We propose a test statistic for nonzero mean abnormal returns based on a Smooth Transition Auto Regressive (STAR) model specification. Estimation of STAR takes into account the probability of contaminated events that could otherwise bias the parameters of the market model and thus the specification and power of the test statistic. Using both simulated and real stock returns data from mergers and acquisitions, we find that the STAR test statistic is robust to contaminated events occurring in the estimation window and in the presence of event-induced increase in return variance. Under the STAR test statistic the true null hypothesis is rejected at appropriate levels. Moreover, it exhibits the highest levels of power when compared with other test statistics that are widely and routinely applied in short-horizon event studies.
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There is a vast amount of theoretical and empirical studies in the research realm of this topic such the ones of Ball and Torous (1988), Corrado (1989), Boehmer et al. (1991), Salinger (1992), Savickas (2003), Dombrow et al. (2000), Cyree and DeGennaro (2002), Harrington and Shrider (2007), Ahern (2009), Campbell et al. (2010) and Kolari and Pynnönen (2010), among others. The landmark work in this topic is that by Brown and Warner (1980, 1985) who investigate the specification (Type I error—rejecting the null when it is true) and power (Type II error—failing to reject the null when the alternative hypothesis is true) of several modifications of the short-horizon event study by assuming that abnormal returns are intertemporally uncorrelated and there is no (significant) impact of event-induced variance.
Abnormal return (AR) is defined to be the difference between the actual return that is observed during the event day(s) (namely, the event window) and the expected return which is provided from a return-generating model estimated using stock returns data that precede the event (namely, the estimation window). Event-induced increase in return variance occurs when variance in the event window exceeds the variance over the estimation window; as a consequence, test statistics that ignore plausible implications of unexplained variation in true abnormal returns for the structure of heteroskedasticity may fail to detect event-related abnormal performance.
Cam and Ramiah (2014) also discuss the possibility that researchers may reach different results depending on the financial econometrics adjustments and asset pricing model used when calculating expected returns.
Although we focus our analysis on M&As as a major corporate event, our inferences could easily be generalized for any other corporate decisions that exhibit similar market performance, such as season equity offerings, share repurchase, goodwill write offs, cross-listings, etc.
Letting the market model parameters being regime-dependent allow a more realistic representation of the return-generating mechanism since prior empirical research has revealed a significant time-variation in the slope parameter which depends on rising and falling market conditions (Hays and Upton 1986; Klein and Rosenfeld 1987; Chang and Weiss 1991; Chiang et al. 2013).
Campbell et al. (2001) document a noticeable increase in firm-level volatility relative to market volatility over the period from 1962 to 1997 which is associated with a decline in the explanatory power of the market model (see also empirical evidence in Aktas et al. 2007b, as well as Arora et al. 2009 for emerging markets). Kothari and Warner (2007) note that this is highly relevant on the implication behind the event study because it suggests a time-variation to the power of test statistics to detect abnormal performance for certain events. Studies that rely on purely simulated variance-induced events may fail to properly capture such stylized (structured) patterns in the returns-generating mechanism.
Both of these elements are deemed important since Harrington and Shrider (2007) identify them to be “troubling features” of the statistical tests reported in many prior studies. In addition, the real return-generating process would allow many different sorts of unrelated events to affect the estimation period, revealing which tests are robust when employed with non-simulated data.
Salinger (1992) also discusses deficiencies of the traditional approach on the estimation of the abnormal returns variance when the market model parameters are not stable and which could lead to incorrect inferences about the detection of abnormal returns.
The starting values of ζ i and c i (with ζ i > 0) are determined by a grid search and are estimated in one step by maximizing the likelihood function while the threshold point between the states is estimated by the model.
These tests are analyzed very briefly. For further information about the tests we refer the reader to the original contributions made by the authors of each test.
Estimation is based on the Maximum-likelihood method using the MSVAR library in the GAUSS software.
Programming code for the STAR event study model is freely available from the authors’ websites.
The one-period lagged return was proved to be the most appropriate transition variable for more than 90 % of the firms in our sample (based on the LM-type test).
We choose to report results using a portfolio size of 50 stocks to maintain conformity with notable previous studies (e.g., Brown and Warner 1980; Savickas 2003; Aktas et al. 2007a; Harrington and Shrider 2007; Kolari and Pynnönen 2010 etc). Nevertheless, some recent studies such as the ones by Ahern (2009) and Campbell et al. (2010) simulate larger stock portfolio sizes. We have repeated the whole analysis with 1000 samples of either 100 or 250 stocks each to find that our results/inferences remain unchanged.
We reach qualitatively similar results for any other abnormal performance above 1 %.
All results are robust when we instead use the CRSP equally weighted index.
The samples for the tests are completed as follows. For the 10 % rejection rates: to construct the 1000 portfolio samples, each 50-firm sample is formed by randomly picking 45 firms from the universe of CRSP stocks (event-free sample) and 5 firms from the M&As data set (contaminated sample). Likewise, for the 5 % rejection rates, in the first (second) 500 samples we randomly pick 3 (2) firms from the M&As data set and 47 (48) firms from the universe of CRSP stocks. For the 1 % rejection rates, in the first (second) 500 samples we randomly pick 1 (0) firms from the M&As data set and 49 (50) firms from the universe of CRSP stocks.
Unreported findings suggest that our results are robust to longer or shorter event windows (e.g. [−20, +20] and [−1, +1].
To further guard against erroneous inferences that may arise in the presence of cross-sectional correlation and non-normal stock returns, we also apply the adjusted BMP test (cBMP) of Kolari and Pynnönen (2010) and the generalized RANK test (GRANK) of Kolari and Pynnönen (2011). Overall, performance of cBMP and GRANK is better when compared to their initial counterparts (i.e., the BMP and RANK tests, respectively). Our empirical results and inferences, however, are unchanged regarding the superiority of the regime-switching models and in particular of the STAR event study method over all other test statistics (the same holds true for the analysis that follows in Sect. 3.2). For the sake of brevity, we omit presenting results of these two tests in the tables; yet for illustration purposes and completeness, we include their size-power curve performance in Figs. 1 and 2.
All conclusions regarding the mean return remain unaltered if we instead pick the 20 % deals with the highest mean returns in the estimation window.
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The authors would like to thank Milto Hadjikyriakou for providing excellent research assistance. The authors also acknowledge comments and constructive suggestions from participants at the 5th CSDA International Conference on Computational and Financial Econometrics (December 2011, UK).
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Andreou, P.C., Louca, C. & Savva, C.S. Short-horizon event study estimation with a STAR model and real contaminated events. Rev Quant Finan Acc 47, 673–697 (2016). https://doi.org/10.1007/s11156-015-0515-3
- Event studies
- Test statistics
- Contaminated events
- Markov switching regression model
- Smooth Transition Auto Regressive model