On 17 April 2008, after trading hours, Google announced its results over the first quarter.
The company’s profits were up 42 per cent compared with the same quarter last year, much more than analysts expected. The next day, Google’s stock price opened almost 20 per cent higher and hovered on that level for some days. As we have seen, that is consistent with an efficient price reaction. However, by the end of the month the price had crept up another 6.5 per cent. Was that due to developments on the market? The Nasdaq Composite Index had gone up 4.1 per cent in the same period.12 Or was it a correction after an initial underreaction to the announcement? The former does not
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12 The Nasdaq Composite Index (ticker: IXIC) is a broader index than the Nasdaq-100 index. IXIC contains all domestic and international-based common type stocks listed on the Nasdaq stock exchange.
contradict the efficient market hypothesis, the latter does. Event studies are designed to answer such questions.
Methodology of event studies
Event studies measure the effect of a well-defined event on firm value. The event can be an announcement of earnings, dividends, a merger, a stock split, etc. but also a price jump on input or output markets, the introduction of regulation, etc. Measuring the effects of such events is complicated because information about an event never comes alone. There is a continuous stream of other, more general financial information about interest and exchange rates, prices of other stocks, bonds and commodities as well as macro-economic information. To assess the impact of the event, the effects of the other information have to be filtered out. The most common way to do this is to use the market model to calculate the normal return that could be expected given the reaction of the market as a whole to the other information. The difference between the realized return and the normal return is then the abnormal return which is attributed to the event. In efficient markets, abnormal returns only occur in the event period, without any predictable pattern afterwards.
The market model postulates a simple, empirical relation between the return of an individual security i, rit, and the return on the market as a whole (approximated by a broad index), rmt:
rit =γ0i+γ1irmt+ εit (4.6) where γ0,1 are estimated coefficients, εit is an error term and t is a subscript for time.
It is important to note that the market model is an empirical, not a theoretical, model.
Its coefficients γ0,1 are obtained by running a regression of the security returns rit on the returns of the index rmt. The estimates of a security’s normal (or expected) return are generated by the market model’s out-of-sample predictions, given the return on the market:
E(rit)=rit =γ0i+γ1irmt (4.7) where the coefficientsγ0andγ1are estimated over a period prior to the predictions. The abnormal return, arit, is the difference between the realized and the expected return:
arit = rit− E(rit)= εit (4.8)
Conclusions are usually based on the aggregated abnormal returns over the prediction period, the cumulative abnormal return, cari:
cari =
t
arit (4.9)
The idea behind this methodology is straightforward. The market model measures how sensitive a stock is to changes in the market index. Given this sensitivity and the change in the index in the event period, it can be calculated what the stock’s return in the event period would have been if only the general, market-related information would have become available. It can reasonably be assumed that the difference with the observed return springs from the event. This assumes that the event date can be observed accurately, which is not trivial since financial information has a tendency to leak out. A simpler ver-sion of the methodology takes the average return, ri, over a prior period as the normal
119 4.2 Empirical evidence
return. More extended versions replace the market model with a multi-factor model, for example the Fama-French three-factor model (3.20) that includes size and book-to-market effects, or Carhart’s (1997) four-factor model, that adds a momentum effect.
The market model is very similar to two other models that we have met in Chapter 3, the characteristic line (3.13) and the single index model (3.15). Although the differences are subtle, it is worthwhile to point them out. The characteristic line differs because it is an empirical expression of the equilibrium theory CAPM, which restricts its use and interpretation. For example, the interpretation of γ0 would be the risk-free interest rate and that of γ1would be the CAPM β. The market model has no theoretical background so the interpretation follows from the statistical relationship between riand rm: γ0is the change in riwhich is statistically independent from rmand γ1is the statistical sensitivity of rifor changes in rm. The coefficients γ0,1are not required to have any specific values.
The single index model differs in underlying assumptions. Recall from Chapter 3 that the single index model assumes that cov(rm, εi) = 0 and cov(εi, εj)= 0, the error term is not correlated with the market return and the error terms of different securities are not correlated. The market model itself makes no assumptions about the error terms, but they may be implicit in the empirical technique used to estimate it (such as classical regression analysis).
