The stock returns for all 38 downsizers were calculated for each day. There were 100 returns for the trading days prior to the announcement, and 1 return for the trading day on which the announcement was made. A return for day j is considered as follows:

where r is the return, and S is the stock price.

The mean returns over the 100 days, as well as the standard deviation of the return were calculated for each stock. The return of the 101^st day (the day on which the downsizing was announced) was then compared to the distribution of the returns for the previous 100 days. If this return was more than two standard deviations above or below the mean return, the return on that day was considered to be a "rare event."

For 11 of the stocks, the return on the day during which a downsizing was announced was more than two standard deviations above the historic mean return. For six, the return was two standard deviations below the mean. For 22 of the stocks, the return fell within two standard deviations of the mean. The following chart displays the results of this calculation:

* Simultaneous announcement with a loss on the income statement

† Simultaneous announcement with a merger or a divestiture of at least 10% of firm's assets.

Clearly, the announcement of a downsizing has a noticeable and substantial impact on the equity value of many of the firms to be studied. Moreover, simply because the announcement of a downsizing did not meet the stringent requirements set herein for a "rare event," that does not imply that the stock did not gain or lose a significant percentage of its value through fluctuations occurring during the trading day. In many cases, the downsizings did not register as rare events because the stock price volatility was high leading up to the announcement.

One important indicator from this first glance is that the announcement of a merger, or of a substantial loss does not readily indicate the market's reaction. Both Sears and Woolworth's announced sluggish sales along with downsizings, yet investors boosted Sears and dumped Woolworth's. Additionally, out of the eleven stocks that significantly appreciated the day of a downsizing announcement, five of the companies were losing money. What could possibly cause the market to bolster DuPont and dump Kodak after both make a similar announcement? There exists no systematic evidence for either a positive or negative effect of downsizing on the price of a stock; the results show all kinds of reactions in the stock price.

If such a "rare event" is truly relevant news, then it will move the stock price, to the extent that the news was not only unanticipated, but also has a significant impact on investors' valuations of the future earnings potential of the company. The absolute deviation of the return from the mean return on the day of the downsizing will be compared to the average deviation from the mean return for the previous 100 days. If the absolute deviation from the mean return the day of the downsizing is significantly different from the average deviation from the mean return for the 100 days prior to the downsizing, then it can be concluded that downsizing is relevant news.

The mean return for the 100 days prior to the downsizing was calculated for each stock as:

The absolute value of deviation on date j from the mean return is calculated as:

The mean and standard deviation of the random variable are computed; as is the sample statistic, , which is the absolute value of the difference between the return the day of the downsizing and the mean return for the past 100 days:

The sample statistic was then compared to the distribution of , to determine if the deviation from the mean return the day of the downsizing was statistically different than a deviation from the mean return on any other day. This can be facilitated with a one-tailed test as follows. The null hypothesis is: the absolute deviation from the mean return the day of the downsizing is the same as the deviation from the mean return on any other day. For a generic distribution that can only take on positive values, the one-tailed test appears as follows:

* Simultaneous announcement with a loss on the income statement

† Simultaneous announcement with a merger or a divestiture of at least 10% of firm's assets.

¤ Can also be rejected at the 5% level.

This analysis proves that downsizing is relevant news for more than half the stocks studied as there is unusual volatility the day of the downsizing announcement. This indicates that downsizing may be relevant news for valuing a stock. Based on the sheer magnitude of the deviation from the return, stocks of companies that downsize are expected to experience wild swings in their returns relative to the mean return. The next section studies the exact content of the firm's downsizing announcement, to see if different kinds of downsizing provoke different kinds of reactions in the market.

Several variables related to the downsizing and its results were measured and regressed in order to determine what impact specific news related to a downsizing has on stock prices. Firstly, the daily return of the stock from the closing price the day before the announcement (day -1) to the closing price the day of the announcement (day 0) was measured. If the announcement was made after the close of trading on one day, it was considered to have been made at the opening of the exchange on the next day. This method of measurement does not account for the large swings that stock prices may undergo during a day in which such an announcement is made, but these data may be too noisy to make instructive comparisons. Typically, in such situations, the company will release no more than one statement to the public per day, so using closing prices allows us to measure the market's reaction to news of a downsizing, once the entire market has had the opportunity to process the information.

Other returns were also calculated to measure the longer-term effects of the downsizings. The 5-day, 25-day, and 100-day return of the stock (from the day before the downsizing was announced) have also been calculated to determine if stocks of downsized companies have a particular pattern in their returns.

One criticism of the use of such returns as the dependent variable is that they ignore that the stock trades within a broader market, which has its own fluctuations and returns. For example, the return to a downsized company in 1996 might look artificially better than that of a downsized company in 1993 simple because equities (as measured by any commonly used stock index) appreciated at a faster rate in 1996 than 1993. Such logic would suggest that the premium of the stock return over the return to the S&P 500 or the Dow Jones Industrial Average be used to measure how the announcement of a downsizing would cause a stock to outperform or underperform relative to a basket of other stocks.

This criticism is flawed, simply because it ignores the possibility that the entire market will rise as the result of a downsizing of one company. Assume that instead of using the return to AT&T the day it announced the downsizing, I used the return of the AT&T less the return on the Dow Jones. The return to AT&T was over 4%, while the Dow as a whole rallied on the news of the AT&T restructuring. Therefore, while AT&T's return itself would be abnormally high, its return over the market index would not be, so the news of a downsizing would be hidden in the data. I believe that the minor intervals of the returns which I am measuring (for example, the daily return) are small enough that they do not necessarily need to be reduced by whatever mood the Dow was in during the era of the announcement.

