
    IN RE VIVENDI, S.A. SECURITIES LITIGATION Miami Group, consisting of the Retirement System for General Employees of the City of Miami Beach, Francois R. Gerard, Prigest S.A. and Tocqueville Finance S.A., Pearson-Doniger Family, consisting of two sisters and their respective family members Beatrice Doniger, Grandchildren’s Trust by Bruce Doniger Trustee, Alison Doniger, Michael Doniger, Edward B. Brunswick and Ruth Pearson Trust Pearson Trustee, GAMCO Investors, Incorporated, Oppenheim Kapitalanlagegesellschaft mbH, Plaintiff KBC Asset Management N.V., Capitalia Asset Management SGR, S.p.A., Capitalia Investment Management S.A., Eurizon Capital SGR S.p.A., Baden-Wurttembergische Investmentgesellschaft mbH, Barclays Global Investors (Deutschland), Cominvest Asset Management GMBH, Deutsche Asset Management Investmentgesellschaft mbH, DWS (Austria) Investmentgesellschaft mbH, DWS Investment GmbH, Erste-Sparinvest Kapitalanlagegesellschaft m.b.H., Forsta AP-fonden, Fortis Investment Management SA, KBC Asset Management S.A., Landesbank Berlin Investment GmbH, LBBW Luxemburg S.A., Oppenheim Asset Management Services S.a.r.l., Pioneer Investment Management Limited, Pioneer Investment Management SGRPA, Pioneer Investments Austria GmbH, Pioneer Investments Kapitalanlagegesellschaft mbH, Raiffeisen Kapitalanlage-Gesellschaft m.b.H., SEB Investment Management AB, Skandia Insurance Company Ltd., Union Asset Management Holding AG, Universal-Investmentgesellschaft mbH, SEB Investment GmbH, Andra Ap-Fonden, Bayern-Invest Kapitalanlagegesellschaft mbH, Deka Investment GmbH, Prigest, S.A., Tocqueville Finance, S.A., Rosenbaum Partners, L.P., on behalf of themselves and all others similarly situated, Ruth Pearson Trust, Deka International (Ireland) Limited, Deka International S.A. Luxemburg, Deka Fundmaster Investmentgesellschaft mbH, Fideuram Investimenti S.G.R., Fideuram Gestions S.A., Interfund Sica V., Frankfurt-Trust Investment-Gesellschaft mbH, Frankfurt-Trust Invest Luxemburg AG, Helaba Invest Kapitalanlagegesellschaft mbH, HSBC Trinkaus & Burkhardt AG, Internationale Kapitalanlagegesellschaft mbH, Meag Munich Ergo Kapitalanlagegesellscfhaft mbH, Meag Munich Ergo Asset Management GmbH, Metzler Investment GmbH, Metzler Ireland LTD, Nordcon Investment Management AG, Norges Bank, Swiss Life Holding AG, Swiss Life Investment Management Holding AG, Swiss Life Asset Management AG, Swiss Life Funds AG, Swiss Life (Belgium) S.A., Swiss Life Asset Management GmbH, Swiss Life Asset Management (Nederlan) B.V., Tredje Ap-Fonden, Westlb Mellon Asset Management Kapitalanlagegesellschaft mbH, Alecta Pensionsforsakring, Omsesidigt, Sjunde Ap-Fonden, Varma Mutual Pension Insurance Company, Danske Invest Administration A/S, AFA Livforsakringsaktiebolag, AFA Trygghetsforsakringsaktiebolag, AFA Sjukforsakringsaktiebolag, AMF Pension Fondforvaltning AB, Arbetsmarknadsforsakringar, Pensionsforsakringsaktiebolag, Pensionskassernes Administration A/S, Arbejdsmarkedets Tillaegspension, Industriens Pensionssforikring A/S, Arca SGR, S.p.A,, Il-marinen Mutual Pension Insurance Company, Prima Societa’ di Gestione del Risparmio S.p.A., Nordea Invest Fund Management A/S, Nordea Fonder AB, Nordea Investment Funds Company I.S.A., Nordea Fondene Norge AS, Nordea Fondbolag Finland AB, Swedbank Robur Fonder AB, Fjarde AP-Fonden, Olivier Chastan, Reed S. Clark, Daha Davis, Collen Dodi, Ruth Pearson Trust Pearson Trustee, Edward B. Brunswick, Michael Doniger, Alison Doniger, Grandchildren’s Trust by Bruce Doniger Trustee, Bruce Doniger, Beatrice Doniger, Jeffrey Kurtz, Price Hal, W. Scott Polland, Jr., Nicholas A. Radosevich, Caisse de Depot et Placement du Quebec, AGF Asset Management, S.A., Irish Life Investment Managers Limited, Plaintiffs-Appellees, Bruce Doniger, Gerard Morel, Oliver M. Gerard, The Retirement System for General Employees of the City of Miami Beach, Plaintiffs-Appellees-Cross-Appellants, William Cavanagh, Cross-Appellant, v. Vivendi, S.A., Defendant-Appellant-Cross-Appellee, Jean-Marie Messier, Guillaume Hannezo, Vivendi Universal, Defendants.
    Nos. 15-180-cv(L), 15-208-cv(XAP)
    August Term 2015
    United States Court of Appeals, Second Circuit.
    Argued: March 3, 2016
    Decided: September 27, 2016
    