A home-made example
A simple, home-made example, using Google’s earnings announcement, may help to clar-ify the methodology of event studies. The first step in the study is choosing the event window, i.e. the period over which we want to analyze the impact of the announcement.
As we shall see later on, earnings announcements are usually studied over comparatively long event windows, e.g. from twenty days before to ninety days after the announce-ment. However, to keep the calculations simple we shall use only ten trading days before and after Google’s announcement. This gives an event window of 4 April to 1 May 2008.
Next, we have to choose the estimation window over which we estimate the market model for Google. We use the three months preceding the event window, from 2 January to 31 March. That period comprises sixty trading days, enough to estimate the market model for this example. We download the daily closing prices of Google (ticker GOOG) and the Nasdaq Composite Index (ticker IXIC) over the period 2 January through 1 May from Yahoo.com. After transforming the closing prices into daily returns and using only the data in the estimation window, we estimate the market model for Google with regression analysis. The results are:
rgoog= −.005 + .922rixic R2= .278 (4.10) The standard errors of the coefficients are .003 and .189 respectively, so that the sensitivity coefficient is significantly =0 but the intercept is not. We can now calculate Google’s expected returns, using (4.7), and abnormal returns, using (4.8) in the event window. For example, on the first trading day after the announcement (day 1) the return on the index is .026. This gives an expected return for Google of −.005 + .922 × .026 = .019. Google’s actual return is .2, so the abnormal return is .2 − .019 = 0.181. Table 4.7 lists the various returns for a few days. The last column shows the cumulative abnormal returns over the event window; these are plotted in Figure 4.6.
–10 –8 –6 –4 –2 0 2 4 6 8 10 0.0
0.1 0.2 0.3
event window car
Figure 4.6 Cumulative abnormal returns of Google
Table 4.7 Returns around event day
Day rixic E(rgoog) rgoog argoog cargoog
10 0.028 0.021 0.033 0.012 0.321
5 0.010 0.004 −0.006 −0.010 0.226
1 0.026 0.019 0.200 0.181 0.209
−5 0.013 0.007 0.011 0.004 0.042
−10 0.001 −0.004 −0.023 −0.018 −0.018
A real event study would involve a sample of earnings announcing firms; the above calculations are then performed for each of them. The results are aggregated over firms, synchronized on the event date (day 0) because the announcements are made on differ-ent calendar dates. The result is a series of cumulative average abnormal returns (caar), which can be tested on their statistical significance. The statistical properties of cumula-tive (average) abnormal returns are a bit complex, particularly for small or thinly traded samples, because they also involve the standard errors of the estimation of the market model. But they are well charted by, among others, Peterson (1989), MacKinlay (1997), Campbell et al. (1997) and Bartholdy et al. (2007). Tests that show a significant post-event drift in cumulative (average) abnormal returns reject the efficient market hypothesis.
Drift in pre-event caar is a bit more difficult to interpret. It can be the result of infor-mation leaking out, which means that the event date is observed with error. But it is also possible that the market recognizes or anticipates information that is later formal-ized in the event. For example, dividend increases and stock splits (discussed below) are usually announced after a period of good performance. Hence, selecting companies that have split their stock implies selecting companies that have done well prior to the split, and that becomes manifest in the pre-event caar. This is usually referred to as sample selection bias.
121 4.2 Empirical evidence
The methodology outlined above was first used in the late 1960s in studies such as Ball and Brown (1968) and Fama et al. (1969). Since then, event studies have been used to analyze the effects of a wide variety of events, ranging from exchange offers, block trades and analysts’ forecasts to the sudden death of chief executive officers. Kothari and Warner (2007) tallied the number of event studies published in five leading finance journals between 1974 and 2000 and report a grand total of 565. Obviously, we can only survey a few highlights of this vast literature.
