Barclays PLC, its American subsidiary Barclays Capital Inc. (collectively, “Bar-clays”), and three senior officers of those companies1 appeal from an order of the United States District Court for the Southern District of New York (Scheindlin, J.) granting a motion for class certification filed by the Plaintiffs-Appellees (“Plaintiffs”), three individuals2 who purchased Barclays’ American Depository Shares (“Barclays’ ADS”)3 during the'class period. The Plaintiffs brought this suit alleging violations of § 10(b) of the Securities Exchange Act of 1934,15 U.S.C. § 78j(b), and the Securities and Exchange Commission’s Rule 10b-5.4
The Defendants-Appellants (“Defen- ■ dants”) contend that the district court erred in granting class certification by: (1) concluding that the Affiliated Ute presumption of reliance applied, see Affiliated Ute Citizens of Utah v. United States, 406 U.S. 128, 92 S.Ct. 1456, 31 L.Ed.2d 741 (1972); (2) determining, alternatively, that the Basic presumption, see Basic Inc. v. Levinson, 485 U.S. 224, 108 S.Ct. 978, 99 L.Ed.2d 194 (1988), applied without considering direct evidence of price impact when it found that Barclays’ ADS traded in an efficient market; (3) requiring the Defendants to rebut the Basic presumption by a preponderance of the evidence (and concluding that the Defendants had failed to satisfy that standard); and (4) concluding that the Plaintiffs’ proposed method for calculating classwide damages was appropriate.
We agree with the Defendants that the district court erred in applying the Affiliated Ute presumption, but reject the remainder of their arguments and conclude that the district court did not err in granting the Plaintiffs’ motion for class certification. Specifically, we hold that: (1) the Affiliated Ute presumption does not apply because the Plaintiffs’ claims are primarily based on misstatements, not omissions; (2) direct evidence of price impact is not always necessary to demonstrate market efficiency, as required to invoke the Basic presumption of reliance, and was not required here; (3) defendants seeking to rebut the Basic presumption must do so by a preponderance of the evidence, which the Defendants in this case failed to do; and (4) the district court’s conclusion regarding the Plaintiffs’ classwide damages methodology was not erroneous. We therefore AFFIRM the order of the district court.
BACKGROUND
I. Barclays’ Recent Involvement in the LIBOR Scandal and Its Investigations
Barclays is a London-based international financial services provider involved in banking, credit cards, wealth management, and investment management services in more than fifty countries.5 Barclays was the subject of a number of investigations and suits involving the misrepresentation of its borrowing data submitted for the calculation of the London Interbank Offered Rate (“LIBOR”).6 Barclays and other financial institutions manipulated LI-BOR, an important set of benchmarks for international interest rates. In June 2012, Barclays was fined more than $450,000,000 as a result of its involvement. As a result of the LIBOR investigation, Barclays’ corporate leadership undertook significant measures to change the company’s culture and develop more integrity in its operations.7
II. LX, Dark Pools, and High-Frequency Traders
From the time it was involved in the' LIBOR investigations to the present, Bar-clays, through its American subsidiary Barclays Capital Inc., has operated an alternate trading system—essentially a private venue for trading securities8—known as Barclays’ Liquidity Cross, or, more simply, as Barclays’ LX (“LX”). LX belongs to a particular subset of alternate trading systems known as “dark pools.” Dark pools permit investors to trade securities in a largely anonymous manner. Neither “information regarding the orders placed into the pool for execution [n]or the identities of subscribers that are trading in the pool” are displayed at the time of the trade.9
The anonymous nature of dark pools makes them popular with institutional investors, who seek to avoid victimization at the hands of high-frequency traders.10,11 High-frequency traders often engage in “front running” or “trading ahead” of the market, meaning that they detect patterns involving large incoming trades, and then execute their own trades before those incoming trades are completed.12 Front running results in the incoming trades being more costly or less lucrative for the individuals or institutions making them.13 Thus, many investors prefer to avoid high-frequency traders, and utilize dark pools to do so. Some literature nevertheless suggests that dark pools are also popular with high-frequency traders, who similarly prefer them because they are anonymous.14
III. Barclays’ Statements Regarding LX and Liquidity Profiling
To address concerns that high-frequency traders may have been front running in LX, Barclays’ officers made numerous statements asserting that LX was safe from such practices, and that Barclays was taking steps to protect traders in LX,
For example, Barclays’ Head of Equities Electronic Trading (and a Defendant in this action) William ■ White told Traders Magazine that Barclays monitored activity in LX and would remove traders who engaged in conduct that disadvantaged LX clients. On a different occasion, White publicly stated that LX was “built on transparency” and had “safeguards to manage toxicity, and to help [its] institutional clients understand how to manage their interactions with high-frequency traders.” J.A. 237. Other examples of purported misstatements made by Barclays include the following allegations:
• Touting LX as encompassing a “sophisticated surveillance framework that protects clients, from predatory trading activity.” J.A. 240.
• Representing that “LX underscores Barclays’ belief that transparency is not only important, but that it benefits both our clients and the market overall.” J.A. 246.
• Stating that Barclays’ algorithm and scoring methodology enabled it “to restrict [high-frequency traders] interacting with our clients.” J.A. 247.
Barclays also created a service for its LX customers entitled “Liquidity Profil'ing.” First marketed in 2011, Liquidity Profiling purportedly allowed Barclays’ personnel to monitor high-frequency trading in LX more closely and permitted traders to avoid entities that engaged in such trading. For example, Barclays issued a press release stating that Liquidity Profiling enabled “Barclays to evaluate each client’s trading in LX based on quantitative factors, thereby providing more accurate assessments of aggressive, neutral and passive trading strategies.” J.A. 246. Based on a numerical ranking system that categorized traders, LX users could, according to Barclays, avoid trading with high-frequency traders. Barclays made numerous other alleged misstatements regarding Liquidity Profiling, such as:
• Claiming in a press release that by , using . Liquidity Profiling,' clients could “choose which trading styles they interact with, instead of choosing by the more arbitrary designa- - tion of client type.” J.A. 246.
• Explaining that “transparency” was the biggest theme of the year 2013, and that “Liquidity Profiling ana- • lyzes each interaction in the. dark pool, allowing us to monitor the behavior of individual participants. This was a very significant step because it ’ was important to provide ... clients • with transparency about the nature of counterparties in the dark pool and how the control framework works.” J.A. 252.
IV. The New York Attorney General’s Lawsuit
On June 25, 2014, the New York Attorney General commenced an action alleging that Barclays was violating provisions of the New York Martin Act15 in operating its dark pool. The complaint alleged that many of Barclays’ representations about protections LX afforded its customers from high-frequency traders were false and misleading. See People ex rel. Schneiderman v. Barclays Capital Inc., 1 N.Y.S.3d 910, 911, 47 Misc.3d 862 (N.Y. Sup. Ct. 2015).
The next day, the price of Barclays’ ADS fell 7.38%. On the following day, news reports estimated that Barclays could face a fine of more than £300,000,000 as a result of the Attorney General’s action, and on June 30th its stock price dropped an additional 1.5%.
V. The Plaintiffs’ Action
The Plaintiffs filed the instant putative class action shortly thereafter. They alleged in a subsequent second amended complaint that Barclays had violated § 10(b) and Rule 10b-5 by making false statements and omissions about LX and Liquidity Profiling.
The Plaintiffs alleged that Barclays’ statements about LX and Liquidity Profiling “were materially false and misleading by omission or otherwise because,” J.A. 227, contrary to its assertions, “Barclays did not in fact protect clients from aggressive high frequency trading activity, did not restrict predatory traders’ access to other clients,” and did not “eliminate traders who continued to behave in a predatory manner,” J.A. 228.
According to the complaint, Barclays “did not monitor client orders continuously,” or even apply Liquidity Profiling “to a significant portion of the trading” conducted in LX. J.A. 228. Instead, the Plaintiffs alleged that Barclays “favored high frequency traders” by giving them information about LX that was not available to other investors and applying “overrides” that allowed such traders to be given a Liquidity Profiling rating more favorable than the one they should have received. J.A. 228.
The result of these fraudulent statements, the Plaintiffs asserted, was that the price of Barclays’ ADS had been “maintained” at an inflated level that “reflected investor confidence in the integrity of the company” until the New York Attorney General’s lawsuit. J.A. 224.
VI.Procedural History
The Defendants moved to dismiss the Plaintiffs’ claims. They contended, among other arguments, that the alleged misstatements recited by the Plaintiffs were not material and therefore could not form the basis for a § 10(b) action. In particular, the Defendants pointed out that the revenue generated by LX was only 0.1% of Barclays’ total revenue, which was, according to the Defendants, significantly below what would ordinarily be considered quantitatively material to investors. The Defendants also contended that the Plaintiffs had not adequately pleaded that the alleged misstatements were qualitatively material because they had not alleged that any Barclays investor had considered them in making investment decisions; the statements were directed only to LX clients, not investors.
