Daubert In Securities Litigation

Daubert arises regularly in securities litigation and regularly in connection with a statistical technique called regression analysis that is in a wide range of forensic finance analysis.

The use of regression in securities litigation is most conspicuous in calculating damages done to stockholders by allegedly inappropriate corporate conduct. The law regarding damages in securities fraud requires that experts calculate damages by the use of a highly intuitive regression technique known as an “event study.” See Romano, THE GENIUS OF AMERICAN CORPORATE LAW 17 (AEI Press 1993), in which the author explained that event study techniques

Examine whether particular information events . . . significantly affect the firm’s stock price (technically, they examine whether the average residuals of a regression of observed stock prices on predicted prices are statistically different from zero). If an information event . . . is considered beneficial for shareholders then stock prices will rise significantly above their expected value on the public announcement of the event. If the event is perceived as detrimental to shareholder wealth, then stock prices will significantly decline. Given the regression methodology, such stock price effects are referred to as average residuals or abnormal returns.

In short, event studies are used to measure the impact on a company’s market value of the release into the market of some significant news about the company.

The statistical concepts developed here generalize immediately to areas of antitrust, employment discrimination, and an array of other practice areas that rely on statistical evidence and proof.

2. Event Studies

a. [§13.26] In Re Oracle Securities Litigation

In an opinion that came down six weeks after Daubert but does not cite it, the Northern District of California generally disparaged the proffer of a damage estimate that was calculated using a “value line” approach and opined that the “[u]se of an event study or similar analysis is necessary more accurately to isolate” damages. In re Oracle Securities Litigation, 829 F.Supp. 1176, 1181 (N.D. Cal. 1993). The court went on to state that, because of the expert’s “failure to employ such a study,” the expert’s results could not be “evaluated by standard measures of statistical significance,” thus making his results unreliable. Id.

Event studies are widely used by economists in nonlitigation settings to investigate the impact of the release of new information on the price of a stock that is actively traded in an efficient market. A properly executed event study apparently meets all of the Daubert criteria. Studies based on the technique have been peer reviewed and published hundreds of times, and the technique is generally accepted in the relevant scientific community. There are well-established standards that govern its use, and these standards point to proper hypothesis tests and the error rates of those tests as the proper instruments of investigation. Event studies use regression analysis, and because the reliability of regression analysis rests on several assumptions, when those assumptions can be shown to be violated, the admissibility of the event study is put into doubt. Because regression is susceptible to successful challenge, when confronted with the proffer of event study damages, the prudent attorney may wish to inquire whether the regression assumptions discussed in this chapter have been met.

Numerous examples exist of the use of an event study in a range of securities fraud matters whose fact patterns are strikingly similar to that of In re Oracle Securities Litigation. Many companies have experienced allegations of irregularities in their financial statements. The companies’ stocks fell sharply following the release of this information, and ensuing lawsuits alleged that a class of each corporation’s stockholders was damaged by purchasing stock the price of which was inflated by the alleged irregularities. As such litigation proceeds, economists will likely estimate the damages that were alleged to have been suffered by this class of stockholders and will probably use an event study for this purpose. This makes event study methods and cases worthy of careful consideration.

