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Event Studies Methodology Frank de Jong Tilburg University January 2007 Lecture notes written for the course Empirical Finance and Investment Cases. The author would like to thank Marc De Ceuster, Peter de Goeij, Theo Nijman, Ailsa Rell and Frans de Roon for very helpful comments on earlier versions. 1 Introduction This lecture note gives an introduction to an important ...eld of the empirical ...nance literature, the event study.1 Event studies are an important tool in ...nance. Much of the corporate ...nance literature is concerned with the valuation of ...rms and the changes in ...rm value resulting from, for example, changes in capital structure. In general, the value of a ...rm is di cult to measure. However, if there is an e cient market for the ...rm's stock, the impact of decisions of this type can be measured by the change in the stock price around the time when the decision becomes public knowledge. Although such events can be studied in many dierent ways, the empirical ...nance literature has taken a particular approach based on statistical tests of the signi...cance of abnormal stock returns around event dates. This type of approach also plays an important role in investment analysis. For example, one can study the performance of stocks or portfolios after an initial public oering. In this lecture note, I give an introduction and guide to this literature. The emphasis is on the methodology of conducting event studies, because an understanding of the methodology is a necessary prerequisite for understanding the literature. No attempt will be made to survey applications of event studies. This lecture note is structured as follows. Section 2 introduces the event study methodology for events with a short event period. Section 3 discusses simulation evidence on the statistical power of the event study method. Section 4 discusses event studies with a long event horizon. Finally, Section 5 concludes with a discussion of the interpretation of the results of event studies. 1 The event study literature has recently been reviewed by Thompson (1995); and there are some good introductions to the literature, for example Bowman (1983), Schweitzer (1988) and Peterson (1989). 1 2 Conducting event studies This section gives an introduction to the empirical methodology of event studies. What exactly do we mean by an event study? To answer this question, let us consider the following well-known example: the paper by Fama, Fisher, Jensen and Roll (FFJR, 1969) that pioneered the event study methodology. We shall use this paper as an illustration throughout these notes. FFJR consider the behaviour of stock prices around stock splits. They ask the following question: do stock prices behave dierently around stock splits than in normal periods? To address this issue, they compare the holding returns on the stock around the event date (i.e. the actual date of the stock split) and the expected return if there had been no event. The dierence between the actual return in the event period and the expected returns is referred to as the abnormal return. To study the eects of, in this case, stock splits the observed return series of one single ...rm is not very informative because returns are stochastic. Therefore, they aggregate abnormal returns over all stock splits in the sample. Statistical tests are then invoked to test the hypothesis that on average, returns around the event date are not dierent from their expected returns. Of course, there are many other interesting events besides stock splits that can be studied. Bowman (1983) identi...es 5 steps in conducting an event study, which I shall reduce to three: 1. Identify the event of interest and in particular the timing of the event. 2. Specify a "benchmark" model for normal stock return behaviour. 3. Calculate and analyse abnormal returns around the event date. The following sections discuss these three stages in more detail. 2 2.1 Identifying the event The type of event studied is usually motivated by economic theory. For example, consider the ex-dividend day behaviour of stock prices. The simplest e cient markets model predicts that the decline in price is equal to the dividend paid. However, there are numerous studies that ...nd price changes signi...cantly smaller than the dividend. In this example, the timing of the event is trivial, as the exdividend day is known. However, in many event studies the timing of the event is more problematic. Consider, for example, the stock price behaviour of a target ...rm in a corporate takeover. Identifying the actual date of the takeover as the event date would not yield meaningful results, as the takeover is usually announced a long time before and potential changes in the value of the target and bidder ...rms should already be reected in the stock price. It is much more interesting to see what happens on the day that the takeover plans become public knowledge (the announcement day) or before that, to form an idea of the pro...ts from insider trading. A common procedure is to pick the date of the ...rst announcement in the Wall Street Journal, or another ...nancial news source, of the takeover bid as the event date. Some uncertainty regarding the event date is often unavoidable, and one has to take some care in interpreting the results of an event study in such cases. 