The independent variables are related to the scope of the downsizing. The number of workers laid off, the total amount of employees at the time of the downsizing, and the percentages of employees laid off are variables for the right-hand side of the regression. These variables are simply the announced number of workers being asked to leave the firm, not the amount that actually will eventually lose their jobs (the two are often not the same). The announced value and not the actual value are used since the market does not know at the time how many layoffs there will actually be, only how many layoffs the company says that there will be. There are also six dummy variables that describe the content of the downsizing announcement:

The dummy variables are meant to capture the differences in the types of downsizings made by each company. For example, a downsizing related to a big merger might not have the same impact as a downsizing related to a disappointing loss of money. The merger variable attempts to account for firings made which are related to the reorganization or restructuring of a business. The technology variable attempts to control for downsizings that are a result of the substitution of capital for labor. The bad news variable should help to control for the market's simultaneous reaction to the announcement of poor financial performance or a financial crisis. The "super big" dummy variable attempts to single out the major downswings from the standard downsizings. This variable will measure if the extra news coverage afforded to this story will have any effect on the actual return.

The accounting variable has an interesting component as well. Many companies perform their downsizings at the end of their fiscal year (November, December, or January for most) in order to manipulate the earnings level. Assume the company's fiscal year coincides with the calendar year. It announces on December 31^st that due to sluggish income, it is laying off 10,000 employees and charging $4 billion to its income this quarter to pay for the severance and restructuring to take place over the next year. This makes net income for the last quarter of the old fiscal year look abhorrent, and makes the net income of the first quarter of the new fiscal year look higher, since the expenditures related to the layoffs were expensed in the previous quarter. The CEO can therefore say to his board and shareholders that net income grew 20% from quarter to quarter because of the downsizings and his new business strategy. While this will be true in an accounting sense, it will not be true in the economic sense of the business. The accounting variable attempts to single out the companies that manipulate earnings based on announced layoffs at the change of the fiscal year. Unfortunately, this variable punishes any company whose layoffs coincidentally happen to fall at the very first few days of the fiscal year, if any such company exists.

The "not first" variable attempts to separate the companies who have already used downsizing in the past. If the market knows the same sort of strategy had been followed in the past by a certain company, it will have witnessed the results of the prior downsizing, and apply the information of its success or failure to the new downsizing.

Any downsizing is certainly accompanied by a set of information available to all investors, including the independent variables (for example: the percentage of workers being downsized) and dummy variables (for example: whether the downsizing is the result of a merger). Econometric tests were conducted to determine whether or not the daily return of the stock on the day on which the downsizing was announced can be predicted using the available date for all 38 companies. The adjusted R-Squared of a regression, as well as the statistical significance of its variables will be used to ascertain the explanatory power of a set of variables for the return of the stock.

The general regression takes the form

where is the regression coefficient for variable n, and there are j dummy variables. is the return of the stock over t days following the downsizing announcement, and the last term is an error component, assumed to have zero expected value. The null hypothesis is: news pertaining to a downsizing, as well as the size and scope of the downsizing have no explanatory power for the sign of the stock return on the day of the downsizing.

Ignoring news variables for the moment, the announcement of a layoff (regression 1, Chapter X) and the percentage of workers laid off (regression 2) did not statistically explain the return of the stock at the 95% level. In both regressions, the null hypothesis could not be rejected, and the variables did such a poor job of explaining the returns, that the adjusted R-Squared was actually negative. A regression including the wealth of information available to investors-dummy variables covering news, plus the layoff variables-also had no explanatory power (regression 3). None of the variables showed up as significant, and the adjusted R-Squared was close to zero. Dropping the layoff variable lowered the adjusted R-Squared even further (regression 4). Regressing the return on only the dummy variables did not display any statistical significance for any of them. In this case, the adjusted R-Squared was also negative (regression 5).

Perhaps some of the variables are merely noise, and some actually had explanatory power, but their confidence intervals were overly large due to the lack of degrees of freedom in the regression. Regressions were conducted for each individual dummy variable to see if it alone had explanatory power for the stock return (regressions 6 - 11). None of the news variables could individually explain the stock return; none had coefficients that were statistically different than zero. The merger variable came close to significant, with a mean of 0.048 and a standard error of 0.026. That would indicate that on average, the announcement of a merger adds 4.8% to the stock return of a downsizing company; yet this 4.8% increase in value is not statistically significant from zero at the 95% level.

To test if there is some sort of delayed reaction, the employment data were tested to ascertain if they could explain the direction of the return for the day after the downsizing. Neither variable could explain this return however (regressions 12 & 13). Further tests were conducted to determine if the 5-day return could be explained by either the number of workers downsized or the percentage of workers downsized. In both cases (regressions 14 & 15), neither variable could explain the stock's return over the trading week.

While the employment data could not explain the 25-day return (regressions 16 & 17), it did have explanatory power for the 100-day return. They number of workers laid off explained the return to the stock over the 100 days following the downsizing (regression 18). Specifically, for every 1,000 workers laid off, the stock price rises 0.374% over the 100 days following the announcement. The standard error to the return is 0.139% per 1,000 workers; the adjusted R-Squared is 14.53%. It is interesting to note that the number of workers laid off, and not the percentage of workers laid off is what explains the return. The percentage of workers laid off does not at all explain the 100-day return; the adjusted R-Squared is negative for this regression (regression 19).