b. [§13.27] Event Study Cases

The court in In re Executive Telecard, Ltd. Securities Litigation, 979 F.Supp. 1021 (S.D. N.Y. 1997), cited the earlier case of In re Oracle Securities Litigation, 829 F.Supp. 1176 (N.D. Cal. 1993), for the proposition that an event study is required to distinguish between fraud-related and non-fraud-related influences on the company’s stock price; it also excluded expert testimony that failed to adequately account for non-fraud-related bad news. (The failure to account for non-fraud-related bad news is a form of the model specification problem discussed in §13.24.) In re Executive Telecard, Ltd. contains several interesting types of analysis that defy easy description. The court recounted Daubert’s basics and stated that “valuation of damages in a securities class action such as this does not appear to be the sort of ‘hard science’ that requires application of the specific factors set forth in Daubert.” In re Executive Telecard, Ltd., 979 F.Supp. at 1024. The court instead required that “an expert’s opinion should at least ‘have a reliable basis in the knowledge and experience’ of the particular ‘discipline’ involved.” Id., quoting Daubert, 509 U.S. at 592. The district court raised several interesting issues. First, Daubert proposed the specific factors as suggestions for proceeding with a flexible inquiry, so none of them have ever been “required,” as is underscored by Kumho Tire Co. Second, it is notable that Daubert made no distinction between “hard” and “not-hard” sciences, relying instead on the scientific method to define science and the various disciplines to establish by the use (or nonuse) of the scientific method in their nonlitigation research whether they are scientific or nonscientific disciplines. Third, other courts have come to precisely the opposite conclusion expressed in In re Executive Telecard, Ltd. on whether regression-based expert testimony falls under Daubert’s purview. In particular, see In re Polypropylene Carpet Antitrust Litigation, 996 F.Supp. 18, 26 (N.D. Ga. 1997) (“multiple regression analysis is a scientific endeavor whose admissibility . . . must be determined using the test set forth in Daubert”), and the prodding of the Eleventh Circuit in City of Tuscaloosa v. Harcros Chemicals, Inc., 158 F.3d 548 (11th Cir. 1999), that the district court should have held a Daubert hearing to decide issues of admissibility of proffered expert testimony because it would have avoided subsequent problems. City of Tuscaloosa is a complex ruling that is discussed further in §13.39. In Rebel Oil Co. v. Atlantic Richfield Co., 146 F.3d 1088 (9th Cir. 1998), 171 A.L.R.Fed. 783, the court discussed with approval the lower court’s Daubert-based admissibility decision on expert economics testimony in a petroleum antitrust case.

When regression-based testimony is being evaluated and the discipline involved is economics, requiring that “an expert’s opinion should at least ‘have a reliable basis in the knowledge and experience’ of the particular ‘discipline’ involved,” it is tantamount to requiring precisely that the testimony be evaluated using Daubert’s factors. In re Executive Telecard, Ltd. Securities Litigations, 979 F.Supp. at 1024, quoting Daubert. See §13.10. This is a theme repeated in §13.58 regarding expert testimony in Florida state courts.

RMED International, Inc. v. Sloan’s Supermarkets, Inc., 2000 WL 310352 (S.D. N.Y. 2000), aff’d 2000 WL 420548, applied these notions in a telling way. The defense had challenged the plaintiff’s damages expert, citing In re Executive Telecard, Ltd. and alleging that the expert’s methodology was “unreliable because she did not employ formal statistical methods — and regression analysis in particular — to isolate and exclude from her damages calculation the portion of the inflation in Sloan’s stock price attributable to company-specific factors unrelated to the alleged fraud.” RMED International, Inc., 2000 WL 310352 at *5. However, in that case, there was insufficient data for the expert to execute the standard statistical and regression analysis, and the court excused the expert from those requirements on that basis.

Here, the expert was presented with a number of legitimate limitations that hindered her ability to estimate plaintiffs’ damages using statistical methods, and it appears that the methodologies she chose, taken together, were a reasonable and generally accepted alternative. Most significantly, Sloan’s life as an operating company and the alleged fraud began at approximately the same time. . . . Accordingly, there did not exist a meaningful price history for Sloan’s stock that Preston could designate as the control or “clean” period from which to estimate its true value using statistical analysis. In order to control for market and industry factors using a regression analysis, or to perform a statistical event study, Preston would have to have known the relationship of Sloan’s stock price to the market (the “company-market relation”) and to the industry (the “company-industry relation”) before the alleged fraud. . . . This would have required the availability of Sloan’s price history prior to the alleged fraud for a period of sufficient length to produce statistically significant estimates of Sloan’s company-market and company-industry relation¬ships. Such data would have produced “betas” or coefficients which could be plugged into a mathematical formula and multiplied by the actual market and industry returns during the fraud period to calculate the portion of Sloan’s stock movement attributable to market and industry factors.

Id. at *7. The court admitted Preston’s testimony, reasoning:

Absent a control period, Preston was limited in her ability to perform a statistical event study, and thereby unable to isolate with mathematical certainty the effect of company-specific, market, or industry factors on Sloan’s stock price. Such limitations are contemplated by the academic sources cited by both plaintiffs and defendants, and require alternative methodologies such as the ones Preston employed.

Id.

That Preston’s damages estimate cannot be measured with mathematical precision because she did not employ statistical methods is an insufficient basis to exclude her proposed testimony, particularly in light of the absence of data from a control period.