Stock splits
A stock split is the exchange of a firm’s outstanding shares for a larger number of new shares. A typical exchange ratio is 2:1 (or a 2-for-1 split), meaning that for every old share the owner receives two new shares, each of which is worth half the value of an old share. Other common exchange ratios are 3-for-2, 5-for-4 and 3-for-1, but 5-for-1 splits also occur. Reverse stock splits work the other way around and reduce the number of shares. Companies usually split their stocks after a period of price increases. The most frequently mentioned reason to split is the enhancement of tradability, for example by keeping the stock price in an affordable range for small investors or by letting the stock appear inexpensive compared with those of similar companies.13Stock splits neither add value nor dilute the claims of the existing shareholders, so in efficient markets their effects on stock prices should be zero (after adjusting for the split, of course). That is what Fama et al. (1969) found in their analysis of 940 splits in the period 1926–1960. Using an event window of twenty-nine months before and thirty months after the split, they report cumulative average abnormal returns (caar) that steadily increase before the event but are stable (around zero) after the event. They then split their sample in a large group (672 out of 940) of companies that increases and a smaller group that decreases its dividends after the split. The former group’s cumulative average abnormal returns increase slightly after the split, but those of the dividend decreasers plummet in the few months after the event.
This leads Fama et al. to the conclusion that investors use stock splits to re-evaluate the expected income from the stock. Anticipated or announced splits cause price adjustments only to the extent that splits are associated with changes in the expected dividends. If these expectations do not materialize after the event, prices revert to their normal level, consistent with market efficiency.
These results are both challenged and confirmed in later work. For example, Iken-berry and Ramnath (2002) examine a sample of more than 3,000 stock splits announced between 1988 and 1997 and estimate abnormal returns of 9 per cent in the year following the announcements of stock splits. Their result is robust to a variety of estimation tech-niques. It is also consistent with the positive drift that other studies observed following stock splits in the 1970s and 1980s. This pattern suggests that the abnormal return drift identified in these studies is not spurious. Their conclusion is that markets underreact to the news in splits, which is inconsistent with market efficiency. However, using an even larger sample of 12, 747 stock splits over the period 1927 through 1996, Byun and Rozeff (2003) come to the opposite conclusion. Although they isolate specific subperiods and
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13 Some companies have the opposite policy; for example, Warren Buffett’s Berkshire Hathaway traded at less than
$6,000 per share in the early 1990s and around $140,000 in 2008, but never split.
methods of estimation that yield significantly positive post-event returns, their overall results indicate that buyers and sellers of splitting stocks do not, on average, earn abnor-mal returns that are significantly different from zero. Their overall conclusion of market efficiency is based on a variety of subperiods and methodologies. Boehme and Danielsen (2007) emphasize the fact that stock split announcements are generally preceded by a period of strong performance. Taking the industry momentum effect into account, they find no consistent evidence of post-split positive abnormal returns, although abnormal returns do occur in some subperiods.
Earnings announcements
In a paper that pioneered event studies, Ball and Brown (1968) analyze the effects of earn-ings announcementsin the annual reports of 261 firms. Using an event window of twelve months before to six months after the announcement, they observe that cumulative aver-age abnormal returns (caar) already begin to drift in the direction of the announcement (upward for positive news, downwards for negative) twelve months before the announce-ment. This is not surprising since earnings information also becomes available from other sources, such as quarterly reports. They also observe that caar continue to drift in the same direction for as long as two months after the event date. By itself, this contradicts market efficiency. But the drift is so small that, unless transaction costs are within one per cent, it offers no opportunity for abnormal profit after the event date. Reinganum (1981) goes one step further and quantifies the surprise element in earnings announcements. He uses a simple time series regression model to forecast earnings per share ( EPS) from historical data. The difference with the earnings per share in the announcement (EPS) is the surprise element, or unexpected earnings: UE = EPS − EPS. These unexpected earnings per share are standardized by scaling them with the standard error of estimate from the regression equation used in the prediction: SUE = ( EPS−EPS)/σeps. With these standardized unex-pected earnings, or SUEs, he constructs two equally risky portfolios, one containing firms with the highest SUEs and the other containing the lowest. The returns of these portfolios over the next 1–4 months are not significantly different from each other, and he concludes that no abnormal returns can be earned by using information in earnings announcements.
Reinganum’s (1981) analyses are re-examined on a larger scale and using more advanced estimation techniques by Rendleman et al. (1982). Unlike Reinganum, they find a SUE effect, with significant differences of 3.4–6 per cent in return between the two extreme SUE portfolios over the next 1–5 months. In the second, frequently cited part of their study, they divide their sample in ten groups according to the size of the SUE, from strongly negative to strongly positive. Using an event window from 20 days before to 90 days after the announcement, they perform an event study for each group.