The district court denied the Defendants’ motion to dismiss, in part. Strougo v. Barclays PLC, 105 F.Supp.3d 330, 353 (S.D.N.Y. 2015). The court explained that it was obligated to consider whether the purported misstatements were quantitatively or qualitatively material. Id. at 349-50. In its quantitative analysis, the court agreed with the Defendants that LX was a small part of Barclays’ business operation and accounted for a small fraction of the company’s revenue. Id. at 349. It nevertheless concluded that the misstatements could be qualitatively material. Id. After the LIBOR scandal, the court explained, “Barclays had staked its long-term performance on restoring its integrity.” Id. (internal quotation marks omitted). Bar-clays’ statements regarding LX and Liquidity Profiling could therefore “call into question the integrity of the company as a whole.”16 Id.
a. The Plaintiffs’ Motion for Class Certification
The Plaintiffs then sought class certification for investors who purchased Barclays’ ADS between August 2, 2011, and June 25, 2014.17
In order to satisfy Federal Rule of Civil Procedure 23(b)(3)’s predominance requirement, the Plaintiffs argued that § 10(b)’s reliance element was satisfied by the members of the proposed class under the presumption of reliance recognized by the Supreme Court in Basic, 485 U.S. at 224,108 S.Ct. 978.
In support of their motion, the Plaintiffs submitted an expert report from Dr. Zachary Nye18 that considered whether the market for Barclays’ ADS was efficient, a necessary prerequisite for the Basic presumption to apply. Dr. Nye’s report applied the five factors identified in Cammer v. Bloom, 711 F.Supp. 1264 (D.N.J. 1989), and the three factors identified in Krogman v. Sterritt, 202 F.R.D. 467 (N.D. Tex. 2001). See In re Petrobras Sec., 862 F.3d 250, 276 (2d Cir. 2017). Dr. Nye explained that all eight factors supported the conclusion that the market for Barclays’ ADS was efficient. Dr. Nye first concluded that the seven factors that rely on “indirect” indicia of an efficient market—the first four Cammer factors and all three Krog-man factors—supported his conclusion.
With respect to the final factor—the fifth Cammer factor, or “Cammer 5,” which is considered the only “direct” measure of efficiency—Dr. Nye conducted an “event study” to determine whether the price of Barclays’ ADS changed when new material information about the company was released. Based on the results of that event study, Dr. Nye concluded that the final factor also weighed in favor of .concluding that the market for Barclays’ ADS was efficient. Thus, relying on Dr. Nye’s report, the Plaintiffs asserted that they were entitled to the Basic presumption.
In the alternative, the Plaintiffs argued that reliance could be established under the presumption of reliance for omissions .of material information, as recognized by the Supreme Court in Affiliated Ute, 406 U.S. at 128, 92 S.Ct. 1456. That presumption, the Plaintiffs asserted, applied because Barclays had failed to disclose material information regarding LX, such as the fact that Liquidity Profiling did not apply to a significant portion of the trades conducted in LX and that Barclays provided advantages such as “overrides” to high-frequency traders.
Dr, Nye also addressed the calculation of class damages. He opined that the damages class members had suffered as a result of Barclays’ fraudulent conduct could be calculated on a classwide basis. According to Dr. Nye, the amount by which á stock’s price was ■ inflated by fraudulent statements or omissions could be calculated by measuring'how much the price of the stock declined when those statements were revealed to be false or when previously undisclosed information was revealed. An event study could then isolate company-specific changes in stock. price from changes resulting from outside fác-tors such as fluctuations in the stock market generally or the particular industry. Once the decline caused by the corrective disclosure was isolated, the- “daily level of price inflation” could be readily calculated for Barclays’ ADS for the class period. J.Á. 348. Then, each class member’s actual trading in the security could be used to determine .individual damages.19
b. The Defendants’ Opposition to Class Certification
In response, the Defendants argued that the Plaintiffs had not made the requisite showing to invoke the Basic presumption because they had. failed to show that the market for Barclays’ ADS was efficient.20 The Defendants pointed to the report of then* expert, Dr, Christopher M. James,21 which claimed that the Plaintiffs had not shown direct evidence of efficiency under Cammer 5 because the event study conducted by Dr. Nye was flawed. The Defendants did not, however, challenge Dr. Nye’s conclusion. that the seven indirect factors demonstrated that the market for Barclays’ ADS was efficient, nor did Dr. James conduct his own event study to demonstrate the inefficiency of the market for Barclays’ ADS. ’
The Defendants also argued that even if the district court were to conclude that the Plaintiffs were entitled to the Basic presumption of reliance, class certification should be denied because the Defendants rebutted that presumption. They asserted that the event study conducted by Dr. Nye indicated that the price of Barclays’ ADS did not increase by a statistically significant amount on any of the days on which the purportedly fraudulent statements had been made. Thus, according to the Defendants, there was no connection between the misstatements and the price of Bar-clays’ ADS.
The Defendants further contended that the Affiliated Ute presumption was inapplicable to the complaint’s allegations. That presumption, they argued, applied only to situations primarily involving omissions, and the complaint alleged affirmative misstatements, not omissions.
Finally, the Defendants contended that the damages model proposed by Dr. Nye failed to satisfy Comcast Corp. v. Behrend, 569 U.S. 27, 133 S.Ct. 1426, 185 L.Ed.2d 515 (2013). Dr. Nye’s model, the Defendants argued, did not disaggregate confounding factors that could have caused the price drop in Barclays’ ADS that occurred when the New York Attorney General announced his action, such as the likelihood of regulatory fines. Nor had the model sufficiently accounted for variations in the time each alleged misstatement became public. According to the Defendants, these deficiencies precluded class certification.
c. The District Court’s Class Certification Decision
The district court granted the Plaintiffs’ motion for class certification. Strougo v. Barclays PLC, 312 F.R.D. 307, 311 (S.D.N.Y. 2016). It concluded that the Affiliated Ute presumption applied. Id. at 319. The court explained that “a case could be made that it is the material omissions, not the affirmative statements, that are the heart of this case.” Id. According to the court, it was “far more likely that investors would have found the omitted conduct,” as opposed to the misstatements, material. Id.
In the alternative, the district court concluded that the Basic presumption of reliance for misrepresentations applied. Id. at 323. The Defendants, the court noted, had conceded that the Plaintiffs had “established four of the five Cammer factors and all three Krogman factors.” Id. at 319-20. They disputed only the sufficiency of Dr. Nye’s event study under Cammer 5. M at 320. Although Dr. Nye’s event study had been presented to the district court (and was the subject of extensive court proceedings), the district court concluded that direct evidence of price impact under Cammer 5 was not necessary to its determination that the markét for Barclays’ ADS was efficient during the class period.22 Id. The district court noted that although an event study may be particularly important where the indirect factors do not weigh heavily in favor of market efficiency, it was not necessary here where the application of the indirect factors, including that the “stock trades in high volumes on a large national market and is followed by a large number of analysts,” weighed so strongly in favor of a finding of market efficiency. Id. at 322-23. Therefore, the court declined to determine whether Cammer 5 was satisfied, but concluded' based on the showing made by the Plaintiffs on all the indirect factors that Barclays’ ADS traded in an efficient market during the class period. Id. at 323.
The district court noted that, based on ■Dr. Nye’s report, Barclays’ ADS had an average weekly trading volume of 17.7% during the .class period. Id. at 323 n.103. That volume far exceeded the 2% threshold for a “strong presumption” of efficiency based on the average weekly trading volume described in Cammer. Id. Additionally, the district court noted that analysts had published more than 700 reports regarding Barclays’ ADS during the class period, and it explained that “the amount of reporting on Barclays[’] [ADS] by security analysts during the Class Period indicates that' company-specific news was widely disseminated to investors.” Id. at 323 n.104. That consideration was directly relevant to a different “indirect” Cammer factor and, like the average weekly trading volume, supported the conclusion that the market for Barclays’ ADS was efficient. Id. at 316.
The court further determined that the Defendants had not rebutted the Basic presumption. Id. at 327. They had failed to demonstrate that the allegedly fraudulent statements did not impact the price of Barclays’ ADS. Id. The “fact that other factors contributed to the price decline does not establish by a preponderance of the evidence that the drop in the price of Barclays!!’] ADS was not caused at least in part by the disclosure of the fraud at LX,” the district court reasoned. Id. (first emphasis added).
Finally, the district court concluded that Dr. Nye’s damages model complied with Comcast Corp. v. Behrend. Id. The methodology proposed by the Plaintiffs fit their legal theory of the .case because they had proposed using an event study and a- constant dollar method that was based on the decline in stock price following the disclosure of the Attorney General’s lawsuit. Id. The court also concluded that individual damages issues would not predominate and could be readily calculated. Id; It therefore granted the Plaintiffs’ motion for class certification. Id. at 328-29.
This Court granted Barclays’ petition for leave to appeal the district court’s class certification order. See Fed. R. Civ. P. 23(f); Fed. R. App. P. 5(a).