Id. at *10.

Thus, while Oracle and Executive Telecard say the expert must do an event study, RMED, which involved another securities litigation issue for which an event study was appropriate but lacked sufficient data, allowed other, less formal techniques to substitute for the formal event study analysis, and the expert’s testimony was admitted. RMED will surely be cited for the proposition that an event study is not necessary to make a securities damages expert’s opinion admissible, but it seems to stand for the more narrowly drawn and well-reasoned notion that, when the data necessary to such an undertaking is absolutely unavailable, conceptual analogues to the event study can stand in its stead.

For example, citing RMED, the court in In re Imperial Credit Industries, Inc. Securities Litigation, 252 F.Supp.2d 1005, 1014, aff’d 145 F.App’x 218 (C.D. Cal. 2003), excluded plaintiff’s damages expert for failing to do an event study, reasoning that:

Plaintiffs’ expert report on damages, the Marek Report, is deficient for failure to provide an “event study” or similar analysis. An event study is a statistical regression analysis that examines the effect of an event on a dependent variable, such as a corporation’s stock price. RMED International, Inc. v. Sloan’s Supermarkets, Inc., 2000 WL 310352, *6 (S.D.N.Y. 2000) (citing Koslow, Estimating Aggregate Damages in Class Action Litigation under Rule 10B, 59 Fordham L. Rev. 811, 822 & n. 50 (1991)). The event study method is “an accepted method for the evaluation of materiality damages to a class of stockholders in a defendant corporation.” In re Gaming Lottery Securities Litigation, 2000 WL 193125, *1 (S.D. N.Y. 2000).

The court also stated:

Damages in a securities fraud case are measured by the difference between the price at which a stock sold and the price at which the stock would have sold absent the alleged misrepresentations or omissions. . . . A proper measure of damages in the securities context thus requires elimination of that portion of the price decline or price difference which is unrelated to the alleged wrong.

Id. at 1014–1015. The court further observed:

Because of the need “to distinguish between the fraud-related and non-fraud related influences of the stock’s price behavior” . . . a number of courts have rejected or refused to admit into evidence damages reports or testimony by damages experts in securities cases which fail to include event studies or something similar. See, e.g., In re Northern Telecom Ltd. Sec. Litig., 116 F.Supp.2d 446, 460 (S.D.N.Y. 2000) (“Torkelson’s testimony is fatally deficient in that he did not perform an event study or similar analysis to remove the effects on stock price of market and industry information and he did not challenge the event study performed by defendants’ expert.”); Executive Telecard, 979 F.Supp. at 1024-26 (finding an expert’s methodology not reliable because he failed to conduct an event study or regression analysis to detect whether stock price declines were the result of forces other than the alleged fraud; applying Daubert . . . to exclude the expert damages report); Oracle, 829 F.Supp. at 1181 (“Use of an event study or similar analysis is necessary more accurately to isolate the influences of information specific to Oracle which defendant[s] allegedly have distorted. . . . As a result of his failure to employ such a study, the results reached by [plaintiffs’ expert] cannot be evaluated by standard measures of statistical significance.”)

Id. at 1015. The bottom line for the court was that, “absent an event study or similar analysis, Plaintiffs cannot eliminate that portion of the price decline of ICII’s and/or SPFC’s stock which is unrelated to the alleged wrong.” Id. at 1016. The court excluded the plaintiff’s expert “pursuant to Daubert and Federal Rule of Evidence 702, on the ground that its methodology [was] flawed,” thus the court could not conclude that the expert’s report “rest[ed] on a ‘reliable basis in the knowledge and experience of [its] discipline.’” Id., quoting Daubert, 509 U.S. at 592.

In In re Cendant Corp. Securities Litigation, 109 F.Supp.2d 235, aff’d 264 F.3d 201 (D. N.J. 2000), the court undertook an extended articulation of the legal and economic issues surrounding the calculation of damages in 10b-5 type securities litigation. This case is interesting for several reasons, one of which is the survey of the pertinent law and econometrics that its final quarter constitutes. This survey is interesting both because of the detail in which it is provided and because the case was lawyered by a who’s who of law firms, some of whose briefs are available to the industrious on PACER (Public Access to Court Electronic Records) at www.pacer.gov.