It remains surprising that the news variables carry no explanatory power on the day of the announcement, and that the employment variables only attain significance for returns over longer periods. The fact that layoffs are positively associated with the stock return in the medium-run (100 days) lends credibility to the notion that the market rewards companies who downsize by boosting their stock prices over the medium run. This conclusion might be suspect, since there is no immediate reaction to the news. Accepting the theory that stock prices change only when news is announced (and that the news is incorporated into the probability distribution governing future cash flows) would cause an observer to expect that employment data has a significant impact on the first day, and little impact following that. Such a result is what the efficient market theory would suggest. These results go counter to that belief.

The lack of reaction in the stock prices to the news variables also seems puzzling. The regressions demonstrate that there is no linear relationship between important news and the return of the stock. This indicates that either there is a missing variable, a non-linear relationship, or that no relationship exists at all. The postulation that no relationship exists at all between news relating to a stock and its price is quite contradictory to the results obtained in section III.2. in which 40% of the stocks had a volatility that stood out even at the 1% level. However, it would not be difficult to imagine that certain elements of news will not have such a major impact on the stock return that they would appear statistically significant. The concept of a missing variable will be explored in section III.5.

Another possible explanation beyond the scope of econometrics is that there exist multiple equilibria. In other words, given the exact same layoff data and news data, it is quite conceivable that that more than one return (dependent variable) can be supported for the same news (independent variables). This seems a reasonable way to explain the case of Sears and Woolworth's. Both had virtually the same news data, and one traded more than two standard deviations above the mean return, and the other traded more than two standard deviations below the mean return. Chapters IV through VII will be concerned with the possibility of multiple equilibria. Game theory and strategic interactions between investors and management will be utilized to explain why several possible values of the firm may emerge for the same set of employment data and firm-specific news.

The event study has made no allowances for expectations surrounding a downsizing, a possible missing variable that could improve the explanatory power of the regressions. A stock price should only react when investors' expectations of future earnings change as the result of information. According to the efficient market hypothesis, if investors expected a downsizing of 10,000 workers, and the company downsized 10,000 workers, then the stock price should not move, as this strategy had already been incorporated into the stock price. In theory, what should move the stock is not how many workers the company downsizes, but how many workers the company downsizes relative to expectations. For example, if the company has no hope unless it undertakes a major downsizing of 40,000 people, and it only cuts 20,000 positions, then even though there has been a downsizing, it has not been enough, as it fell short of expectations.

There is no direct way of measuring people's psychological perceptions, however, I have attempted a crude estimation variable to measure how an actual downsizing compared with expectations of a downsizing. News articles from the television, Internet, wire reports, and newspaper sources described in section III.1. were assembled for each day on and following a major downsizing. Every article was scanned for reported commentary from Wall Street analysts that cover the stock. Two dummy variables were created to measure how the downsizing compared to the expectations that these analysts expressed.

The following are examples of statements by analysts would cause the above expectations variable to equal 1, and the below expectations variable to equal 0.

1. The downsizing was more "far-reaching and comprehensive" than expected. (said of General Motors)
2. The large "magnitude" of the downsizing is "quite surprising." (said of Procter & Gamble)

The following are examples of statements by analysts which would register as a "0" for the above expectations variable and a "1" for the below expectations variable.

1. "The actual figure was smaller than expected." (said of NYNEX)
2. "We wanted more job cuts." (said of Kodak)

The following are examples of analysts' statements that would cause both dummy variables to be zero.

1. "The total number is what we were looking for." (said of Boeing)
2. "The announcement appears on target." (said of Bank of America)

In the sample of 38, there were no conflicting reports by analysts, which indicated that the downsizing was both above and below expectations. These random variables would be highly questionable if I were to assert that they are perfect proxies for market sentiment. To the extent that Wall Street analysts represent the market's expectations, and to the extent that the newspapers report the views of analysts accurately and without bias, then these dummy variables are fairly accurate, although they lack the scientific precision of the other variables.

The returns of the stock on the day of the downsizing as compared to the mean return were computed in section III.2.. The stock returns were highly irregular, and not at all consistent with the theory that downsizing companies are bid up in the market. That analysis did not include the role of expectations of downsizings. Now that there exists a rough estimate of investors' expectations regarding downsizing, the chart can be re-configured as follows in Figure III.6.

* Simultaneous announcement with a loss on the income statement

† Simultaneous announcement with a merger or a divestiture of at least 10% of firm's assets.

When coupled with expectations, the market's reaction to a downsizing makes much more sense. Without expectations, the return following a downsizing seems almost haphazard, with several firms registering losses two standard deviations below the mean, several with unusual gains, and several with no apparent fluctuation. Once expectations are considered, it is clear that the market punishes firms which don't downsize enough relative to expectations, remains statistically neutral about firms that downsize relative to expectations, and rewards firms that downsize above expectations. The implicit message to CEOs is clear: cut as many workers as you can, and more than Wall Street expects, and your stock price will soar. If you don't cut enough workers to please the Wall Street analysts, your stock will be dumped.