DISCUSSION
The Defendants: argue that the district court erred in four respects by granting the Plaintiffs’ motion for class certification. First, they assert that the district court incorrectly concluded that the Plaintiffs properly invoked the Affiliated Ute presumption. Second, the Defendants contend that the court improperly concluded that the Basic presumption applied without considering direct evidence of market efficiency under Cammer 5. Third, they argue that the district court erroneously required them to rebut the Basic presumption by a preponderance of the evidence (and wrongly concluded that they failed to satisfy that standard). Finally, the Defendants assert that the Plaintiffs’ damages model violates Comcast Corp. v. Behrend.
We agree with the Defendants’ contention that the Affiliated Ute presumption is inapplicable. We reject their other arguments. We affirm the district court’s class certification order because the Basic presumption ■ of reliance for misrepresentations applies, was not rebutted by the Defendants, and renders the district court’s erroneous decision regarding the Affiliated Ute presumption for omissions harmless. Further, we conclude that the damages aspect of the district court’s certification decision was within its discretion.
I. Standard of Review
“We review a district court’s class certification determination for abuse of discretion.... While we review the district court’s construction of legal standards de novo, we review the district court’s application of those standards for whether the district court’s decision falls within the range of permissible decisions.” Roach v. T.L. Cannon Corp., 778 F.3d 401, 405 (2d Cir. 2015).
II. Class Certification Requirements
In addition to satisfying the requirements set forth in Federal Rule of Civil Procedure 23(a), a plaintiff seeking class certification must establish one of the bases for certification identified in Federal Rule of Civil Procedure 23(b). See Fed. R. Civ. P. 23(b). One such basis, at issue here, permits certification if “questions of law or fact common to class members predominate over any questions affecting only individual members,” and “a class action is superior to other available methods for fairly and efficiently adjudicating the controversy.” Fed. R. Civ. P. 23(b)(3). “Predominance is satisfied if resolution of some of the legal or factual questions that qualify each class member’s case as a genuine controversy can be achieved through generalized proof, and if these particular issues are more substantial than the issues subject only to individualized proof.” Roach, 778 F.3d at 405 (internal quotation marks omitted).
III. The Presumptions of Reliance
In a securities fraud action under § 10(b), one of the elements that a plaintiff must prove is that he relied on a misrepresentation or omission made by the defendant.23 In re Am. Int’l Grp., Inc. Sec. Litig., 689 F.3d 229, 234 n.3 (2d Cir. 2012).
“The traditional (and most direct) way a plaintiff can demonstrate reliance is by showing that he was aware of a company’s statement and engaged in a relevant transaction—e.g., purchasing common stock—based on that specific misrepresentation.” Erica P. John Fund, Inc. v. Halliburton Co., 563 U.S. 804, 810, 131 S.Ct. 2179, 180 L.Ed.2d 24 (2011) (“Halliburton I”).
Alternatively, a plaintiff may also seek to take advantage of two presumptions of reliance established by the Supreme Court.
The first—the Affiliated Ute presumption—allows the element of reliance to be presumed in cases involving primarily omissions, rather than affirmative misstatements, because proving reliance in such cases is, in many situations, virtually impossible.24 Wilson v. Comtech Telecomms. Corp., 648 F.2d 88, 93 (2d Cir. 1981); see also Affiliated Ute, 406 U.S. at 153-54, 92 S.Ct. 1456.
The second—the Basic presumption—permits reliance to be presumed in cases based on misrepresentations if the plaintiff satisfies certain requirements.25 ,26 See Halliburton Co. v. Erica P. John Fund, Inc., — U.S. -, 134 S.Ct. 2398, 2413, 189 L.Ed.2d 339 (2014) (“Halliburton' IF’). .One of them, and the only one at issue in this appeal, is that “the stock [at issue] traded in an efficient market.” Id. An efficient market is “one in which the prices of the [stock] incorporate most public information rapidly.”27 Teamsters Local 445 Freight Div. Pension, Fund v. Bombardier Inc., 546 F.3d 196, 204 (2d Cir. 2008). In other words, an efficient market is one in which “market professionals generally consider most publicly announced material statements about companies, thereby affecting stock prices.” Id. at 199 n.4 (internal quotation marks omitted).
We have, repeatedly—and recently-declined to adopt a particular test for market efficiency. Petrobras, 862 F.3d at 276. However, district courts in this and other Circuits regularly consider five factors first set forth in Cammer v. Bloom, 711 F.Supp. at 1286-87. See Petrobras, 862 F.3d at 276. Those factors are:
(1) the average weekly trading volume of the [stock], (2) the number of securities analysts following and reporting on [it], (3) the extent to which market makers traded in the [stock], (4) the issuer’s eligibility to file an SEC registration Form S-3, and (5) the demonstration of a cause and effect relationship between unexpected, material disclosures and changes in the [stock’s] price[ ].
Bombardier, 546 F.3d at 200.
The first four “Cammer factors examine indirect indicia of market efficiency for a particular security.” Petrobras, 862 F.3d at 276. However, the fifth factor—“Cammer 5”—permits plaintiffs to submit direct evidence consisting of “empirical facts showing a cause and effect relationship between unexpected corporate events or financial releases and an immediate response' in the stock price.” Id. (internal quotation marks omitted). Plaintiffs generally attempt to satisfy Cammer 5 by submitting an event study. Such studies are “regression analyses that seek to show that the market price of the defendant’s stock tends to respond to pertinent publicly reported events.” Halliburton II, 134 S.Ct. at 2415.
In addition to the Cammer factors, courts often consider what are known as the three Krogman factors when analyzing whether the market for a stock is efficient. Petrobras, 862 F.3d at 276. Those factors are ■ “(1) the capitalization of the company; (2) the bid-ask spread of the stock; and (3) the percentage of stock not held by insiders (‘the float’).” Krogman, 202 F.R.D. at 474.
If a plaintiff demonstrates to the district court that the market for the stock is efficient and that the other requirements for the Basic presumption are met, the presumption applies and § 10(b)’s reliance requirement is satisfied at the class certification stage. Hevesi v. Citigroup Inc., 366 F.3d 70, 77 (2d Cir. 2004). If, however, a plaintiff fails to qualify for the Basic presumption, and the Affiliated Ute presumption for omissions does not apply, then class certification under Rule 23(b)(3) is usually impossible because reliance would have to be proven on a plaintiff-by-plaintiff basis. Halliburton II, 134 S.Ct. at 2416.
Even if a plaintiff successfully invokes the Basic presumption, however, defendants may rebut the presumption through “any showing that severs the link between the alleged misrepresentation and either the price received (or paid) by the plaintiff, or his decision to trade at a fair market price.” Id. at 2408 (alteration and internal quotation marks omitted).' '
IV. The Defendants’ Arguments
With that background in mind, we now address the Defendants’ specific arguments.
a. The Applicability of the Affiliated Ute Presumption
The Defendants first argue that the district court erred by concluding that the Affiliated Ute presumption applies béeause the Plaintiffs’ complaint is based primarily on allegations of affirmative misrepresentations, not omissions. We agree.
When the Supreme Court first recognized the Affiliated Ute presumption, it explained that under the circumstances of that case, a case “involving primarily a failure to disclose, positive proof of reliance is not a prerequisite to recovery.” Affiliated Ute, 406 U.S. at 153, 92 S.Ct. 1456 (emphasis added). We later determined that the presumption was inapplicable in two cases because the claims of fraud at issue were not based primarily on omissions. Those decisions are particularly helpful in discerning whether the allegations here principally concern misrepresentations or omissions.
In the first, Wilson v. Comtech Telecommunications Corp., 648 F.2d 88 (2d Cir. 1981), we cautioned that the labels “misrepresentation” and “omission” “are of little hélp” because in “many instances, an omission to state a material fact relates back to an earlier’ statement, and if it is reasonable to think that that prior statement still stands, then the omission may also be termed a misrepresentation.” Id. at 93. We explained that what “is important is to understand the rationale for á presumption of causation in fact in cases like Affiliated Ute, in which no positive statements exist: reliance as a practical matter is impossible to prove.” Id. (italics added). In Wilson,’ the president of the defendant corporation made sales and earnings projections at a conference of investors and securities analysts. Id. at 89. Several months later, those projections were shown to be materially inaccurate. Id. The earlier projections became misleading when subsequent corrective information was not timely disclosed.- In other words, as we explain in somewhat more detail, the projections eventually became “half-truths.” Unlike in Affiliated Ute, however, in Wilson the omissions alone were not the actionable events and proving reliance on them was therefore not “impossible”; accordingly, we concluded that the plaintiff was required to demonstrate that he relied on the earlier misrepresentations in executing his stock purchases. Id. at 94.