In In re Cendant, the defendants challenged the methodology of the plaintiffs’ expert. The plaintiffs responded that the event study methodology their expert

Used to calculate shareholder damages during the class period “has been used by financial economists since 1969 as a tool to measure the effect on market prices from all types of new information relevant to a company’s equity valuation.” . . . It is so accepted, plaintiffs add, that courts now reject expert damage estimates which do not use event study methodology to evaluate the impact on the market of a company’s disclosures: “Use of an event study or similar analysis is necessary more accurately to isolate the influences of information specific to Oracle which defendants allegedly have distorted. [. . . ]As a result of his failure to employ such a study, the results reached by [the expert] cannot be evaluated by standard measures of statistical significance.” In re Oracle Securities Litig., 829 F.Supp. 1176, 1181 (N.D.Cal.1993).

In re Cendant, 109 F.Supp.2d at 253–254. The plaintiffs argued that a similar plan of allocation had been praised by Judge Walker in In re California Micro Devices Securities Litigation, 965 F.Supp. 1327, 1332 (N.D. Cal. 1997), as “by far the most thorough, sophisticated and well substantiated” plan he had seen in a securities class action. This plan is analogous to the analysis contained in §§13.25–13.26 and is an excellent example of its application. The Cendant court analyzed the damages calculation methodology carefully:

Plaintiffs’ expert . . . uses event study methodology to calculate the losses suffered by shareholders and allocate damages. This study attempts to calculate out-of-pocket damages suffered by shareholders due to Cendant’s fraudulent accounting practices. Out-of-pocket damages for shares bought during the class period and held until the end of the period are defined as “the price paid for a security minus the ‘true value’ of the security on the date of purchase—i.e., the value absent the [artificial] inflation caused by claimed misrepresentations or omissions.” . . . For shares bought during the class period and sold before its end, the damages “generally equal the artificial inflation at purchase minus the artificial inflation at sale.” . . . A summary of the methodology is as follows:

First, an event study is prepared. This measures the day-to-day changes of share price and isolates times when the disclosure of information is accompanied by a stock price return outside the stock’s normal volatility . . . (a “return” is a day-to-day change in share price illustrated as a percentage). This is done by estimating an appropriate market model to measure returns — here the S & P 500 Index was used. . . . Dorkey [plaintiff’s expert] then examined the stock’s volatility on the following dates in 1998: April 16–20th, to measure the impact of the April 15, 1998 disclosure; July 13–14th, for the preliminary announcement of the results of the WF & G/AA Report on July 14th; and August 27–31, for the release which detailed the report and stated that Cendant’s income was artificially increased by $500 million. . . . Trading volume and price changes on these dates exceeded “normal” volume and returns under the market model. For the first event dates, the statistically significant total excess return is -33.65%; the second, -29.67%; and the last, -9.10%. [Emphasis added] Also considered were other news items disseminated to the market between April 15th and August 31st; other shifts in returns in this time span “were likely to have been caused by the highly volatile market prices of Cendant common stock . . . rather than fraud.”

Second, a value line is constructed which represents the “true value” of Cendant stock (price absent fraud). Two basic steps are involved: (1) estimate the maximum artificial inflation in the market price of CUC or Cendant common stock, expressed as a percentage of closing market price as of April 15, 1998; and (2) apportion that maximum inflation among the twelve reporting periods between May 31, 1995 and April 15, 1998 when inflated earnings were released
. . . . Dorkey states that he used the method found in Bradford Cornell & R. Gregory Morgan, Using Finance Theory to Measure Damages in Fraud on the Market Cases, 37 U.C.L.A. L.Rev. 883 (1990) (hereinafter “Cornell & Morgan”) to set the value line. This method assumes that “the [trading] price and [true] value of the security move in tandem except on days when fraud-related information is disclosed.” Id. at 886. Here, there are 8 days where the movement of the security cannot be correlated to actual trading results.

Following Cornell & Morgan, Dorkey “constructed returns” to chart the day-to-day changes of Cendant’s price; constructed returns equal actual returns except for the eight days targeted by the event study. For these 8 days, returns are predicted under the market model. Cornell & Morgan at 899.