There are no cases in which a stock of a company that downsized below expectations ever jumped more than two standard deviations. 80% of companies that downsized below expectations lost a statistically significant share of their equity value. As for stocks that downsized above expectations, no stock return ever dropped more than two standard deviations. Out of the nine companies which that downsized greater than expectations, seven of them experienced returns that were higher than two standard deviations from the mean. Overall, companies that downsized relative to expectations did not demonstrate a return that could be considered any different than the average return, with 95% confidence.

This may be direct evidence that expectations of downsizing are already incorporated into the stock price. Downsizing has an undoubtedly positive correlation with stock returns in the mid 1990s. The more a company downsizes relative to expectations, the higher its return will be. So a strong company, which no one expects will downsize, has a strong incentive to slash its work force, and watch its stock price soar. Xerox, a clear leader in the market for business products, and undeniably experiencing growth in many of its core business areas, was such a company that shocked the financial community by eliminating 10,000 workers in the midst of a record quarter for net income.

The expectations data were used as the independent variable in a regression with the return the day of the downsizing. The null hypothesis was: expectations of a downsizing being either above or below the actual downsizing have no effect on the return the day of the downsizing. The above expectations variable was not significant, but the below expectations variable was highly significant, with a t-statistic of -4.743. Every time the expectation of downsizing was higher than the actual downsizing, the stock return fell 10.6% (standard error 2.2%, regression 35). This proves conclusively that the market punishes companies that don't downsize enough. Presumably, investors believe that the small downsizing is an indication that the senior management believes that the company's problems are not as bad as they really are. Since the managers do not realize what a precarious position the company is in, the investors decide to get rid of the stock of this company with (in the investors' opinions) incompetent management. The above expectations dummy variable was insignificant, so the null hypothesis cannot be rejected: if a downsizing is above expectations, it does not guarantee the sign of the return the day of the downsizing. Not all companies who downsize more than the market thinks they should will be rewarded. This could be the case if investors believe the company has cut too many workers. Or, such a result could stem form a situation in which the investors believe the company will trim its labor force, but when the company fires massive amount of employees, it signals that the company's business prospects are not as rosy as once imagined.

The addition of the layoff variable to the independent variables does little to improve the explanatory power on the regression, and does not really alter the coefficient on the below expectations dummy, or its standard error (regression 36). The same applies to a regression in which the percentage of employees laid off is added as a dependent variable. The coefficient and standard error of the below expectations dummy are not really affected by the new variable (regression 37). When the two expectations dummies are regressed including the six news dummies presented in section III.3., the only variable to maintain any significance is the below expectations dummy, which reduces the return by 9.63% (standard error 2.53%). The adjusted R-Squared of this regression is 35.63% (Regression 38).

The expectations variables were also regressed against returns for days following the downsizing. For the return the day following the downsizing, the above expectations variable is not significant, but the below expectations variable remains significant at the 95% level. Every time the downsizing does not meet expectations, the return on the day following the downsizing falls by 3.34% (standard error 1.1%). This might be consistent with a story of under-reaction to the news of a downsizing. Even after the downsizing has been made, and the expectations have been re-adjusted, the effect of old expectations are still being felt when the efficient market theory claims they are no longer valid. Since the below expectations variable and the return the day of the downsizing are so highly correlated, this result is not a surprise (regression 39).

The below expectations variable does not just have an impact on the immediate return of the stock, but also on the medium-run returns. The null hypothesis is that the expectations of a downsizing relative to the actual downsizing will not impact the stock returns over 5, 25, or 100 days. This hypothesis cannot be rejected at the 95% for the above expectations variable. However, it remains rejected for the below expectations variable in for all three time horizons. Every time expectations are not met, the stock return will decrease by 12% over 5 days (standard error 3.5%, regression 40), 17.6% over 25 days (standard error 3.5%, regression 41), and 16.7% over 100 days (standard error 6.5%, regression 42).

Further regressions were conducted to determine the impact of the expectations variables on the T-statistic of the return. The T-statistic is calculated as

where is the return the day of the downsizing, is the mean return for the 100 days prior to the downsizing, and is the standard deviation of the daily return for the past 100 days. The T-statistic is a measure of how the return the day of the downsizing fits in the distribution of the mean return. A T-statistic above two in absolute value would indicate with 95% confidence that the return the day of the downsizing is statistically significant from the mean return. The null hypothesis to be tested is: expectations of downsizing have no impact on the T-statistic of the return.

A rejection of the null was not possible for the above expectations variable, but the hypothesis could be rejected for the below expectations variable. Every time the below expectations variable was unity, the T-statistic would fall by 5.37 units (standard error 1.70, regression 43). Addition of the layoff variable did not alter the significance of either expectations variable but lowered the adjusted R-squared (regression 44). Neither the percentage of workers laid off nor the set of dummy news variables added to the explanatory power of the regression, or changed the significance of the expectations variables (regressions 45, 46).

There might be some self-fulfilling prophecies at work. When a downsizing falls short of expectations, investors dump the stock. On the next day, after witnessing that the stock price has fallen, the investors will justify their initial pessimistic beliefs, and decide to dump the stock again. In fact, every time a downsizing is not as large as investors would have hoped, the stock return suffers for at least 100 days. No definitive conclusions can be drawn for the above expectations variable. This might be linked to risk aversion: losing $x will be quite awful, but winning $x will be only moderately pleasant. In this respect, investors severely punish companies that don't downsize enough, and may slightly reward companies that downsize more than expected.