Similarly, in Starr ex rel. Estate of Sampson v. Georgeson Shareholder, Inc., 412 F.3d 103 (2d Cir. 2005), we concluded that the Affiliated Ute presumption did not apply because the plaintiffs’ claims in that case were “not ‘primarily’ omission claims.” Id. at 109 n.5. We explained that the plaintiffs’ claims there, as in Wilson, focused on “misleading statements” that were not corrected. Id. The plaintiffs asserted that the omissions only “exacerbated the misleading nature of the affirmative statements.” Id.
In this case, the Affiliated Ute presumption does not apply for the same reasons that it was inapplicable in Wilson and Starr. First, the Plaintiffs’ complaint alleges numerous affirmative misstatements by the Defendants. The Plaintiffs are therefore not in a situation in which it is impossible for them to point to affirmative misstatements. Second, the Plaintiffs focus their claims on those .affirmative misstatements. In arguing that class certification was proper, for example, the Plaintiffs stated that Barclays had “touted LX as a safe trading venue” and “consistently assured the public that its dark pool was a model of transparency and integrity.” J.A. 280-81.
Indeed, the omissions the Plaintiffs list in their complaint are directly related to the earlier statements Plaintiffs also claim are false. For example, the Plaintiffs argue that Barclays failed to disclose that Liquidity Profiling did not apply to a significant portion of the trades conducted in LX. That “omission” is simply the inverse of the Plaintiffs’ misrepresentation allegation: Barclays’ statement that Liquidity Profiling protected LX traders was false. Thus, as alleged in Stair, the omissions here “exacerbated the misleading nature of the affirmative statements.” Starr, 412 F.3d at 109 n.5. The Affiliated Ute presumption does not apply to earlier misrepresentations made more misleading by subsequent omissions, or to what has been described as “half-truths,” nor does it apply to misstatements whose only omission is the truth that the statement misrepresents. See Joseph v. Wiles, 223 F.3d 1155, 1162 (10th Cir. 2000), abrogated on other grounds by Cal. Pub. Emps.’ Ret. Sys. v. ANZ Sec., Inc., — U.S. —, 137 S. Ct. 2042, 198 L.Ed.2d 584 (2017).
For these reasons, the Affiliated Ute presumption does not apply.
b. The Applicability of the Basic Presumption
We next turn to the Defendants’ challenge to the district court’s conclusion that the Basic presumption applied.
The Defendants assert three reasons why the district court incorrectly found that the Basic presumption applied and was not rebutted. First, the Defendants contend that the court erred by failing to consider whether direct evidence of price impact under Cammer 5 showed that Bar-clays’ ADS traded in an efficient market. Second, the Defendants argue that even if the failure to make that finding was not erroneous, the court erred by shifting the burden of persuasion, rather than imposing only the burden of production, on the Defendants to rebut the Basic presumption. Third, the Defendants assert that even if they, bore the burden of rebutting the Basic presumption by a preponderance of the evidence, the district court incorrectly concluded that they had failed to satisfy that standard.
We are not persuaded by the Defendants’ arguments. We conclude that direct evidence of price impact under Cammer 5 is not always necessary to establish market efficiency and invoke the Basic presumption, and that such evidence was not required in this case at the class certification stage. Also, the Defendants were required to rebut the Basic presumption by a preponderance of the evidence, and they failed to do so.
1. Whether “Cammer 5” Must Be Satisfied
Whether direct evidence of price impact under Cammer 5 is required to demonstrate market efficiency is a question of law over which we exercise de novo review. See Roach, 778 F.3d at 405.
As previously discussed, we recently once again declined to adopt a particular test for market efficiency in Petrobras. See 862 F.3d at 276. Although we also declined in Petrobras to decide “whether plaintiffs may satisfy the Basic presumption without any direct evidence of price impact,” id. at 276-77, i.e., without producing evidence under Cammer 5, we nevertheless explained that the “district court properly declined to view direct and indirect evidence as distinct requirements, opting instead for a holistic analysis based on the totality of the evidence presented,” id. at 277.
We then also rejected the argument that “directional” direct evidence of price impact28 was required by Cammer 5. Id. at 277-78. In so doing, we explained that we have “never suggested” that an event study “was the only way to prove market efficiency.” Id. at 278. We then noted that the Supreme Court has suggested that the burden required to establish market efficiency “is not an onerous one.” Id. Lastly, we explained that “indirect evidence of market efficiency” under the other four Cammer factors would “add little to the Basic analysis if courts only ever considered them after finding a strong showing based on direct evidence alone.” Id. Indeed, we noted that indirect evidence regarding the efficiency of a market for a company’s stock under the first four Cam-mer factors “is particularly valuable in situations where direct evidence does not entirely resolve the question” of market efficiency. Id.
Here, building on Petrobras, we conclude that a plaintiff seeking to demonstrate market efficiency need not always present direct evidence of price impact through event studies.
In so concluding, we do not imply that direct evidence of price impact under Cammer 5 is never important. Indeed, as the Defendants point out, we have recognized that Cammer 5 has been considered the most important Cammer factor in certain cases because it assesses “ ‘the essence of an efficient market and the foundation for the fraud on the market theory.’” Bombardier, 546 F.3d at 207 (quoting Cammer, 711 F.Supp. at 1287). In Bombardier, we concluded that the district court did not err in rejecting the plaintiffs’ particular event study, but also emphasized that Cammer 5’s importance was greater because a number of the indirect Cammer factors suggested the inefficiency of the market. Id. at 210. Those factors were “the absence of market makers for the Certificates [at issue in that case], the lack of analysts following the Certificates, and the absence of proof that unanticipated, material information caused changes in- the Certificates’ prices—as well as the infrequency of trades- in the Certificates.” Id. ■
Direct evidence of an efficient market may be more' critical, for example, in a situation in which the other four Cammer factors (and/or the Krogman factors) are less compelling in showing an efficient market'. In Bombardier, the district court concluded that the Cammer factors were split: two supported the conclusion that the market for the certificates issued by -Bombardier was efficient while the three other factors—including Cammer 5—weighed against finding an efficient market. Id. at 200. The certificates in Bombardier were relatively few in number and of high dollar denominations, and they traded infrequently—primarily “in large amounts by sophisticated institutional investors.” Id. at 198. Hence, establishing market efficiency was undoubtedly more difficult there "than it is in cases involving the common stock of large financial institutions, traded frequently on a national exchange. -
The Cammer and Krogman factors are simply tools to help district courts analyze market efficiency in determining whether the Basic presumption of reliance applies in class certification decision-making. But they are no more than tools in arriving at that conclusion, and certain factors will be more helpful than others in assessing particular securities and particular markets for efficiency.
2. Whether “Cammer 5” Was Required Here
We now consider whether evidence of price impact under Cammer 5 was required here in determining whether the market-for Barclays? ADS was efficient during the class period.
Because the resolution of this issue required the district court to apply the applicable law to the facts before it, we ask only “whether the district court’s decision falls within the range of permissible decisions.” Roach, 778 F.3d at 405.
Applying that deferential standard of review, we conclude that the district court’s decision not to rely on direct evidence o'f price impact under Cammer 5 in this case fell comfortably .within the range of permissible decisions. All seven.of the indirect factors considered by the district court (the'first four Cammer factors and the three Krogman factors) weighed so clearly in favor of concluding that the market for Barclays’ ADS was efficient that the Defendants did not even challenge them. The district court explained that Barclays’ ADS had an average weekly trading volume many times higher than the volume found to create a “strong presumption” of market efficiency in Cammer, and it further noted that Barclays is closely followed by many analysts. Strougo, 312 F.R.D. at 323 nn.103-04. In'its analysis, the court cited Dr. Nye’s report favorably, which had addressed all of the Cammer factors and concluded that they supported a finding that the market for Barclays’ ADS was efficiént. Id.
This case is different from the situation in Bombardier, where we concluded that certain of the indirect factors did not demonstrate market efficiency, and that the plaintiffs’ event study was flawed. Bombardier, 546 F.3d at 210. Barclays’ ADS is effectively Barclays’ common stock on the New York Stock Exchange. Because Bar-clays is one of the largest financial institutions in the world, it is unsurprising that the market for Barclays’ ADS is efficient. Indeed, this conclusion is so clear that the Defendants failed to challenge such efficiency—based on seven other factors— apart from their attack on Dr. Nye’s Cam-mer 5 event study. This case is more similar to the situation in Petrobras, where holders of ADS of Petrobras, a multinational oil and gas company headquartered in Brazil that was “once among the largest companies in the world,” whose shares traded on the New York Stock Exchange, brought suit. Petrobras, 862 F.3d at 256. In particular, the strong indirect evidence of an efficient market, which' showed that Barclays’ ADS was actively traded “in high volumes,” Strougo, 312 F.R.D. at 322, on the New York Stock Exchange, on over-the-counter markets, and in the secondary market, and had “heavy analyst coverage,” id. at 323, as well as the evidence related to the other indirect factors, tipped the balance in favor of the Plaintiffs on their burden to demonstrate market efficiency. Under the circumstances here, the district court was not required to reach a conclusion concerning direct evidence of market efficiency.29 It therefore acted within its discretion in finding an efficient market based on the remaining seven factors.30
c. Rebutting the Basic Presumption
We now turn to the Defendants’ argument that the district court erred by shifting the burden of persuasion, rather than the burden of production, to rebut the Basic presumption.
