Single-firm event studies, securities fraud, and financial crisis: problems of inference.

• Author: Baker, Andrew C.
• Position: III. Literature Review on Event Study Models through Conclusion, with footnotes, p. 1233-1261

3. Literature Review on Event Study Models

   The event study is "one of the most frequently used analytical tools" in corporate finance research. (158) Before the advent of the modern event study in 1969, there was little empirical evidence of the central issues of financial economics, whereas "[n]ow we are overwhelmed with results, mostly from event studies." (159) The ability to isolate the impact of a broad range of corporate events occurring in capital markets led to a dramatic increase in published articles using the event study technique; Kothari and Warner report that between 1974 and 2000, 565 papers containing event studies were published in five finance journals alone. (160)

   The event study method as commonly used was established in an influential 1969 paper by Eugene Fama, Lawrence Fisher, Michael Jensen, and Richard Roll. (161) In examining the effect of stock split announcements on the value of common equity, the authors established the textbook table layout that is still the basis of the standard event study. (162) Although the structural format of an event study has remained stable, significant intellectual resources have been devoted to researching more sophisticated statistical modeling techniques and more accurate means of adjusting the measure of statistical significance to ensure the validity of inferences drawn from event studies. (163)

   Beginning in the 1980s, a parallel literature developed analyzing the comparative ability of the various preexisting statistical models to detect abnormal performance. A pair of seminal companion articles written by Stephen Brown and Jerold Warner analyzed the specification properties of these models and their ability to detect abnormal performance using monthly (164) and daily (165) data. Brown and Warner's 1985 paper, which "has since come to eponymously define the genre," (166) found that event studies presented few practical difficulties when using daily data. (167) Although daily returns clearly departed from normality, methodologies based on OLS market models were "well-specified under a variety of conditions." (168) The academic community was generally convinced that event studies represented an empirically valid method of testing financial hypotheses, even given the strict assumptions generally required in parametric hypothesis testing.

   Dozens of papers have been published testing the properties of competing event study methods. (169) These studies analyze two primary characteristics: how frequently the statistical test rejects the null hypothesis of no abnormal price performance, and how frequently the null hypothesis is rejected in the presence of a known abnormal return. (170) The first inquiry, often known as the "analysis of specification," tests whether the Type I error rate (i.e., when the null hypothesis of no abnormal performance is falsely rejected) approaches the error rate of the assumed size of the test. (171) The second inquiry, called the "analysis of power," tests the ability of a model to detect abnormal price performance when it exists; the failure to do so is known as a Type II error. (172) When comparing tests that are well specified, the test with higher power is preferred. Using pseudo-simulations, "artificial" abnormal performance is imputed into actual stock returns, and the ability of different models to detect statistically significant abnormal returns is analyzed. (173)

   The initial comparative performance studies evaluated the mean-adjusted return model, the market-adjusted return model, and the OLS market model. The mean-adjusted model calculates abnormal returns by simply subtracting the average return of the stock during the estimation period and comparing each out-of-sample daily abnormal return to the standard deviation of the average. (174) This method does not explicitly control for the idiosyncratic risk of the stock or the contemporaneous return on the market. The market-adjusted return model subtracts the return on the market from the daily return and compares the difference in the event period to its mean and standard deviation in the control period. (175) As detailed in Part II above, the market model approach calculates abnormal performance by using pre-event period returns and an OLS regression. This approach controls for both the risk of the stock (as measured by its market beta) and the simultaneous returns on the market. (176)

   The initial Brown and Warner studies were notable for finding that modeling choice did not have a material impact on the performance of event studies. (177) Although the authors found that daily data presented few difficulties for properly conducting an event study, they did acknowledge that an increase in security variance could lead to too many rejections of the null hypothesis that the average excess return is zero. (178)

   Later empirical studies questioned the findings of these initial counterintuitive results. Ramesh Chandra, Shane Moriarity, and G. Lee Willinger demonstrated that the comparability in performance of the mean adjusted and market-adjusted return models was largely a statistical artifact of model implementation. (179) More generally, many academics challenged the notion that violations of normality in the underlying returns of the security were irrelevant to the performance of the model. Subsequent research verified the Brown and Warner conclusion that abnormal returns are not normally distributed, but it instead found this violation to cause significant problems of inference, leading to both under- and overrejection of the null. (180) For "outlier-prone data," prevalent in financial markets, the true Type I error rate will be larger than that associated with particular asymptotic values, with greater discrepancies found in stock returns with higher levels of kurtosis. (181)

   Recognizing the limitations of standard inference tests in the presence of normality violations, scholars searched for alternative statistical models that would be robust to the empirical distribution of abnormal returns. Some have proposed using nonparametric tests of abnormal performance, which make no assumption about the probability distribution of the variables. The most successful of the nonparametric tests have been the rank and sign tests. More applicable to the context of single-firm, single-event studies, the nonparametric rank test transforms the distribution of the abnormal returns into a uniform distribution across rank values irrespective of the original distribution. (182) An alternative method is to normalize the conventional t-statistics from the market model regression with bootstrap resampling. (183) Evidence on the performance of bootstrap methods has been mixed and varies with the bootstrap resampling's application; as a result, it has not enjoyed popular support in the event study literature. (184) The overall conclusion from these articles is that alternative event study methods, whether parametric or variations based on empirical resampling of the abnormal return distribution, should be implemented when the data are distributed non-normally.

   Scholars have recently scrutinized the application of event studies in particular relation to their use in litigation. Corrado notes that single-security event studies are rarely reviewed in academic literature but are routinely used in legal proceedings. (185) He advises legal practitioners to use a simple modification of the standard event study approach, which "merely involves counting the number of returns from the control period that are larger or smaller than the event date return." (186) In reviewing event studies as applied to Rule 10b-5 securities fraud cases, Gelbach et al. propose a similar modified event study procedure called the "SQ test." (187) Like the test endorsed by Corrado, the SQ test involves ranking the abnormal returns from the market model regression and testing whether the event-date abnormal return is larger (or smaller) than the abnormal return quantile corresponding to a given confidence level. (188) Refuting the doctrinal reliance on the central limit theorem, (189) the authors prove that the large-sample behavior of the f-statistic will be normal only if the abnormal return distribution is itself normal. (190) As a result, standard parametric approaches may yield biased results depending on the size of the event effect and the deviation of the empirical return values from the normal distribution. (191) Using a dataset containing the returns for all securities in the Center for Research in Security Performance's (CRSP) database from 2000 to 2007, the authors find evidence of substantial bias against finding statistically significant abnormal returns. (192)

   There has also been increased scholarly interest in the effect of changes in volatility on the inference properties of event studies. Brown and Warner's initial comparative review using daily data noted that an increase in variance would lead to too many rejections of the null hypothesis of no abnormal performance. (193) Aktas, De Bodt, and Cousin note that idiosyncratic volatility is not constant through time and that individual stocks have become more volatile over recent decades. (194) Although they do not find an effect on specification tests, the power of event studies to detect abnormal performance varies with idiosyncratic volatility. (195) The authors ultimately conclude that "there is no practical solution to this problem" outside of "increas[ing] the sample size to compensate for the increase in ... volatility." (196)

4. Data and Methodology

   1. The Financial Crisis and Return Series Data

      This Note attempts to answer the questions whether the standard OLS market model or the alternative model proposed by Gelbach perform adequately when used to analyze return series during the financial crisis of 2007-2008, and if not, whether there are readily available alternatives that can be substituted by courts. As previously discussed in Part...