2.2 Models for the abnormal returns An important step in conducting an event study is the choice of a benchmark model for stock return behaviour. There is a wide variety of models available in the literature, which I try to summarize here. The main dierences among the models are the chosen benchmark return model and its estimation interval. Abnormal returns (AR) are de...ned as the return (R) minus a benchmark or normal return (N R) ARit = Rit N Rit (1) For several methods, the determination of the normal returns requires estimation of some parameters. This estimation is typically performed over an estimation period, [T1 ; T 2], which precedes the event period, [t1 ; t2 ]. The event period is 3 Post-Event Window t1' T2 T1 t1 Event (t=0) t2 Event Window Estimation Window typically indicated by t = 0. Notice that the time index t counts "event time", i.e. the number of periods (days, months) from the event and not the usual calendar time. Graphically, the time line around the event then looks like this: 2.2.1 Mean-adjusted returns In the mean-adjusted model, the benchmark is the average return over some period, say between T1 and T2 . The normal returns are then de...ned as T2 1 X N Rit = Ris T s=T (2) 1 where T = T2 T1 + 1 equals the number of time periods used to calculate the average return (the length of the estimation period). The choice of the benchmark period is rather arbitrary. In an inuential study, Brown and Warner (1980) use a 35-month period that ends 10 months before the event. Copeland and Mayers (1982) advocate the use of a period after the event. Many other choices are found in the literature. 4 2.2.2 Market adjusted returns An obvious disadvantage of the mean-adjusted method is the omission of marketwide stock price movements from the benchmark return. Especially if the events for dierent ...rms occur at the same point in time (e.g. option expiration), the results might be biased if the whole market goes up or down in the event period. In such a case, signi...cant abnormal returns will be detected, which may not be due to the event but rather to marketwide price movements. To correct for this omission, the return on a market index, Rmt , can be chosen as the benchmark: (3) N Rit = Rmt The resulting abnormal returns are referred to as market adjusted returns. A point of interest is which market index to choose. The standard choice for US research are the CRSP equally weighted and value weighted indexes.2 Brown and Warner (1980) compare an equally weighted and a value weighted index, and conclude that they give similar results. 2.2.3 Market model residuals and CAPM The market adjusted returns method implicitly assumes that the "beta" of each stock is equal to one. This is obviously not always the case, and it is better to account for dierences in "beta" in de...ning abnormal returns. Therefore, a good way to de...ne abnormal returns is as residuals of the market model: Rit = i + i Rmt + it (4) The abnormal returns are then de...ned as the residuals or prediction errors of this model, N Rit = b i + bi Rmt (5) where b and b are OLS estimates of the regression coe cients. The period over which the market model is estimated diers among studies, but most studies use an estimation period preceding the event period or surrounding (but not including) the event period. 2 Both these indexes are available in WRDS (the Wharton Research Data System), for which Tilburg University has a licence. 5 FFJR use a sample of monthly stock returns starting in 1926 and running to 1959. The parameters of the market model, (4), are estimated using the whole sample, but the period running from 15 months before the split to 15 months after the split is excluded. Note that this concerns a dierent calendar time period for each ...rm, as the events do not occur simultaneously (except by coincidence). They use the return on the equally weighted CRSP index as the benchmark market return. An alternative to the market model is a CAPM type model, where excess returns are modeled as: Rit Rf t = i (Rmt Rf t ) + it (6) The associated normal return of the CAPM is N Rit = Rf t + bi (Rmt Rf t ) (7) Calendar time eects are a potential problem with the market model. It is well documented that returns on Monday are lower, and on Friday slightly higher, than on other trading days. If events are clustered on one of these days, the usual abnormal returns may be biased. A simple solution for this problem is to include calendar (i.e. day-of-the-week) dummies in the market model from which abnormal returns are computed (de Jong, Kemna and Kloek, 1992). 2.3 Analysing abnormal returns In analysing abnormal returns, it is conventional to label the event date as time t = 0. Hence, from now on ARi;0 denotes the abnormal return on the event date and, for example, ARi;t denotes the abnormal return t periods after the event. If there is more than one event relating to one ...rm or stock price series, they are treated as if they concern separate ...rms. We typically consider an event period, running from t1 to t2 . Assuming there are N ...rms in the sample, we can construct 6 a matrix of abnormal returns of the following form: 0 1 AR1;t1 .. ARN;t1 C B C B | .. | C B C B B AR1; 1 .. ARN; 1 C C B C B AR1;0 .. AR N;0 C B C B B AR1;1 .. ARN;1 C C B C B | .. | A @ AR1;t2 .. ARN;t2 Each column of this matrix is a time series of abnormal returns for ...rm i, where the time index t is counted from the event date. Each row is a cross section of abnormal returns for time period t. In order to study stock price changes around events, each ...rm's return data could be analysed separately. However, this is not very informative because a lot of stock price movements are caused by information unrelated to the event under study. The informativeness of the analysis is greatly improved by averaging the information over a number of ...rms. Typically, the unweighted cross-sectional average of abnormal returns in period t is