The burden defendants face to rebut the Basic presumption is a question of law that we review de novo. Roach, 778 F.3d at 405. Applying that standard, we conclude that defendants must rebut the Basic presumption by disproving reliance by a preponderance of the evidence at the class certification stage.
The Basic presumption is rebuttable. Halliburton II, 134 S.Ct. at 2405. The Supreme Court held so when it first articulated the presumption in Basic, 485 U.S. at 224, 108 S.Ct. 978, and when it reaffirmed the presumption of reliance in Halliburton II, stating that “any showing that severs the link between the alleged misrepresentation and either the price received (or paid) by the plaintiff, or his decision to trade at a fair market price, will be sufficient to rebut the presumption of reliance.” Halliburton II, 134 S.Ct. at 2408 (alteration omitted) (quoting Basic, 485 U.S. at 248,108 S.Ct. 978).
In assessing whether the Supreme Court has indicated that the burden on defendants to rebut the Basic presumption of reliance is one of merely production or one of persuasion, it is first important to consider the development of the presumption and the burden the Court imposed on plaintiffs to invoke it at the class certification stage, as well as the specific language of Basic and Halliburton II concerning the showing defendants must make to rebut the presumption.
In Basic, Basic Incorporated, a chemical manufacturing firm, repeatedly denied in public statements that it was involved in merger discussions with Combustion Engineering, another chemical firm, shortly before it announced a merger of the two firms. See Basic, 485 U.S. at 226-28, 108 S.Ct. 978. Former Basic shareholders who had sold their stock before the merger was announced sued under § 10(b), claiming that the company’s prior statements constituted misrepresentations. Id. at 227-28, 108 S.Ct. 978. The district court applied a presumption of reliance and certified the plaintiffs’ class. Id. at 228, 108 S.Ct. 978. The Supreme Court agreed that reliance on the statements that no merger would occur would be presumed because of the “well-developed market” for the securities, and the fact that the Basic stock was sold in an “efficient market.” Id. at 247-48, 250, 108 S.Ct. 978. The Court explained, however, that the presumption of reliance could be rebutted if the defendants “could show that the ‘market makers’ were privy to the truth about the merger discussions” in that case “and thus that the market price would not have been affected by” the defendants’ misrepresentations. Id. at 248, 108 S.Ct. 978. Such a showing would break the causal connection for the inference that the fraud had been incorporated into the market price. Id. The Court further stated that the defendants would have successfully rebutted the Basic presumption if they established that “news of the merger discussions credibly entered the market and dissipated the effects of the misstatements.” Id. at 249, 108 S.Ct. 978. Finally, the Court acknowledged that the defendants “could rebut the presumption of reliance as to plaintiffs who would have divested themselves of their Basic shares without relying on the integrity of the market.” Id. at 249,108 S.Ct. 978.
In Halliburton II, the Supreme Court pointed to Basic as establishing that “if a defendant could show that the alleged misrepresentation did not, for whatever reason, actually affect the market price, or that a plaintiff would have bought or sold the stock even had he been aware that the stock’s price was tainted by fraud, then the presumption of reliance would not apply.” Halliburton II, 134 S.Ct. at 2408.
The Court also restated the burden plaintiffs must meet at the class certification stage to satisfy the predominance requirement:
The Basic presumption does not relieve plaintiffs of the burden of proving—before class certification—that this requirement is met. Basic instead establishes that a plaintiff satisfies that burden by proving the prerequisites for invoking the presumption—namely, publicity, materiality, market efficiency, and market timing.
Id. at 2412. It would be inconsistent with Halliburton II to require that plaintiffs meet this evidentiary burden while allowing defendants to rebut the Basic presumption by simply producing some evidence of market inefficiency, but not demonstrating its inefficiency to the district court.31 The presumption of reliance would also be of little value if it were so easily overcome. Both in Basic and again in Halliburton II, the Supreme Court recognized the importance of the presumption of reliance in putative class actions where, without such a presumption, there would be “ ‘an unnecessarily unrealistic evidentiary burden on the Rule 10b-5 plaintiff who has traded on an impersonal market.’ ” Halliburton II, 134 S.Ct. at 2407 (quoting Basic, 485 U.S. at 245, 108 S.Ct. 978).
Quoting Basic, the Halliburton II Court also explained that the showing to sever the link between the misrepresentation and the price received or paid would rebut the Basic presumption “because ‘the basis for finding that the fraud had been transmitted through market price would be gone.’ ” Halliburton II, 134 S.Ct. at 2415-16 (quoting Basic, 485 U.S. at 248, 108 S.Ct. 978). The Court then stated that although “Basic allows plaintiffs to establish [price impact] indirectly, it does not require courts to ignore a defendant’s direct, more salient evidence showing that the alleged misrepresentation did not actually affect the stock’s market price.” Id. at 2416 (emphasis added).
A concurring opinion in Halliburton II by Justice Ginsburg and joined by Justices Breyer and Sotomayor stated that the majority recognized “that it is incumbent upon the defendant to show the absence of price impact.”32 Id. at 2417 (Ginsburg, J., concurring) (emphasis added).
This Supreme Court guidance indicates that defendants seeking to rebut the Basic presumption must demonstrate a lack of price impact by a preponderance of the evidence at the class certification stage rather than merely meet a burden of production.
First, the phrase “[a]ny showing that severs the link” aligns more logically with imposing a burden of persuasion rather than a burden of production. See Halliburton II, 134 S.Ct. at 2408 (alteration in original). The Supreme Court has described the burden of production as being satisfied when a litigant has “come forward with evidence to support its claim,” Dir., Office of Workers’ Comp. Programs, Dep’t of Labor v. Greenwich Collieries, 512 U.S. 267, 272, 114 S.Ct. 2251, 129 L.Ed.2d 221 (1994), or, alternatively (in the Title VII context), when a defendant has “articulate[d]” a “legitimate, nondiscriminatory reason for the employee’s rejection,” O’Connor v. Consol. Coin Caterers Corp., 517 U.S. 308, 311, 116 S.Ct. 1307, 134 L.Ed.2d 433 (1996). Thus, the Court has defined the burden of production as one that could permit a trier of fact to rule in favor of the party in question. By requiring that the “showing” defendants must make to rebut the Basic presumption actually “sever[ ] the link” between the misrepresentation and the price a plaintiff paid or received for a stock, the Court requires defendants to do more than merely produce evidence that might result in a favorable outcome; they must demonstrate that the misrepresentations did not affect the stock’s price by a preponderance of the evidence.
Second, the language chosen by the Court in Halliburton II demonstrates that the Court understood the burden that shifts to defendants as one of persuasion rather than production. As mentioned above, the majority in Halliburton II explained that evidence that satisfied the “severing the link” standard would rebut the Basie presumption because “ ‘the basis for finding that the fraud had been transmitted through market price would be gone,’ ” and the defendants’ “direct, more salient evidence” that the misrepresentations did not affect the stock, price would rebut the Basic presumption, Halliburton II, 134 S.Ct. at 2415-16 (quoting Basic, 485 U.S. at 248, 108 S.Ct, 978),
In addition to this Supreme Court guidance, our own Court’s prior decisions ap-. plying, the presumptions of reliance support our conclusion that defendants bear the burden of persuasion to rebut the Basie presumption. of reliance at the class certification stage. ■
First, we held that the Affiliated Ute presumption is rebutted if a defendant proves “by a preponderance of the evidence that the plaintiff did not rely on the omission [at issue] in making” his investment decision. duPont v. Brady, 828 F.2d 75, 76 (2d Cir. 1987). Although our decision in duPont predated Basic and the Affiliated Ute presumption differs from the Basic presumption in several respects, both allow reliance to be presumed.
Second, we held in Black v. Finantra Capital, Inc., 418 F.3d 203 (2d Cir. 2005), that a district court correctly instructed the jury when it charged that the defen- -' dants in a securities fraud case could overcome the presumption that the “plaintiff relied on the market price to his detriment” if the defendants proved “by a -preponderance of the evidence that [the] plaintiff did not in fact rely on the‘market price.”33 Id. at 209. Although the claims of fraud in that case focused largely on omissions, and the jury instruction stage follows class' certification, it is nevertheless helpful guidance.
Third, we have explained that when the plaintiffs have demonstrated, that they are entitled to the Basic presumption by showing “that the alleged, misrepresentation was material and publicly transmitted into a well-developed market,” plaintiffs “do hot bear the burden of showing an impact on price.” In re Salomon Analyst Metromedia Litig., 544 F.3d 474, 483 (2d Cir. 2008), abrogated in part on other grounds by Amgen Inc. v. Conn. Ret. Plans & Tr. Funds, 568 U.S. 455, 133 S.Ct. 1184, 185 L.Ed.2d 308 (2013).34 But the “burden of showing that there was no price impact is properly placed on defendants' at the rebuttal stage.” Id. at 483 (emphasis added).