The series of constructed returns are then used to create the value line. The end of the class period is assumed as the point at which, if plotted on a graph, the market price and the true value of the stock converge — there is no more artificial inflation. On August 31, 1998, Cendant closed at $11.63. Working backward, the artificial inflation rates are then calculated for the period covered by the correcting disclosures. The true value for August 28th is determined by dividing the value on August 31st ($11.63) by [1 + the predicted return on August 31st (under the market model,
-6.8%)]. This yields a true value of $12.47. See Cornell & Morgan at 899 (the predicted return under the market model is used for this date because it is one of the 8 days altered by disclosure of fraud). This calculation is repeated for each trading day to determine the true value line through April 15, 1998, the date of the first disclosure of fraud. On that date, the true value of Cendant stock is calculated to be $14.92, 58.1% of the actual closing price on that date. This date, April 15, 1998, yields the maximum percentage of artificial inflation.

Third, the maximum artificial inflation is allocated over the class period. Dorkey relies on the premise that the maximum level of inflation did not remain constant over the class period but gradually increased in the three years over which fraudulent earnings statements were released. Dorkey explains that throughout the class period, the fraudulent releases generally met market earnings expectations, creating a stock price that gradually appreciated with the market model. . . . The rate of artificial increase over the class period links the percentage of artificial inflation over the class period (increasing to the maximum percentage of 58.1%) to the actual amount by which each earnings release was overstated over the three year period. This is called the “Ross” approach, developed by David L. Ross of Lexecon, Inc. . . . (“The Ross approach is generally characterized as allocating the maximum artificial inflation in direct proportion to the total cumulative amount of earnings overstatement”); see also In re California Micro Devices Securities Litig., 965 F.Supp. 1327, 1332–33 (N.D.Cal. 1997) (approving settlement with Plan of Allocation developed by Ross).

To illustrate, for the quarter ending April 30, 1995, the percentage of the maximum inflation allocated is equal to a fraction of: the amount of earnings per share disclosed as overstated for that quarter, or $.04 per share, over the total overstatement of earnings per share of $.61. For the second quarter of 1995, the fraction is expressed as $.08 (the cumulative amount of overstatement for the first and second quarters) over $.61.

* * *

Fourth, aggregate damages for the class are calculated. To arrive at the total damages, artificial inflation is “applied” to all shares acquired during the class period that were held until at least April 15, 1998, the date of the first corrective disclosure. . . . Dorkey did not allocate any damage to those who sold before this date because the shares were still artificially inflated at sale, in fact more so than at purchase under Dorkey’s methodology. It is impossible to determine the date on which each and every share was purchased or sold, thus Dorkey used a trading model to simulate actual trading. . . . (citing Dean Furbush & Jeffrey Smith, Estimating the Number of Damaged Shares in Securities Fraud Litigation: An Introduction to Stock Trading Models, Bus. Lawyer (Feb.1994)). The model identifies the fraction of each day’s volume that represents shares likely purchased and held through April 15th. The model assumes that each share purchased during the class period is more likely to have been traded than the other outstanding shares (the float). . . . Using his model, Dorkey estimated that 488.5 million shares were purchased and held beyond the class period and 617.9 million were purchased but sold before the end of the class period. Based on Dorkey’s calculation of the total amount of shares traded in the class period, he finds aggregate damage of $8.8 billion.

In re Cendant, 109 F.Supp.2d at 264–266. The court rejected the defendant’s Daubert motion and admitted the testimony of the plaintiff’s expert. This is analogous to the analysis contained in §§13.25–13.26 of this chapter. The entire final quarter of In re Cendant is worth careful analysis by anyone with an interest in this type of litigation

Daubert played a key role in litigation issuing from the WorldCom financial restatement fraud scandals. A series of opinions styled In re WorldCom, Inc. Securities Litigation relate to the dimensions of the expert testimony. In In re WorldCom, Inc. Securities Litigation, 2005 WL 375313 and 2005 WL 375314 (S.D. N.Y. 2005), the court rejected the defendant’s motion to preclude evidence of aggregate damages and to require that damages for each class member be determined on an individual basis through a post-trial claims process. In particular, in In re WorldCom, Inc. Securities Litigation, 2005 WL 375313, *4, the defendant moved to preclude evidence of aggregate damages, challenging, inter alia, plaintiff’s expert’s “use of a ‘proportional trading’ model to calculate shareholder damages.” The court denied the motion, noting that this “model has survived repeated Daubert challenges in other cases.” Id.