considered: AARt = N 1 X ARit N i=1 (8) Large deviations of the average abnormal returns from zero indicate abnormal performance. Because these abnormal returns are all centered around one particular event, the average should reect the eect of that particular event. All other information, unrelated to the event, should cancel out on average. Often, we are interested not only in performance at the event date, but also over longer periods surrounding the event. The usual way to study performance over longer intervals is by means of cumulative abnormal returns, where the abnormal returns are aggregated from the start of the event period, t1 , up to time t2 , as follows: CARi = ARi;t1 + :: + ARi;t2 = t2 X ARit (9) t=t1 Again, in event studies the CARs are aggregated over the cross-section of events 7 to obtain cumulative average abnormal returns (CAAR): N 1 X CARi CAAR = N i=1 (10) Note that the CAAR can also be obtained by aggregating the AARt 's over time, as is easily checked from (8) and (9): CAAR = t2 X AARt t=t1 An example of a graph of CAR's is given in Figure 1 from Vermaelen (1981). This graphs plots the average stock price reaction in a period from 60 days before a stock repurchase to 60 days after the event. Hence, in our timing convention. the start of the event period is t1 = 60 and the end, t2 , runs from -60 to 60. FFJR calculate AARs for 29 months prior to the event through 30 months after the event. The AAR's are graphed in Figure 2a, and the CAAR's in Figure 2b. The evidence presented by these graphs is clear. In the 30 months before a stock split, the stock has performed excessively well. On average, stocks which split have had a 33% higher return than comparable stocks that did not split. However, there is no price eect of the split itself. The AAR at the event date is very small, and the CAAR remains at after t = 0. 2.4 Testing abnormal performance Although graphical reporting of cumulative abnormal returns is instructive and often suggestive, in almost all event studies the graphical analysis is supported by statistical tests. These tests are designed to answer the question whether the calculated abnormal returns are signi...cantly dierent from zero at a certain, a priori speci...ed, signi...cance level. The null hypothesis to be tested is of the form H0 : E(ARit ) = 0 (11) Which statistical test of this hypothesis is appropriate depends on the way in which the abnormal returns are constructed and on the statistical properties of stock returns. In this section we discuss several test statistics. We pay particular attention to some pitfalls that a researcher might encounter when conducting an event study. 8 2.4.1 The basis: t-tests The most common test of the null hypothesis of no abnormal return, equation (11), is a simple t-test. In order to introduce this test, we make some restrictive assumptions, but these will be relaxed later on. Speci...cally, assume that the abnormal returns ARit that together make up the average abnormal return AARt are independently and identically distributed. Moreover, we assume that they follow a normal distribution with mean zero (under the null hypothesis) and variance 2 . The independence assumption implies, for example, that all abnormal returns are cross-sectionally uncorrelated: E(ARit ARjt ) = 0 for i 6= j. Hence, the variance of the average, AARt , is equal to 1=N times the variance of a single abnormal return, so that AARt N (0; 2 =N ). If Z= 2 were known, a test statistic for (11) is given by p AARt N N (0; 1) (12) Under the stated assumptions, Z follows a standard normal distribution. Of course, in practice is unknown. An estimator of can be constructed from the cross- sectional variance of the abnormal returns in period t: v u N u 1 X t st = (ARit AARt )2 N 1 i=1 (13) This yields the following test statistic for the average abnormal return G= p AARt N st tN 1 (14) Under the stated assumptions, this test statistic follows a Student-t distribution with N 1 degrees of freedom. However, there is strong evidence that stock returns do not satisfy the normality assumption imposed to derive the distribution of the Z and G test statistics. FFJR provide an interesting plot of the empirical distribution of the abnormal returns in their study. They graph the empirical distribution function against the normal distribution function. If the empirical distribution were normal, this graph would be approximately a straight line. However, as can be seen from Figure 1, the extreme ends of the distribution are atter than the normal distribution. This indicates that there are more and larger extreme 9 observations than predicted by the normal distribution. This phenomenon is observed in almost all stock return series and is generally referred to as leptokurtosis or a fat tailed distribution. If stock returns do not follow a normal distribution, the exact small sample distribution result that G follows a Student-t distribution does no longer hold. If we maintain the assumptions that the abnormal returns are independent and have the same mean and variance, it can be shown that in large samples, G approximately follows a standard normal distribution. This is a result of the Central Limit Thep orem, which states that under these assumptions, N times the average, divided by the standard deviation converges to a standard normal random variable G= p AARt N st N (0; 1) (15) Hence, if N is large enough, the quantiles of the normal distribution can be used as critical values for the t-test. In event studies, N > 30 is typically su cient for this. For example, for a two-sided test at 5% con...dence level, the critical value is 1.96. So, if G > 1:06 or G