Another major issue in this study is how the market reacts to a downsizing over time. The econometrics in this paper have failed to establish a statistically significant correlation between news and the return on the day of the downsizing, but the relationship between the return the day of the downsizing and subsequent returns merits exploration. The return on the day of the downsizing (no matter how it is determined) could have some relationship with subsequent returns. This section of the chapter moves the return from the dependent variable (explained by news) to the independent variable (explaining the future returns). The previous section asked the question "What should an investor, hearing the company's announcement the morning of the downsizing, expect the return to be on that particular day?" This section asks the question "Given the return on the first day, what sort of return can be expected in the near future for the stock?" The null hypothesis to be tested is: the return on the first day is an optimal forecast for the stock; the return on the first day should not predict the sign of the return on subsequent days. This is the hypothesis that the efficient market theory would suggest.

The general regression takes the form

where is the regression coefficient for variable n, and there are j dummy variables. is the return of the stock over t days following the downsizing announcement, and the last term is an error component, assumed to have zero expected value. The null hypothesis is that the term will be zero. If the null is rejected because is negative at the 95% level, this will indicate over-reaction on the first day. Investors hoard (dump) the stock on day 0, and on day 1, they correct their over-zealousness by selling (buying) the stock. If the null is rejected at the 95% because is positive, this will indicate under-reaction. If investors don't fully incorporate the news of the downsizing into the return on the first day, then if they bought (sold) the stock on day 0, they will continue their buying (selling) spree on day one.

A fascinating event study by Barberis, Shleifer, and Vishny investigates the validity of such a hypothesis for earnings announcements. They conclude that there exists systematic under-reaction to earnings news in the market. Impressive (disappointing) earnings are associated with an appreciation (depreciation) of the stock price in the future. The news is not incorporated immediately upon the announcement, but over a longer period of time. However, security prices are proven to overreact to consistent patterns of similar news. For example, if the market is inundated with a string of positive (negative) news about a company, the stock return will tend to be below-average (above-average) over a time horizon of three to five years. This reversion to the mean is inconsistent with the efficient market hypothesis, which states that the stock price should immediately correct itself once news is announced at a level consistent with how the news is expected to affect the future earnings power of the firm.

Studies by Chan, Jegadeesh, and Lakonishok, as well as Jegadeesh and Titman point to positive auto-correlation in stock prices, indicating a certain momentum in a stock price consistent with under-reaction. Whether or not an earnings report is good (bad) has a statistically significant positive (negative) impact on the stock returns over a six-month horizon. The idea behind systematic over-reaction suggests the opposite. After a long series of announcements of good (bad) news, the investor becomes overly optimistic (pessimistic) about a stock, and assumes that future news will be good (bad). This excessive enthusiasm (aversion) will lead the stock to trade at too high (low) of a price. Subsequent news will contradict the initial impressions, and the stock price should fall (rise). This may be the case when investors receive consistently good news about a company, and irrationally expect its business prospects to be forever strong.

Two types of returns will be studied to determine if they are functions of the return the day of the downsizing. The first will be a daily return on the day following the return from the day of the downsizing (here, the time period given as X). The second type of return is the return over several days that includes the return to the downsizing. Regressions will determine if the one-day return from the day of the downsizing will have predictive power for both classes of returns, X and Y.

Assume it is the evening following the announcement of a downsizing (the end of trading on day 0). The markets have just closed, and the return on the stock, given the news and employment information is calculated by all investors. What sort of return on the next trading day can investors expect, given the return on the day of the announcement? A simple regression of the return the day of the downsizing and the return the following day demonstrates a statistically significant relationship between the two, rejecting the null hypothesis of efficient markets. The direction of the return of the return on day 0 (the day of the downsizing) predicts the direction of the return on day 1. However, the return on the second day is only 22.16% of the return of the previous day (standard error of 6%, adjusted R-Squared of 25.41%). If the stock price shot up on the first day, we expect it to rise, but only 22.16% of its rise the previous day. If the stock price fell on the first day, it is expected to fall on the second day, but only by 22.16% of its initial decline (regression 20). This is consistent with a hypothesis of under-reaction. As in previous regressions, the economic variables, such as the amount of people laid off, do not affect the return for the next day (regression 21). The addition of the news (dummy) variables did not explain the next day's return; the R-Squared was 42.42%, while the adjusted R-Squared was only 26.54% (regression 22). The regression which maximized the adjusted R-Squared included the return from the first day, the number of workers laid off, the accounting variable, the bad news variable, and whether or not the downsizing was a major news event. No variable except the return from the first day carried any significance. In this case, the day 1 return was always 22.6% of the return from the day of the downsizing (6% standard error). The addition of the news dummy variables did not alter the coefficient of the first day's return (regression 23).

The stock market clearly under-reacts to the news of a downsizing; this finding is consistent with Barberis, Shleifer and Vishny's finding of under-reaction to earnings reports. If the stock price rose (fell) on day 0, it is expected to rise (fall) again on day 1. However, the return on day 0 has no predictive power for the returns on days 2, 3, or 4. We cannot reject the null hypothesis of efficient markets on any of these days, since the return on day 0 cannot predict the sign of the return on days 2, 3 or 4 (regressions 24, 25, 26). Presumably, by the end of day 1, the market has fully incorporated the news of a downsizing into the price of the stock, and it is considered a past event, and has no bearing on the future pattern of returns.