One additional issue raised in WorldCom has to do with a proponent’s strategy of disguising an expert witness as a fact witness to escape the rigorous demands of the Daubert progeny. Fed.R.Evid. 701, which concerns the admissibility of lay testimony, read as follows at the time of the Worldcom decision (and still reads substantially the same):

If the witness is not testifying as an expert, the witness’ testimony in the form of opinions or inferences is limited to those opinions or inferences which are (a) rationally based on the perception of the witness, (b) helpful to a clear understanding of the witness’ testimony or the deter¬mination of a fact in issue, and (c) not based on scientific, technical, or other specialized knowledge within the scope of Rule 702.

The WorldCom court cited the notes of the Advisory Committee on Rule 701 for the proposition that the 2000 amendments were

Aimed at two goals: “eliminating the risk that the reliability requirements set forth in Rule 702 will be evaded through the simple expedient of proffering an expert in lay witness clothing” and “ensur[ing] that a party will not evade the expert witness disclosure requirements set forth in Fed.R.Civ.P. 26 . . . by simply calling an expert witness in the guise of a layperson.” . . . According to the Advisory Committee, what separates expert and lay testimony is that “lay testimony results from a process of reasoning familiar in everyday life,” whereas “expert testimony results from a process of reasoning which can be mastered only by specialists in the field.”

In re WorldCom, Inc. Securities Litigation, 2005 WL 675601, *2 (S.D. N.Y. 2005).

c. [§13.28] Economics Of Event Studies

Event study logic flows from economists’ belief that the current value of a security is equal to the present value of all of the payments that the security is expected to make to its owners throughout its life. An immediate implication of this is the belief that the value of the security changes when new information is released into the market that changes the market’s assessment of the future payments that the security will make to its holders. When information comes into the market that is hypothesized to affect the value of a particular stock, economists test that hypothesis by comparing how that particular stock performed right after the release of the information to how the stock would have been expected to perform in the absence of the release of the new information.

To see how information changes securities prices, one should start with a day when no information is released into the marketplace that alters the market’s perception of the value of any stock: no Federal Reserve announcements made of actual or potential interest rate movements; no big contracts awarded; no lawsuits filed, won, or lost; no new inventions or patents introduced. On such a day, every publicly traded stock would close essentially where it had opened. Now, one should imagine a similar day when only one piece of new information is released into the market and that this information affects the value of only one stock. If the news is good, the price of that one stock will rise, but, assuming that the information has no secondary effects on any other stock and that the stock is not part of the Dow Jones Industrial average, the Dow will not move. It is then possible to calculate the impact of the newly released information on the value of a share of the stock. If the stock opens at $100 and closes at $103 while no other stock moves, economists would say that the information raised the value of the stock by three dollars.

Of course, such no-news days do not exist, so estimating the impact of the release of new information on the value of a stock is a little more complicated. But it still involves comparing the return on the particular stock with the return to an index of stocks that have not been affected by the information. For example, if the day’s news, including some news about Stock A, caused the market to rise by 4%, while causing Stock A to rise by 3%, the economist would conclude that the news about Stock A was not good, because, on that news, the value of Stock A fell by 1% relative to the market.

The event study technique ascribes this change in the stock’s value to the event that the information disclosed. In the case of the corporations mentioned in §13.26, this information is the release of allegations that reported sales figures were inflated. Because the event study is the financial economist’s standard technique for determining the impact of mergers, dividend and earnings announcements, management changes, and a host of other phenomena on the value of the subject firm’s stock, it has well-established nonlitigation uses. The heart of the technique is a test of the null hypothesis (see §13.31) that the information had no impact on the price of the stock. The economist will reject this null hypothesis if and only if the hypothesis test yields both an estimate of the change in the stock’s value that is nonzero and an error rate of the test that convinces the economist that sampling error has not caused the nonzero estimate of the change in the stock’s value. This technique meets all of the Daubert criteria: it poses and tests a hypothesis, reports the pertinent error rates, and is based on peer-reviewed and published techniques that are so pervasively used within the relevant scientific community that they are the generally accepted tool for evaluating the impact of the release of new information on the value of a publicly traded security.