      JefpRey A. Lamken, MoloLamken LLP, Washington, D.C. (Robert K. Kry, Lauren M. Weinstein, MoloLamken LLP, Wash-ington, D.C.; Arthur N. Abbey, Stephen T. Rodd, Jeremy Nash, Abbey, Spanier, LLP, New York, N.Y.; Matthew Gluck, Michael C. Spencer, Milberg LLP, New York, N.Y.; Brian C. Kerr, Brower, Piven, P.C., New York, N.Y., on the brief), for Plain-tiffs-Appellees-Cross-Appellants
    
      Miguel A. Estrada, Gibson, Dunn & Crutcher, LLP, (Mark A. Perry, Lucas C. Townsend, Gibson, Dunn &, Crutcher LLP, Washington, D.C.; Caitlin J. Halli-gan, Gibson, Dunn & Crutcher LLP, New York, N.Y.; Daniel, Slifkin, Timothy G. Cameron, Cravath, Swaine & Moore, LLP, New York, N.Y.; James W. Quinn, Grego-ry Silbert, Weil, Gotshal & Manges LLP, New York, N.Y., on the, brief), for Defen-dant-Appellant-Cross-Appellee.
    Before: CABRANES, LIVINGSTON, and LYNCH, Circuit Judges.
    
      
      . The Clerk of the Court is directed to amend the caption of the case,
    
   DEBRA ANN LIVINGSTON, Circuit Judge:

Prior to 1998, Compagnie Générale des Eaux was a French utilities company, best known for supplying water to households across France. By the close of 2000, that same company, now touting the name Vi-vendi Universal, S.A, (“Vivendi”), was a global media conglomerate with extensive dealings in the film, music, telecommunica-tions, publishing, and Internet industries, among related others. What followed on the heels of Defendant-Appellant-Cross-Appellee Vivendi’s seemingly overnight transformation gives rise to the securities-fraud allegations now at issue.

To pull off its transformation and but-tress its position as a mover-and-shaker in the global media-and-telecommunications market, Vivendi spent much of 2000 and 2001 acquiring a diverse array of media and communications businesses in the United States and abroad. Naturally, these acquisitions required money, and Vivendi did not have an unlimited supply. By 2001 and especially by 2002, Vivendi was run-ning critically low. Indeed, Vivendi was in danger of not being able to meet all of its various payment obligations, including payments on loans it had taken out for the very purpose of financing its buying spree. In the worst case scenario, which inquiries later revealed was not an altogether un-likely one, Vivendi was months away from bankruptcy or insolvency. Yet, up until approximately July 2002, Vivendi made nu-merous representations to the market sug-gesting that the course ahead for the com-pany was smooth sailing. That all came to a halt when Vivendi’s stock price came tumbling down in the middle of 2002, after a series of credit downgrades and revela-tions that Vivendi was strapped for cash.