Figure III.8. outlines what returns an investor could expect to make if she places $1 in the stock of a downsizing company at the closing price on the day of the downsizing, assuming that the stock return was positive on the day of the downsizing. It also demonstrates what the value of $1 would be if she sold the stock short the day of the downsizing, assuming that the stock return was negative the day of the downsizing. The middle line is the expected value of that dollar at the close of trading for the following four days. This analysis ignores the time value of money, assumed negligible for these four days. The upper and lower bands represent the 95% confidence intervals for the mean expected return. At the end of trading on day 1, the lower band is greater than $1, signifying that with 95% confidence, the investor will make money by holding the stock on day 1. This is the pictorial demonstration of under-reaction. On day 0, the stock does not go up enough, so it rises again on day 1. On day 2, the stock goes up again, but $1 is within the confidence interval this time, so the efficient market hypothesis cannot be rejected at the 95% level. Values ranging from $0.93 to $1.09 are all within the confidence band on day 2, so it cannot be asserted with certainty that an investor who puts $1 into the stock at the end of day 0 will have made money at the end of day 2. Similar conclusions can be drawn for days 3 and 4. On day 4, the mean value of the $1 invested is actually only $0.995, with the confidence band including $1. The actual mean and standard error for each day are included in the appendix for reference.

The evidence points to a rejection of the efficient market theory over the short-run, but an acceptance beginning for the return on the second day. This analysis suggests that on the morning of the day following the downsizing (day 1), investors should bet money that the stock will follow the direction that it took the day of the downsizing. Within this data sample, the investor's hunch will be correct, and she will make money with at least 95% confidence. Of course, this analysis abstracts away from transaction costs, taxes, and exchange-imposed limits on short selling.

It appears as if the market moves too slowly to digest relevant news from a downsizing. However, it could be the case that after having sluggishly incorporated the news into the share price, it eventually over-emphasizes the news, and reacts too strongly to the announcement of a downsizing. A story of over-reaction to the news could emerge on day 1. The mean return of day 1 lies above the upper band of the confidence interval of the return for day 2. This could be preliminary evidence of over-reaction to downsizing: first the news is not incorporated fast enough, and then it is incorporated too much. This result is highly consistent with the event study of Barberis, Shleifer, and Vishny mentioned earlier.

Further tests were conducted to examine the alternative hypothesis of over-reaction, and to determine if the initial daily return on the day of the downsizing explained returns projected into the future. This test is quite different to the one conducted above, since the dependent variable in the above regressions did not include the day of the downsizing. The prior tests compared two daily returns: one for the day of the downsizing, and one for the day following the downsizing. These tests compare the return on the day of the downsizing to the five-day return, beginning the night before the downsizing and ending on the evening of the fourth day following the downsizing. They ask the question: if the investor bought the stock the night before the downsizing, and observes his one-day return (the day of the downsizing), what is the distribution of his n-day return (n = 5, 25, 100)?

The previous regressions to predict the return on day 1 took the form

where the null hypothesis (efficient market hypothesis ) was that the coefficient on the return the day of the downsizing was not statistically significant from zero. One could imagine an entire series of bivariate regressions spanning (n - 1) days for this situation, all with the hypothesis that the return on the day of the downsizing cannot explain the return for future days.

The first subscript on regression coefficients corresponds to the number of days since the downsizing; the second corresponds to its order in the equation. Summing these regressions, one obtains

The efficient market hypothesis would indicate that the coefficient on the return the day of the downsizing, , will not be statistically significant from zero. Adding the term to both sides of the equation, one obtains

Now, the efficient market hypothesis will indicate that the observed coefficient on the return the day of the downsizing, , will not be statistically significant from one.

The dependent variable, , is observable, and can be re-written as

Any sufficiently small may be approximated by . The dependent variable can be expressed as:

But the quantity on the right hand side is simply the cumulative return, , to the stock for an n-day time period, beginning at the closing price of day -1, and ending at the closing price on day n-1. Making use of the log approximation of sufficiently small numbers, this cumulative return can be re-written as

The coefficient on the independent variable (the return the day of the downsizing), and the regression constant can be redefined as

Since the error terms in each regression are independent and identically distributed with mean zero, so is their sum. They can be expressed as

The regression from above

can now be re-written as

The cumulative return over n days is expressed as a function of a constant, a linear transformation of the return the day of the downsizing, and an error term with mean zero. Recall that the efficient market hypothesis requires that the coefficient on the return the day of the downsizing be unity.

If the coefficient is so large that it is statistically discriminate from unity, this will cause me to reject the hypothesis of efficient markets, and instead accept the alternative hypothesis of under-reaction. A positive (negative) return for the holding period of one day would imply an even more positive (negative) return for the week. I can only offer such a rejection very delicately, as for large returns, the log-approximation used above no longer holds. If the coefficient is so small that an F-test will reject the possibility that it is unity, then I will accept the hypothesis of over-reaction. The return for holding periods of one day will always have a larger magnitude than returns for longer holding periods. If the stock price rises (falls) on the first day, it will be expected to fall (rise) over time if the coefficient is statistically less than 1.