Unsurprisingly, the abnormal return on the event day strongly depends on the size of the SUE. However, in the post-event period (day 1 to 90) the caar of all groups continue to drift in the direction of the earnings surprise and these post-event caar are statistically significant for all but one group. This clearly contradicts the efficient market hypothe-sis (even though the post-event caar are small, <2 per cent, for five middle groups). For example, the group with the highest SUE has a caar of 8 per cent over the entire event window. Of this, 2.4 per cent occurs in the pre-event period, 1.3 per cent on the event day
123 4.2 Empirical evidence
and 4.3 per cent in the post-event period. The group with the lowest SUE has corre-sponding negative caar of −8.7 per cent over the entire window, −3.3 per cent before,
−1.4 per cent on and −4 per cent after the event date. This is strong evidence against market efficiency.
Since then, the post-earnings-announcement drift has been confirmed in numerous other studies and various explanations for this phenomenon have been proposed. For example, Chordia and Shivakumar (2005) suggest that investors fail to account for the impact of inflation on their forecasts of future earnings growth. This causes firms with positive earnings sensitivities to inflation to be undervalued and stocks with negative earnings sensitivities to inflation to be overvalued. Alternatively, Battalio and Mendenhall (2005) argue that small investors (trading less than 500 shares) use an incomplete infor-mation set for their decisions. Compared with more sophisticated, large investors they ignore, or at least significantly underweight, the implications of the surprise in earnings announcements for future earnings levels. This leads to the underreaction that gives rise to the post-earnings-announcement drift. Mendenhall (2004) is among the researchers who ask why earnings announcements, which are easily observable, can have a predictable effect that has survived for several decades without being arbitraged away. His answer is that the practical possibilities to profit from arbitrage trades are limited. To exploit underreaction, specialized arbitrageurs would have to hold a few, relatively large posi-tions and this would expose them to the stocks’ unsystematic risk. He quantifies this arbitrage risk by the residual variance from a market model regression, i.e. the part of a stock’s volatility that is not explained by movements of the market. Using this risk measure, he finds that the magnitude of post-earnings-announcement drift is significantly positively correlated to arbitrage risk. For example, firms in the highest arbitrage risk quintile experience drifts that are, ceteris paribus, 3–4 percentage points per quarter larger than those of firms in the lowest arbitrage risk quintile. These results are robust to a wide range of explanatory variables used in prior research. His conclusion is that arbitrage risk and transactions costs impede arbitrageurs who attempt to profit from the post-earnings-announcement drift.
Other event studies
Merger and acquisition announcementsare generally analyzed to determine whether or not mergers create value, and if so, for whom: the bidder, the target or both. However, the pattern of abnormal returns over time may also allow conclusions regarding market efficiency. Early studies such as Keown and Pinkerton (1981) and Travlos (1987) show very little post-event drift, concurring with semi-strong market efficiency.14Later studies more often report significant post-acquisition caar, particularly for certain types of merg-ers. For example, Loughran and Vijh (1997) find insignificant caar for mergers that are paid for in cash, but significantly negative ones if the merger is paid for in stocks of the acquiring firm. This raises the question whether these returns are due to the merger or the associated stock issue.
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14 Keown and Pinkerton (1981) report suspiciously large abnormal returns on days just before the event and conclude that merger announcements are poorly held secrets.
A long line of research investigates the effects of stock issues, both initial public offer-ings (IPOs), seasoned equity offeroffer-ings (SEOs) and reverse issues, i.e. stock repurchases.15 A representative example of these studies is the large-scale test by Pontiff and Woodgate (2008), who find a negative relation between net stock issues and average returns for the period after 1970, and no significant relation before 1970. Fama and French (2008) report
A long line of research investigates the effects of stock issues, both initial public offer-ings (IPOs), seasoned equity offeroffer-ings (SEOs) and reverse issues, i.e. stock repurchases.15 A representative example of these studies is the large-scale test by Pontiff and Woodgate (2008), who find a negative relation between net stock issues and average returns for the period after 1970, and no significant relation before 1970. Fama and French (2008) report