-Apart from their arguments that Basic and Halliburton II. do not support the conclusion that it is a burden of persuasion that applies to defendants attempting to rebut the Basic presumption at the class certification stage, the Defendants have relied on Federal Rule of Evidence 301 in arguing that it is merely a burden of production that is placed upon defendants. Rule 301 provides:
In a civil case, unless a federal statute or these rules' provide otherwise, the party against whom a presumption is directed has the burden of producing evidence to rebut the presumption. But this rule does not shift the burden of persuasion, which remains on the party who had it originally.
Fed. R. Evid. 301.
The Defendants assert that because no federal statute or other rule of evidence “provide[s] otherwise,” we are required to conclude that defendants bear only the burden of producing evidence when they seek to rebut the Basic presumption. We disagree.
The Basic presumption was adopted by the Supreme Court pursuant to federal securities laws. Thus, there'is a sufficient link to those statutes to meet Rule 301⅛ statutory element requirement. In United States Department of Justice v. Landano, 508 U.S. 165, 113 S.Ct. 2014, 124 L.Ed.2d 84 (1993), the Court referred to the Basic presumption as one of several “judicially created presumptions under federal statutes that make no express provision for their use,” id. at 174-75, 113 S.Ct. 2014; see also Amgen, 568 U.S. at 462, 133 S.Ct. 1184 (referring to the Basic presumption as “a substantive doctrine of federal securities-fraud law”); Basic, 485 U.S. at 245, 108 S.Ct. 978 (“The presumption of reliance ... supports[ ] the congressional policy embodied in the 1934; Act.”).
While in Stoneridge Investment Partners, LLC v. Scientific-Atlanta, Inc., 552 U.S. 148, 128 S.Ct. 761, 169 L.Ed.2d 627 (2008), the Supreme Court stated that “narrow dimensions” must be given to a plaintiffs cause of action not specifically set forth in a statute, that was in the context of determining that Rule 10b-5 liability did not extend to suppliers and customers of stock issuers, id. at 167, 128 S.Ct. 761, that had not issued public statements themselves, see Salomon, 544 F.3d at 481. That holding does not undermine the language of Basic and Halliburton II that indicates defendants have the obligation to rebut the Basic presumption of reliance by a preponderance of evidence. Even in Stoneridge the Court stated that “there is an implied cause of action only if the underlying statute can be interpreted to disclose the intent to create one.” , 552 U.S. at 164,128 S.Ct. 761. Thus, the Court again acknowledged the statutory source for the 10b-5 implied cause of action.
In Halliburton II the Supreme .Court stated that “[although the [Basic] presumption is a judicially created doctrine designed to implement a judicially created cause of action, we have described the presumption as a substantive doctrine of federal securities-fraud law.” 134 S.Ct. at 2411 (internal quotation marks omitted). Rule 301 therefore imposes nó impédiment to our conclusion that the burden of persuasion, not production, to rebut the Basic presumption shifts to defendants.35 36
d. Whether the Basic Presumption Was Rebutted Here
That leaves the question of whether the Defendants met their burden of persuasion and rebutted the Basic presumption by a preponderance of the evidence.
The Defendants contend that they rebutted the presumption because (1) the Plaintiffs’ event study showed that the alleged misstatements did not affect the price of Barclays’ ADS, and (2) Dr. James, the Defendants’ expert, concluded that the decline in the price of the stock following the disclosure of the New York Attorney General’s action was due “to potential regulatory action and fines, not the revelation of any allegedly concealed truth.” Appellants’ Br. 40. We find these arguments unpersuasive and conclude that the district court did not err in concluding that the Defendants failed to rebut the Basic presumption.
This issue once again required the district court to apply the relevant law to the facts before it. As we see no error of law or clear error in any findings of fact, our review is therefore limited to determining whether the court abused its discretion when it concluded that class certification was proper. Roach, 778 F.3d at 405.
As the district court concluded, it is unsurprising that the price of Barclays’ ADS did not move in a statistically significant manner on the dates that the purported misstatements regarding LX and Liquidity Profiling were made; the Plaintiffs proceeded on a price maintenance theory. That theory, which we have previously accepted, recognizes “that statements that merely maintain inflation already extant in a company’s stock price, but do not add to that inflation, nonetheless affect a company’s stock price.” In re Vivendi, 838 F.3d 223, 256 (2nd Cir.2016). Thus, the district court was well within its discretion in con-, eluding that the lack of price movement on the dates of the alleged misrepresentations does not rebut the Basic presumption.37 38
As to the Defendants’ assertion that Dr. James concluded that the post-disclosure drop in stock price was the result of investor concern regarding regulatory action and potential fines, the record supports the district court’s conclusion that such a concern was merely a contributing factor to the decline. For example, Dr. James opined that “the alleged corrective disclosure regarding LX may have had a bigger impact on Barclays’ ADS price due to the announcement of the [New York Attorney General’s] lawsuit” and that “some of the price reaction was independent of the specific allegations relating to LX,” and was instead “a response to the regulatory action itself.” J.A. 613 (emphases added). Dr. James also noted that all of the analyst reports that Dr. Nye had reviewed in conducting his event study had discussed “potential regulatory action and fines.” Id.
Dr. James concluded that a portion of the 7.38% decrease in the price of Bar-clays’ ADS following the announcement of the New York Attorney General’s action resulted from concerns about that action itself and the potential fines that might accompany it. But merely suggesting that another factor also contributed to an impact on a security’s price does not establish that the fraudulent conduct complained of did not also impact the price of the security.
Thus, the district court did not abuse its discretion when it concluded that the Defendants had failed to rebut the Basic presumption.
e. The Classwide Damages Issue
Finally, the Defendants argue that the Plaintiffs’ classwide damages model fails to comply with Comcast Corp. v. Behrend, 569 U.S. 27, 133 S.Ct. 1426, 185 L.Ed.2d 515 (2013). They contend that the Plaintiffs’ model fails to (1) disaggregate damages that resulted from factors other than investor concern about Barclays’ integrity (namely, the New York Attorney General’s regulatory action and the potential fines associated with it), and (2) account for variations in inflation in stock price over time. We review the district court’s decision to certify the Plaintiffs’ class in light of this challenge to their classwide damages model for abuse of discretion. Roach, 778 F.3d at 405; see also In re U.S. Foodservice Inc. Pricing Litig., 729 F.3d 108, 123 n.8 (2d Cir. 2013). We find no abuse of discretion here.
In Comcast, the plaintiffs alleged that Comcast had violated antitrust law in its telecommunications business under four distinct legal theories. 569 U.S. at 30-31, 133 S.Ct. 1426. The district court concluded that only one of those theories—the “overbuilder theory”—was amenable to classwide proof. Id. at 31, 133 S.Ct. 1426. The district court further concluded that the damages that resulted from that theory of liability “could be calculated on a classwide basis.” Id. In so concluding, the district court relied on a damages model that “did not isolate damages resulting from any one theory, of antitrust impact,” but instead calculated the damages that occurred due to the antitrust violations collectively. Id. at 32,133 S.Ct. 1426.
The Supreme Court reversed the district court’s grant of class certification. Id. at 38,133 S.Ct. 1426.- It concluded that the plaintiffs’ damages “model failed to measure damages resulting from the particular antitrust injury on which [the defendants’] liability” was premised. Id. at 36,133 S.Ct. 1426. In light of that deficiency, the damages model could not support class certification by satisfying Federal Rule of Civil Procedure 23(b)(3)’s predominance requirement. Id. at 38, 133 S.Ct. 1426. The Court explained:
[A] model purporting to serve as evidence of damages in this class action must measure only those damages attributable to [the overbuilder theory]. If the model does not even attempt to do that, it cannot possibly establish that damages are susceptible of measurement across the entire class for purposes of Rule 23(b)(3).
Id. at 35,133 S.Ct. 1426.
We have since interpreted Comcast as precluding class certification “only ... because the sole theory of liability that the district court determined was common in that antitrust action, overbuilder competition, was a theory of liability that the plaintiffs’ model indisputably failed to measure when determining the damages for that injury.” Sykes v. Mel S. Harris & Assocs. LLC, 780 F.3d 70, 88 (2d Cir. 2015) (internal quotation marks omitted). In other words, we have stated that Comcast “held that a model for determining class-wide damages relied upon to certify a class under Rule 23(b)(3) must actually measure damages that result from the class’s asserted theory of injury.” Roach, 778 F.3d at 407.