The results of this study were quite startling. The sign on the five-day return was found to be statistically determined by the one-day return, and consistent with the hypothesis of over-reaction. The return for holding the stock for one week following the downsizing was the same sign as the initial return, but only 52.55% as large. For every dollar that the stock rose (fell) on the first day, it will rise (fall) only 52.55 cents for the week. The standard error was 21.4%, so the 95% confidence interval indicated that the stock could rise over 5 days as much as 95.9% of the initial day's return, and it could rise as little as 9.3%. This striking result has two major implications. Firstly, the sign of the return for the first day will be the sign of the return for the week. Secondly, the return for the week will never be as high as the return for the first day. This suggests a systematic over-reaction on the part of the market. The stock appears to peak (bottom out) on the day 1-as the previous section suggests-and close for the week lower (higher) relative to the day of the downsizing, but higher (lower) relative to the day before the downsizing (regression 27). An F-test rejected the possibility that the coefficient was 1; the F-statistic was 4.92.

Adding the news variables decreased the adjusted R-Squared to 8.34%, and none were statistically significant. This time, the return on the day of the downsizing could not explain the sign on the five-day return, but it was still significantly different from 1, with an F-statistic of 5.36. The adjusted R-Squared was much lower; perhaps the increase in the degrees of freedom resulting from unnecessary variables increased the standard error on the initial return too much (regression 28). The adjusted R-Squared was maximized for this regression to 18.22% when only the initial daily return and the dummy variable "not first" were included. Whether or not this was the first downsizing for the corporation was not statistically significant, but the initial return the day of the downsizing did help to explain the sign of the five-day return. The coefficient was very similar to the previous regression; the return over the week was only 45.4% as large as the return on the first day; the standard error was 20.9% (regression 29). Once again, the coefficient could be judged different than 1; with an F-statistic of 6.79, the efficient market hypothesis was rejected.

Yet, while over-reaction on the first day appears evident when compared to the five-day return, this phenomenon does not appear when compared to the 25-day return. Specifically, if the stock price rises 1 unit during the first day of trading, it rises 1.14 units over the 25 days following the downsizing. The standard error is 18.75%, so 1 is well within the confidence interval, and the efficient market hypothesis is accepted. The F-statistic of 0.6 was not large enough to reject the hypothesis. The return the day of the downsizing is statistically significant enough to explain the sign of the 25-day return, but cannot testify to over or under-reaction. A rise in the stock price on the first day guarantees a rise over the first 25 days, at the 95% level (regression 30). When the news variables are added in, the adjusted R-Squared shoots up to 53.16%, and the coefficient on the return on the first day rises to 1.30. For every one point that the stock rises on the first day, it is expected to rise 1.30 points for the month (regression 31). Over-reaction on the first day cannot be ruled out or accepted, since the 95% confidence interval indicates that the stock can rise as much as 1.70 points and as little as 0.92 points during the month for every 1 point the stock rises on the first day. While the direction relative to the first day will always be the same, the probability distribution over the magnitude of the return is large enough that the efficient market hypothesis cannot be rejected for the month following the downsizing.

A similar conclusion can be reached for the 100-day return. For every 1 dollar the stock price rises from the evening the day before the downsizing to the evening the day of the downsizing, it is expected to rise 1.23 points over the 100 days from the day before the downsizing to the 99^th day following the downsizing (regression 32). The 95% confidence interval around this return is as low as 0.49 points and as high as 1.97 points. Once again, the efficient market hypothesis cannot be rejected for the 100-day return, the F-statistic is merely 0.4. As before, the return on day 0 determines the sign of the 100-day return at the 95% level. The sign of the return the day of the downsizing is positively linked to the sign of the return over the 100 trading days following the announcement.

Addition of the news variables to the regressions pertaining to the 100-day return raised the adjusted R-Squared slightly. All of the news elements were statistically insignificant, but the return the day of the downsizing retained its significance. As with all prior regressions, the coefficient on the return did not change. In this case, for every dollar the stock price rose the day of the downsizing, it rose $1.19 during the 100 days following the downsizing. The standard error was 40 cents, so they hypothesis of over-reacting cannot be accepted (regression 33). The maximum adjusted R-Squared was achieved for this regression when the 100-day return was regressed on the number of workers laid off, whether or not a merger was taking place, and the initial daily return. The adjusted R-Squared was 33.96%, and all except the merger variable were statistically significant (regression 34). The direction of the initial return is positively linked to the direction of the 100-day return, but the hypothesis of overreaction cannot be accepted.

An initial examination of the returns to downsizing companies relative to their mean returns was unfavorable for the hypothesis that downsizing increases equity value. Downsizing produced a wide array of returns, from those that were two standard deviations below the mean return, to those that were far above. The announcement of a downsizing was linked to variability in the stock price. The absolute deviation from the average return was much higher for downsizing companies, and could be statistically differentiated from the mean absolute deviation in over half of the cases at the 15% level. Once expectations of downsizing were incorporated in section III.5., the original hypothesis that downsizing companies are bid up seemed to make sense. It was not the case that the stock of downsizing companies rose, but rather the stock rose of companies that fired more workers than they were expected to. Conversely, downsizing companies that did not cut enough positions relative to what the market thought they should experienced a drop in their stock price. This lends credence to the counter-intuitive anecdotal observation that the equity value of strong companies who downsize will rise. Presumably, the market does not anticipate that the company will need to fire workers since its business is booming, so when the company lays off may workers relative to expectations, the stock price soars. This goes directly against any common sense argument that if a strong company is firing workers, perhaps its business prospects were not as optimistic as the market had anticipated, and the stock price should be bid down. Exactly why the market rewards strong companies that downsize will be the subject of the next chapter.

