In June 2014, the Supreme Court issued its second decision in the Halliburton securities fraud litigation.[i]  Halliburton II reaffirmed the court’s prior decision in Basic Inc. v. Levinson,[ii] which provided plaintiffs in federal securities fraud litigation with a presumption of reliance based on the fraud on the market theory.  Halliburton II also heightened the importance for both plaintiffs and defendants of using event studies at the class certification stage in order to address price impact. Price impact concerns whether allegedly fraudulent statements significantly affected market price.  Event studies had already become a critical litigation tool for establishing or rebutting changes in price related to elements of securities fraud.  By placing increased emphasis on price impact at the class certification stage, Halliburton II ratchets up the importance of properly using and understanding the statistical methodology undergirding event studies.

In our working paper, available here, we explore a variety of considerations related to the use and misuse of event studies in securities fraud litigation. We start with an explanation of the event study methodology.  The basic function of an event study is to determine whether a highly unusual price movement has occurred.  We explain how economists determine the expected return for a security, how they calculate the excess return on the date of an alleged fraudulent statement or corrective disclosure, and how they typically determine whether the excess return is statistically significant.

We go on to identify several special features of securities fraud litigation that distinguish litigation from the scholarly context in which event studies were developed.  We flag four reasons why the standard approach to event studies can lead to statistical mistakes, and we describe straightforward modifications necessary for event studies to fit the litigation context.

First, the standard event study uses a two-sided testing approach, which makes sense only if unusually large price changes in either the positive or negative direction would be considered evidence of price impact. In securities fraud litigation, a price impact must be both statistically significant and in a particular direction.  Thus a plaintiff who proves that stock price fell by a statistically significant amount following the release of false but positive statements about the issuer has failed to establish price impact.   Correcting this mistake is simple and expands the set of cases in which plaintiffs will be able to prove price impact.

Second, standard event study methodology assumes that excess returns are normally distributed, even though it is well documented that this is often not the case.  Incorrectly assuming normality of excess returns can lead experts to find a significant price impact either too often or too rarely, depending on the true distribution of excess returns.  This mistake is also simple to correct using the SQ test recommended in earlier work published by two of us.[iii]  Using the SQ test may either expand or reduce the set of cases in which plaintiffs will be able to prove price impact.

Third, standard event study methodology ignores the fact that in many cases, experts must separately test for price impact on multiple event dates.  Depending on the nature of the case at hand, the standard threshold for finding price impact may be either too demanding for plaintiffs or too forgiving. Properly addressing this issue may expand or reduce the set of cases in which plaintiffs will be able to prove price impact.

Fourth, standard event study methodology assumes that excess returns have the same standard deviation on all dates, even though this measure of an excess return’s volatility may vary dynamically.[iv] We highlight adjustments needed to address the problem of dynamic changes in the excess return’s volatility in a way that incorporates the other three corrections discussed above.  As with non-normality and multiple testing, ignoring dynamic volatility can lead to either too many or too few cases in which price impact is found; properly addressing the problem can thus either expand or reduce the set of cases in which plaintiffs are able to prove price impact.

Using the example of six dates in the Halliburton litigation, we illustrate these points and their practical relevance.  After properly addressing the four issues above, we find that the district court should have found statistically significant price impacts on two dates (rather than one) at issue in the Halliburton litigation. This example illustrates the real-world import of using correct statistical methodology to test for price impact.

Finally, we explore the limitations of event studies – what they can and cannot prove.  A first limitation is that event studies can do no more than demonstrate significant price changes, over and above what otherwise would have been expected, on dates when information is released to the public. Event studies do not speak to the rationality of those price changes.[v]  Second, event studies cannot be used to measure the effect of so-called confirmatory disclosures – fraudulent statements that falsely confirm prior statements – or to separate out the effect of multiple disclosures that are bundled together simultaneously, such as in a single press release.  Third, although the standard event study can produce evidence of a highly unusual price effect, its failure to do so does not necessarily mean there was no price effect; the price effect may simply be too small to lead to a finding of statistical significance.

Importantly, we explain that academic event studies incorporate a 95 percent standard for statistical significance, which is the equivalent of a requirement that the rate of false positives be less than 5 percent.  The consequence of applying this standard in securities litigation, where the focus is on only one firm’s excess returns, is usually a very high frequency of false negatives — or, equivalently, a very low-power test.  The result is to create an extremely high risk of false negatives, even when the four issues we discuss above are properly dealt with. In other words, the existing event study methodology will predictably fail to find a statistically significant price impact in a substantial number of cases where actionable fraud really did occur.  The trade-off between false positives and false negatives engendered by the academic standard has important normative consequences. Courts and policymakers should more carefully consider the role event studies should play in securities fraud litigation.

Halliburton II raised a variety of legal issues concerning establishing and rebutting price impact and the role of event studies in addressing those issues.  Many of these issues are currently pending in the lower courts.   For example, the U.S. Court of Appeals for the Second Circuit will hear appeals of class certification decisions in three separate cases involving challenges to the proof necessary to rebut the Basic presumption of reliance.[vi]   These developments underscore the importance of a better understanding of event studies in securities litigation.

ENDNOTES

[i] Halliburton Co. v. Erica P. John Fund, Inc., 134 S. Ct. 2398 (2014) (Halliburton II).

[ii] 485 U.S. 224 (1988).

[iii] See Jonah B. Gelbach, Eric Helland, and Jonathan Klick, Valid Inference in Single-Firm, Single-Event Studies, 15 Am. L. & Econ. Rev. 495 (2013).

[iv] For more on this issue, see Andrew C. Baker, Note, Single-Firm Event Studies, Securities Fraud, and Financial Crisis: Problems of Inference, 68 Stan. L. Rev. 1207 (2016) and Edward G. Fox , Merritt B. Fox, and Ronald J. Gilson, Economic Crisis and the Integration of Law and Finance: The Impact of Volatility Spikes, 116 Colum. L. Rev. 325, 407 (2016).

[v] This question was raised by Justice Alito at the oral argument in Halliburton II.  See Transcript of Oral Argument at 24, Halliburton II, 134 S. Ct 2398 (No. 13-317)..

[vi] See In re Petrobras Sec. Litig., No. 16-463, Dkt. 119; In re Goldman Sachs Group, Inc. Sec. Litig.,

No. 16-250, Dkt. I, 80; Strougo v. Barclays PLC, No. 16-450, Dkt. 1, 55 (June 15, 2016). In addition, the Fifth Circuit heard an interlocutory appeal of class certification in the latest iteration of the Halliburton case last month. Erica P. John Fund, Inc. v. Halliburton Company, et al., No. 15-90038, 2015 U.S. App. LEXIS 19519 (Nov. 4, 2015).

This post comes to us from professors Jill Fisch, Jonah Gelbach and Jonathan Klick at the University of Pennsylvania Law School. It is based on their article, “After Halliburton: Event Studies and Their Role in Federal Securities Fraud Litigation,” which is available here.