The Plaintiffs’ damages model in .this case complies with Comcast. The .Plaintiffs’ allegations are that shareholders of Barclays’ ADS were harmed when statements that maintained the impression that Barclays was protecting its LX investors were shown to be false, thereby exposing Barclays’. business practices and culture, and causing a substantial drop.in share price. Their damages model directly measured that harm by examining the drop in price that occurred when the New York Attorney General’s action revealed ongoing problems related to Barclays’ management. This is not a case where a plaintiff's damages model does not track his theory of liability. Instead, this is a case in which the Plaintiffs’ “proposed measure for damages is ;.. directly linked with their underlying theory of classwide liability .!. arid is therefore in accord with the Supreme Court’s ... decision in Comcast.” U.S. Foodservice, 729 F.3d at 123 n.8.
The Comcast standard is, met notwithstanding that some of the decline in the price of Barclays’ ADS may have been the result of the New York Attorney General’s action and potential fines. Investors were concerned with lack of management honesty and control because, as had happened in the past following the LIBOR scandal, such problems could result in considerable costs related ■ to defending a regulatory action and, ultimately, in the imposition of substantial fines. Thus, the regulatory action and any ensuing fines were a part of the alleged harm the Plaintiffs suffered, and the failure to disaggregate the action and fines did not preclude class certification.
Finally, we are not persuaded by the Defendants’ argument that class certification was improper under Comcast because the Plaintiffs’ damages model failed to account for variations in inflation over time. Comcast does not suggest that damage calculations must be so precise at' this juncture. To the contrary, Comcast explicitly states’that “[calculations need not be exact.” 569 U.S. at 35, 133 S.Ct. 1426. Thus, even accepting the Defendants’ premises that inflation would have varied during the class period in this case and that such variation could not be accounted for, the Defendants’ argument fails.
Dr. Nye explained that damages for individual class members could be calculated by applying a method across the entire class that focused on the decline in stock price following the disclosure of the New York Attorney General’s lawsuit and then isolating company-specific' event's from market arid industry events. His model also accounted for calculating the damages for individual class members based on their'investment history.
Therefore, we conclude that the district court did not abuse its discretion when it certified the Plaintiffs’ class over the Defendants’ damages-related objections.
CONCLUSION
To summarize, we hold that: (1) the Affiliated Ute presumption does' not apply in this case; (2)'direct evidence of price impact under Gammer 5 is not always necessary to demonstrate market efficiency, and was not required in .this case; (3) defendants seeking to rebut the Basic presumption must do so by a preponderance of the evidence, which the Defendants in this case failed to do; and (4) the Plaintiffs’ damages methodology posed no obstacle to certification. We therefore AFFIRM the district court’s order granting the Plaintiffs’ motion for class certification,
. The individual defendants are Robert Diamond, Barclays' former CEO, Antony Jenkins, Barclays’ CEO at the time this action was filed, and William White, the former Head of Equities Electronic Trading at Barclays Capital Inc. The district court previously dismissed claims against two other individual defendants, Chris Lucas and Tushar Morzaria.
. The Plaintiffs are Joseph Waggoner, Mohit Sahni, and Barbara Strougo.
. As we recently explained:
American Depository Shares represent an interest in the shares of a non-U.S. company that have been deposited with a U.S. bank. ADS allow U.S. investors to invest in non-U.S. companies and also give non-U.S. companies easier access to the U.S, capital markets. Many non-U.S. issuers use [ADS] as a means of raising capital or establishing a trading presence in the U.S.
In re Petrobras Sec., 862 F.3d 250, 258 n.6 (2d Cir. 2017) (citation and internal quotation marks omitted).
The Plaintiffs’ expert in this case described Barclays’ ADS as the rough U.S. equivalent of Barclays’ stock on the London Stock Exchange: “In the U.S., Barclays’ stock was listed on the [New York Stock Exchange], under the symbol ‘BCS,’ and traded in the form of American Depository Shares (ADSs), each of which represented four ordinary shares (i.e., four BARC [the symbol for Bar-clays’ stock on the London Stock Exchange] shares).” J.A. 310.
. The Plaintiffs also brought claims against the individual defendants under § 20(a) of the Securities Exchange Act of 1934, 15 U.S.C. § 78t. Those claims are not at issue in this appeal.
. In stating the facts of this case, we rely in part on the allegations of the Plaintiffs' operative second amended complaint, which we accept as true in this context. See Shelter Realty Corp. v. Allied Maint. Corp., 574 F.2d 656, 661 n.15 (2d Cir. 1978) (explaining that it is proper for a district court "to accept the complaint allegations as trae in a class certification motion”).
.LIBOR is used to set benchmark interest rates for many world currencies. We recently explained LIBOR rates and their importance in greater detail in United States v. Allen, 864 F.3d 63, 69-72 (2d Cir. 2017). We also discussed Barclays’ participation in the LIBOR investigations and settlements in greater detail in Carpenters Pension Trust Fund of St. Louis v. Barclays PLC, 750 F.3d 227, 230-32 (2d Cir. 2014).
. Among other steps, Barclays commissioned • an independent review of the company’s business practices, and then indicated it would implement dozens of changes proposed in a report produced by Sir Anthony Salz (a lawyer and former chairman of the BBC). Those changes were aimed at, inter alia, developing a culture that valued long-term success as opposed to short-term profit, and measures aimed at providing greater transparency regarding operations.
.- The Securities and Exchange Commission defines alternate trading system as “any organization, association, person, group of- persons, or system” that "constitutes, maintains, or provides a market place or facilities for bringing together purchasers and sellers of securities or for otherwise performing with respect to securities the functions commonly performed by a stock exchange” that does not set’ "rules governing the conduct of subscribers other than the conduct of such subscribers' trading on such organization, association, person, group of persons, or system” or " [discipline subscribers other than by exclusion from trading.” 17 C.F.R. § 242.300(a). Alternate'trading systems are regulated by the Securities and Exchange Commission. See id. §§ 242.301-.303.' They have grown significantly over the last decade, in part because of the advantages offered by a sdbset of alternate trading systems known as "dark pools,” which we discuss infra. See, e.g., Matthew S. Freedman, Rise in SBC Dark Pool Fines, 35 Rev. Banking & Fin. L. 150, 150-52 (2015) (rioting that approximately 40% of all trades occurred in alternate trading systems in 2014, up from 16% in 2008, and explaining that there are approximately forty dark pools in existence),
. In the Matter of ITG Inc. & Alternet Sec., Inc., Respondents, Exchange Act Release No. 9887, 112 SEC Docket 887, ¶ 18 (Aug. 12, 2015).
. In a report, the Securities and- Exchange Commission has loosely defined high-frequency traders "as 'market makers' with very large daily trading frequency.” Findings Regarding the Market Events of May 6, 2010: Report of the Staffs of the CFTC and SEC to the loint Advisory Committee on Emerging Regulatory Issues, at 13, available at https:// www. sec. gov/news/studies/2 010/ marketevents-report.pdf,
. See Edwin Batista, A Shot in the Dark An Analysis of the SEC's Response to the Rise of Dark Pools, 14 j. High Tech; L. 83, 84 (2014) (explaining that traders use dark pools "to avoid front running by high-frequency traders”); see also Freedman, supra note 8, at 150 (noting that dark pools "were largély created to allow institutional investors to execute large volume trades without creating an unfavorable impact on market prices”).
. See Batista, supra note 11, at 84.
. Id.
. See, e.g., Michael Morelli, Regulating Secondary Markets in the High Frequency Age: A Principled and Coordinated Approach, 6 Mich. Bus. & Entrepreneurial L. Rev. 79, 92-93 (2016) (explaining that high-frequency trading firms.like dark pools in part because of their anonymity).
. N.Y. Gen. Bus. Law §§ 352-359. The Mar-tín Act grants New York’s Attorney General the power to "investigate and enjoin fraudulent practices in the marketing of stocks, bonds and other securities within or from New York,” Assured Guar. (UK) Ltd. v. J.P. Morgan Inv. Mgmt. Inc., 18 N.Y.3d 341, 939 N.Y.S.2d 274, 962 N.E.2d 765, 768 (2011) (internal quotation marks omitted).
.The district court dismissed the Plaintiffs' claims related to two other categories of purported misstatements. See id. at 343-47. The first related to Barclays’ general business practices, and relied on purportedly false statements that asserted that Barclays was changing its values to conduct its "business in the right way.” Id. at 343. The second category of alleged false statements focused on Bar-clays’ commitment to enacting the recommendations made by the Salz report. See id. at 344-47. The court concluded that both of these categories of statements were "inaction-able puffery.” See id. at 347.
. These dates encompass the time period between when Barclays first made purportedly false statements regarding LX and the public disclosure of Barclays’ misstatements by the New York Attorney General’s-action.
. Dr. Nye is a financial economist and the Vice President of Stanford Consulting Group, Inc. He holds a bachelor's degree in economics from Princeton University, a master’s degree in finance from the London Business School, and a Ph.D. from U.C. Irvine. He has conducted research in areas including market efficiency.
. A security purchased during the class period and sold before the first corrective disclosure would1 not support a claim for damages.