3. Econometrics Of Event Studies:
Applied Regression Analysis

a. [§13.29] In General

To determine how much a security’s price moves as new information about an event that affects the security enters the market, one need only compare the return on the security over the time that the market receives the news, called the observed return, to the return on the security that would be expected during that time period in the absence of any news, called the expected return. See, e.g., Brown & Warner, Measuring Security Price Performance, 8 J.Fin.Econ. 205 (Sept. 1980) (developing event study technique); see also Brown & Warner, Using Daily Stock Returns: The Case of Event Studies, 14 J.Fin.Econ. 3 (March 1985) (continuing development of event study technique).

The period during which the news is thought to affect the security’s return is called the “event window.” Researchers typically use an event window that begins just before the news is publicly announced to capture the price effects that are associated with pre-announcement information leakage. An event window of one day before the announcement to one day after the announcement is a very popular choice among financial economists, but the event window specified tends to vary. See Black, Bidder Overpayment in Takeovers, 41 Stan.L.Rev. 597, 602 (1989) (collecting event study results for “narrow (one to four day) ‘window’ periods”). For example, if a security is thinly traded, it may take longer for information to be fully incorporated, requiring a longer event window. The longer the event window, the more certain is the analyst that the full effect of the announcement has been measured. However, the longer the event window, the more likely it is that other value-affecting information will enter the market during the event window, with the undesirable result that the analyst’s estimates of the impact of the news of the event under consideration will actually reflect the impact of more than one event on the security. Thus, one choice of the expert witnesses that can immediately be seen as suspect is that of extending the event window to cover the entire class period. See Beaver & Malernee, ESTIMATING DAMAGES IN SECURITIES FRAUD CASES (Cornerstone Research 1990) (detailing procedure like event study but not in event study terminology). See also Alexander, The Value of Bad News in Securities Class Actions, 41 U.C.L.A.L.Rev. 1421 (1994) (providing example of rough version of such approach). This technique attributes all new information released on the security over the entire class period to the “news” that has come into the market. In a securities fraud matter, the “news” in the event study will be news of the fraud, and the entire movement of the security’s price during the event window will be attributed to the fraud. This is an especially attractive technique for plaintiffs’ experts in cases in which the value of the security has fallen dramatically during the class period for reasons unrelated to the fraud, because such decrements to value increase the resulting damage estimates. This can be made to sound reasonable, even benign. It is not.

b. [§13.30] Abnormal Return

The abnormal return for a day is the actual return for that day minus the return predicted for that day. Once the size of the abnormal return has been estimated for each day in the event window, the daily abnormal returns can be summed to find the cumulative abnormal return, or CAR, which is a measure of the impact of the event on the security’s return. Hypothesis testing is used to test the statistical significance of the CAR to determine the probability that a CAR of that particular size had occurred due to random chance rather than in response to the incorporation of new information.

c. [§13.31] Hypothesis Tests And Statistical
Significance Of Estimates

Hypothesis testing is the process of deriving a proposition (or hypothesis) about an observable group of events from accepted scientific principles, then investigating whether, on observation of data regarding that group of events, the hypothesis seems true. It is hypothesis testing that distinguishes the scientific method of inquiry from nonscientific methods, and the scientific method of inquiry is required for the resulting inferences to be the basis of admissible expert testimony.

In the basic model of hypothesis testing, scientists pose hypotheses in pairs. The hypothesis that is actually tested is called the “null hypothesis,” and it alleges that there is “no difference” between populations or “no effect” of some treatment or event. A null hypothesis might say that there is no difference among the probabilities of a certain number coming up on a die or that there is no effect of a merger announcement on the value of a firm’s common stock. The “alternate hypothesis” is that there is a difference in the die-face probabilities or that the announcement of a merger does affect the price of the acquired firm’s stock. One tests the null hypothesis (often called just “the null”) and either rejects it at a certain level of confidence or fails to reject it. Although there is no scientific means for accepting a null or alternate hypothesis, if one tests the null and fails to reject it, one says that there is no effect or, speaking more carefully, that the attempt to reject the null failed. If one rejects the null hypothesis, one is left only with the alternate hypothesis, and, again, while no mechanism exists for accepting either hypothesis, a rejection of the null constitutes strong evidence that the alternate hypothesis is true. See Kmenta, ELEMENTS OF ECONOMETRICS 110–114 (McMillan Pub. Co. 1971).