The event study succeeded in using returns the day of the downsizing to predict the future behavior of the stock, but failed to attach significance to the underlying news factors that determine the original return. News pertaining to the stock, such as bad earnings, or the announcement of a merger failed to have any explanatory power for the sign of the return (positive or negative). This applied not only to the immediate return of the stock, but also to the 5-day, the 25-day, and the 100-day return. The percentage of workers laid off also failed to explain these returns. The amount of workers laid off was found to predict the sign not of immediate returns, but of the 100-day return. Specifically, laying off workers was associated with a rise in the stock price over 100 days at the 95% level.

To conclude that the news does not have a substantial impact on stock prices seems inconsistent with observable phenomena in the market. Companies with virtually the same data are found to generate wildly varying returns. This either indicates that there is a significant explanatory variable that I have failed to measure and include in the regressions, or that there are multiple equilibria possible for a given set of data. The news itself did not matter as much as the market's expectations relative to the news. For example, downsizing 10,000 employees cannot predict the stock return. However, downsizing 10,000 workers when the market expected 20,000 is a statistically significant predictor that the stock price will fall. The next few chapters will explore the second possibility of why news variables fail: multiple equilibria surrounding a downsizing many yield many possible returns for one set of data.

Predicting the longer-period returns from the immediate daily return was a success. The direction of the investors' immediate reaction is also the direction of its medium-term reaction. A positive (negative) return on the first day is associated with a positive (negative) return over 5 days, over 25 days, and over 100 days, at the 95% level. Additionally, the sign of the immediate return on the first day was also the sign of the return on the second day. With 95% confidence, investors can be certain that a buying spree on the first day will not lead to a selling panic on the second day, or vice-versa.

The other major issue is whether or not the market over-reacts to the downsizing. The answer to this question seems quite complex. There appears to be under-reaction on the first day. If the stock price rises (falls) on day zero, it is expected to rise (fall) again, on day one, but with a smaller magnitude. This lead to a rejection of the efficient market hypothesis over that time interval. But the magnitude of the price change over five days is always smaller than the magnitude for one day. This suggests that if the stock immediately rises (falls) on the day of the downsizing, it will fall (rise) over time, until the fifth day, but not completely erase the gain (loss) from day zero. This observation is consistent with over-reaction.

There was no evidence of over-reaction in longer time intervals. With 95% accuracy, if the stock is above (below) its closing price from day 0 on day 1, it will be above (below) that benchmark closing price on days 25 and 100. However, market efficiency could not be rejected, since the regressions could not determine a relationship between the price on day 1 and the price on day 25 or 100.

The appearance of under-reaction on day 0 relative to day 1 and over-reaction on day 0 relative to a holding period spanning five days is not inconsistent. This suggests that the stock might over-react to news on day 0, continue over-reacting on day 1, and eventually fall into place by day 5. Since the overreaction continues from day 0 to day 1, it appears as if the stock has immediately underreacted to news. The comparison between the two is not direct, since the underreaction result was obtained by using one-day returns following the downsizing, and the overreaction data was obtained by the use of longer-period returns including the day of the downsizing.

Based on this study, what should an investor holding the stock of the downsized company do? It is 9:30 a.m. on day 0, and the market has just opened. At 9:29 a.m., the company announced a downsizing of x workers, y% of its workforce, and values for a set of news dummy variables. The investor is highly risk averse, and will only participate if she is confident she will make money with 95% certainty. Based on these regressions, investors should do nothing on day 0, since the closing price at the end of the day is anyone's guess. Nevertheless, if the downsizing came in below expectations, the investor should sell the stock on day 0. At 4:30 p.m. on day 0, the investor will know the return for the day. If it is positive, she can expect the stock to rise the next day, but fall below this closing price by the end of day 4. There will be an initial over-reaction during the first week of trading, but not in further time periods. The stock can go above or below day 1's closing price in the subsequent 25 or 100 days, but the investor can be sure (with 95% certainty) that it will never fall below the opening price on day 0. Markets are efficient in the medium run. If the return from the day of the downsizing is negative, the investor can expect the stock price to fall on day one. However, the stock is expected to trade at the end of day 4 somewhere between the opening price on day 0 and the closing price on day 0. This implies an initial overreaction: investors were quick to dump the stock (for whatever reason), but seem to be buying it back by the end of the 4^th day, though not enough to boost the stock above its pre-downsizing price. It remains unclear as to whether the over-reaction will continue, but the investor can be fairly certain that the stock will not attain its pre-downsizing price over the next 25 or 100 days.

This chapter represents only a starting point in the econometric analyses of companies that downsize. Further studies could examine the return of a downsized company compared to a basket of other companies in the industry that have not downsized. Regression with other time-specific returns can determine how long the 5-day over-reaction phenomenon is expected to last, and where the inflection points in the pattern of the stock prices seem to occur.

The next few chapters will build on the empirically-verified fact that the sign of the return on the first day will be the sign of the return over the 100-day period following the downsizing. Therefore only the market's initial reaction to buy or sell the stock is relevant to the stock's short-run performance. With this assumption, tools of game theory will be used to extract and analyze the multiple equilibria possible in a downsizing. These equilibria will be applied to three specific cases: why strong companies downsize (AT&T: Chapter IV), and why similar companies pursue different employment polices (Delta Airlines and United Airlines: Chapter VII).