. The Defendants did not contest the fact that the Plaintiffs satisfied the requirements of Federal Rule of Civil Procedure 23(a).
. Dr. James is a professor of finance and economics at the University of Florida. He ‘•previously worked for the Department of Treasury and the Securities and Exchange Commission, in addition to holding several other teaching positions. He has also served as an expert witness on matters including market efficiency prior to this case.
. The district court also indicated its skepticism of the reliability of single-company event studies, as well as when only a few unexpected events are examined during a class period, especially in a' lengthy class period. Id. at . 321-22.
. The six elements of a § 10(b) claim are: “(1) a material misrepresentation or omission by the defendant; (2) scienter; (3) a connection between the misrepresentation or omission and the purchase or sale of a security; (4) reliance upon the misrepresentation or omission; (5) economic loss; and (6) loss causation.” Matrixx Initiatives, Inc. v. Siracusano, 563 U.S. 27, 37-38, 131 S.Ct. 1309, 179 L.Ed.2d 398 (2011).
. That the Affiliated Ute presumption applies only in cases involving primarily omissions has been recognized by other Circuits. See, e.g., In re Interbank Funding Corp. Sec. Litig., 629 F.3d 213, 215 (D.C. Cir. 2010); Desai v. Deutsche Bank Sec. Ltd., 573 F.3d 931, 940 (9th Cir. 2009); Regents of the Univ. of Cal. v. Credit Suisse First Bos. (USA), Inc., 482 F.3d 372, 384 (5th Cir. 2007).
. Those requirements are that ‘‘(1) the alleged misrepresentations were publicly known, (2) they were material, (3) the stock traded in an efficient market, and (4) the plaintiff traded the stock between when the misrepresentations were made and when the truth was revealed.” Halliburton Co. v. Erica P. John Fund, Jnc., — U.S. -, 134 S.Ct. 2398, 2413, 189 L.Ed.2d 339 (2014).
. The Supreme Court adopted the Basic presumption in large part because of the realities of the "modem securities markets,” which involve "millions of shares changing hands daily” and therefore "differ from the face-to-face transactions contemplated by parly fraud cases” in which reliance was required. Basic, 485 U.S. at 243-44, 108 S.Ct. 978. The Supreme Court, quoting the district court in Basic, also noted that the presumption “provided a practical resolution to the problem of balancing the substantive requirement of proof of reliance in securities cases against the procedural requisites of Federal Rule of Civil Procedure 23.” Id, at 242, 108 S.Ct. 978 (alteration and internal quotation marks omitted). Finally, the Court explained that the presumption was “supported by common sense and probability” because empirical studies suggested that the "market price of shares traded on well-developed markets re-flecte 1 all publicly available information, and, hence, any material misrepresentations.” Id. at 246, 108 S.Ct. 978.
. Market efficiency is required because the Basic presumption is premised on the "fraud-on-the-market doctrine.” Hevesi v. Citigroup Inc., 366 F.3d 70, 77 (2d Cir. 2004). That doctrine relies on the "efficient market hypothesis, which postulates that an efficient market incorporates fraudulent statements into a price viewed by investors as based on available accurate information.” Pa. Pub. Sch. Emps.’ Ret. Sys. v, Morgan Stanley & Co., 772 F.3d 111, 121 n.3 (2d Cir.), as amended (Nov. 12, 2014), certified question accepted, 24 N.Y.3d 1028, 997 N.Y.S.2d 679, 22 N.E.3d 187 (2014), certified question answered, 25 N.Y.3d 543, 14 N.Y.S.3d 313, 35 N.E.3d 481 (2015), Hence, absent an efficient market, the basis for the Basic presumption does not exist.
. Direct evidence of price impact under Cammer 5 may simply determine whether the price of a stock moves, in one direction or the other, when new information becomes available. Alternatively, such evidence may determine whether the stock price moves in the direction that it would be expected to move in light of the new information, In other words, this latter lype of evidence, directional direct evidence of price impact, asks not just whether the stock price moved at all in response to new material information, but whether it increased in response to "good” news and decreased in response to "bad” news. See id.
. We therefore have no occasion in this case to identify all the circumstances in which direct evidence of price impact under Cam-mer 5 might be required. Nor does our conclusion here—that a finding as to direct evidence of price impact was not required— indicate that securities of large publicly traded companies always trade in an efficient market; the specific circumstances may require plaintiffs to present direct evidence of efficiency in cases involving such securities, and defendants always have the opportunity to present their own event studies demonstrating that Cammer 5 is not satisfied, as well as the other Cammer and Krogman factors.
, We note that several of bur sister Circuits have concluded that Cammer 5 is not necessary but nevertheless often helpful. See Local 703, I.B. of T. Grocery & Food Emps. Welfare Fund v. Regions Fin. Corp,, 762 F.3d 1248, 1256 (11th Cir. 2014) ("Neither are we persuaded by [the defendant’s] argument that a finding of market efficiency always requires proof that the alleged misrepresentations had an immediate effect on the stock price. ... [The defendant] does not point us to any court that has adopted the unwavering evidentiary requirement- it urges upon ús. Nor could it. Even the Cammer court itself did not establish such a strict evidentiary burden at the class certification stage.”); Unger v. Amedisys Inc., 401 F.3d 316, 325 (5th Cir. 2005) (explaining that the district court improperly used three of the Cammer factors, including Cammer 5, "as a- checklist rather than an analytical tool”); see also Gariety v. Grant Thornton, LLP, 368 F.3d 356, 368 (4th Cir. 2004) (ex- ' plaining that courts "should consider factors such as” the Cammer factors (emphasis added)); Cammer, 711 F.Supp. at 1287 (stating only that it would be "helpful” for a plaintiff to demonstrate "a cause and effect relationship between unexpected corporate events ... and an immediate response in ... stock price”).
. Although in Halliburton II the Court identified the prerequisites plaintiffs must meet to invoke the Basic presumption of reliance, that burden should not be regarded as "onerous.” Petrobras, 862 F.3d at 278.
. The concurring opinion also stated that the "Court’s judgment, therefore, should impose no heavy toll on securities-fraud plaintiffs with tenable claims.” Id. at 2417 (Ginsburg, J., concurring).
. Two other Circuits’ model jury instructions similarly place the burden of persuasion on defendants seeking to rebut the Basic presumption. See Ninth Circuit Jury Instructions Committee, Manual of Model Civil Jury Instructions for the District Courts of tKe Ninth Circuit, § 18.7 (2017); Committee on Pattern Jury Instructions, District Judges Association, Fifth Circuit, Pattern Jury Instructions (Civil Cases), § 7.1 (2016).
. In Amgen, the Supreme Court held that a plaintiff does not have to prove that a misrepresentation is material at the class certification stage. Amgen, 568 U.S. at 459, 133 S.Ct. 1184, That holding abrogated this Court’s contrary conclusion in Salomon.
. The Defendants note that Rule 301 was cited in Basic. But the Supreme Court relied on Rule 301 merely for the proposition that "presumptions are ... useful devices for allocating the burdens of proof between parties.” Basic, 485 U.S. at 245, 108 S.Ct. 978.
. The Defendants also note that the Eighth Circuit cited Rule 301—that the party seeking to rebut a presumption “has the burden of producing evidence,” Fed. R. Evid. 301—for the conclusion that defendants seeking- to rebut the Basic presumption have “the burden to come forward with evidence showing a lack of price impact." IBEW Local 98 Pension Fund v. Best Buy Co., 818 F.3d 775, 782 (8th Cir. 2016), To the extent that the Eighth Circuit imposed only a burden of production on defendants, we disagree with its conclusion. We do not, however, read the Eighth Circuit's decision as being in direct conflict with our holding. The Eighth Circuit’s statement appears, to be dictum because the extent of the burden was not at issue. Id. at 782-83. The Eighth Circuit ultimately concluded that the “overwhelming evidence” in the case demonstrated that there had been no price impact and that the Basic presumption had therefore been rebutted. Id. at 782. Thus, the Eighth Circuit’s ruling did not depend on the standard of proof.
. In conjunction with their argument regarding lack of price movement, the Defendants assert that the Plaintiffs have not offered evidence of how the inflation they claim was “maintained” initially entered the price of Barclays' ADS. Although it is true that the Plaintiffs did not identify a specific date on which inflation entered Barclays’ ADS, Dr. Nye opined that inflation would have entered the stock when Barclays marketed "IX in a way that promised io filter out high frequency predatory trading.” 5.A. 669.
. The Defendants further suggest that the "price maintenance theory is entirely inconsistent with [the] Plaintiffs’ theory of the case and the District Court’s ruling on [the] Defendants’ motion to dismiss” because the district court ruled that the purported misstatements did not become material until after Barclays admitted to wrongdoing in the LIBOR scandal in June 2012. Appellants’ Br. 38. Thus, the Defendants assert that statements made prior to that date were not material and therefore could not have maintained any price inflation. However, the majority of the statements cited by the Plaintiffs occurred after June 2012.