As a simple example of hypothesis testing, looking at a single six-sided die might lead one to the proposition (or hypothesis) that each of the six numbers is equally likely to be rolled on each roll of the die. This hypothesis is tested scientifically by proposing the “null hypothesis” that each number is equally likely to land face up, and then rolling the die, e.g., 600 times, and recording the number of times that each number is actually found face up. If an appropriate statistical test is used, and if each number occurred about 100 times, the statistical test will be unable to reject the null hypothesis of equal probabilities, and the scientist will be left with the likelihood that the die is fair. However, if the number ‘3’ occurs a disproportionate number of times, say 200 times out of 600 rolls, the statistical test will be likely to reject the null hypothesis of equal probabilities and the scientist will interpret this as evidence that the die is loaded, thus rejecting the null hypothesis.

In actual research, the null hypothesis is denoted “H0”, so named because it hypothesizes no effect, and an alternative hypothesis is denoted “H1”. This pair of hypotheses is written by economists and other scientists as:

H0:CAR = 0

H1:CAR  0.

This two-line expression is read as “the null hypothesis is that the cumulative abnormal return of the subject security during the event window is zero, so the event did not affect the return on the security. The alternate hypothesis is that the cumulative abnormal return on the subject security during the event window differs from zero, so the event did affect the return on the security.”

Economists say that the null hypothesis is rejected “at the 5% level” if the absolute value of the CAR is more than about double its standard deviation. The use of 5% is intended to mean that only 1/20 of the time would a CAR that large be observed if it were being measured over an event window that did not include an event that had truly affected the security’s return.

Conducting the hypothesis test that the Supreme Court describes in Daubert is mathematically equivalent to constructing the confidence intervals that other courts have used. See Berry v. CSX Transportation, Inc., 709 So.2d 552 (Fla. 1st DCA 1998); Turpin v. Merrell Dow Pharmaceuticals, Inc., 959 F.2d 1349 (6th Cir. 1992). The use of a confidence interval often makes the discussion of the statistical significance of an event more intuitive than the hypothesis testing technique can. The “5% confidence interval” is written as:

[CAR - (2 x standard deviation), CAR + (2 x standard deviation)].

If the estimated CAR is 0.02 and the standard deviation is 0.007, the confidence interval is

[0.02 - (2 x 0.007), 0.02 + (2 x 0.007)], which is [0.006, 0.0314].

In other words, for the data that generated this CAR and standard deviation, the scientist is 95% certain that the CAR is above 0.006 and below 0.0314. So in this case, the scientist is 95% confident that the CAR of 0.02 is statistically significant, which means that the scientist is 95% sure that the true abnormal return was not zero, and 95% sure that, in this case, the event contained in the event window increased the price of the security. On the other hand, if one considers the same example, but changes the assumed standard deviation from 0.007 to 0.011, the 5% confidence interval would be [-0.002, 0.042]. This says that one is 95% confident that the true CAR is between -0.002 and 0.042. Because this interval contains zero, one can no longer say that the event contained in the event window increased the price of the security and be sure that he or she is right 95% of the time. Many scientists believe that the 95% confidence level is the “correct” confidence level to use and stop there. Others feel that there is nothing sacred about 95% confidence and would proceed to calculate the 90% confidence interval, which is:

[0.02 - 1.64 x 0.011, 0.02 + 1.64 x 0.011], or [0.00196, 0.03804],

Which does not contain zero. So in this case the null hypothesis can be rejected at the 90% level, even though the null cannot be rejected at the 95% level.

d. [§13.32] Summary

Daubert, 509 U.S. at 593, articulates five criteria for the admissi¬bility of scientific expert testimony but points out that “[m]any factors will bear on the inquiry [of what is scientific knowledge], and we do not presume to set out a definitive checklist or test.” Science does presume, however, and science’s checklist has so informed Daubert that it is difficult to imagine much flexibility in applying Daubert’s factors to scientific testimony that would not offend science. This has not, however, kept the courts from misapplying Daubert or the scientific principles that it articulates.

The important role of Daubert in securities class actions is discussed in §§13.49–13.55.