In a class-action suit they initiated against Vivendi in 2002, Plaintiffs-Appel-lees and Plaintiffs-Appellees-Cross-Ap-pellants (collectively, “Plaintiffs”), inves-tors in Vivendi’s stock during the relevant time period, alleged that Vivendi’s persis-tently optimistic representations during the period from October 30, 2000 to Au-gust 14, 2002, constituted securities fraud under § 10(b) of the Securities Exchange Act of 1934 (“Exchange Act”), 15 U.S.C. § 78j(b), as well as the Securities Ex-change Commission’s (“SEC”) Rule 10b-5 (“Rule 10b-5”) promulgated thereunder, 17 C.F.R. § 240.10b-5. Vivendi now ap-peals from a December 22, 2014 partial final judgment of the United States Dis-trict Court for the Southern District of New York (Scheindlin, J:), following a three-month jury trial that started in late 2009 and resulted in a jury verdict finding Vivendi liable for securities fraud under § 10(b) and Rule 10b-5.

We affirm as to Vivendi’s claims on ap-peal, concluding as follows:

(1) Plaintiffs relied on specifically identi-fied false or misleading statements at trial and thus, contrary to Vivendi’s argument on appeal, did not fail to present an actionable claim of securities fraud by “elimi-natfing] the foundational element of .,. a specific false or misleading statement,” Vi-vendi Br. 41;

(2) Vivendi’s claim that certain state-ments constituted non-actionable state-ments of opinion is not preserved for ap-pellate review;

(3) Vivendi’s claims that certain state-ments constituted non-actionable puffery and that others fall under the Private Se-curities Law Reform Act’s (“PSLRÁ”) safe harbor provision for “forward-looking statements,” see 15 U.S.C. § 78u-5(c), is without merit;

(4) the evidence was sufficient to sup-port the jury’s determination that the fifty-six statements at issue here were materially false or misleading with respect to Vi-vendi’s liquidity risk;

(5) the district court did not abuse its discretion in admitting the testimony of Plaintiffs’ expert, Dr. Blaine Nye (“Nye”); and

(6) the evidence was 'sufficient to sup-port the jury’s finding as to loss causation. As to the Plaintiffs’ cross-appeal, we like-wise affirm, concluding that the district court:

(1) did not abuse its discretion in ex-cluding certain foreign shareholders from the class at the class certification stage; and

(2) did not err in dismissing claims by American purchasers of ordinary shares under Morrison v. Nat’l Austl. Bank Ltd., 561 U.S. 247, 130 S.Ct. 2869, 177 L.Ed.2d 535 (2010).

I. Background

At the helm of Vivendi’s transition from a centuries-old French utilities conglomerate into a modern global media power-house was a man named Jean-Marie Messier, who had been the chief executive and chairman of the executive committee since 1994, and chairman of the company since 1996. Messier was nots by trade, an expert in French utilities, but rather- a former investment-banker at the firm La-zard Fréres & Co. LLC. Soon after be-coming chairman of the company’s execu-tive committee, Messier formulated an ambitious plan to transform the company completely. In broad strokes, Messier’s plan was to merge the company with two other large companies that had significant media dealings; steadily supplement this new company’s core media operations with various additional media acquisitions; and gradually divest the new company of its utilities and environment divisions.

The plan largely got underway in May 1998, when the shareholders of Compagnie Genérale des Eaux approved the compa-ny’s name change to Vivendi, S.A. Over the course of the following year, Vivendi, S.A., contributed or sold its interests in certain water-related holdings to a subsid-iary, Vivendi Environnement, and acquired scattered interests in various media and telecommunications firms.

The most aggressive foray in Messier’s plan came on June 20, 2000, when Vivendi, S.A., formally announced its intent to enter into a three-way merger with Canal Plus, S.A. (“Canal+”), a French film and television production company; and The Sea-gram Company Ltd. (“Seagram”), a Cana-dian entertainment and beverage company that owned, among other things, Universal Studios and Universal Music Group. Shortly after the announcement of the merger, credit-rating agencies Moody’s and Stan-dard & Poor’s (“S&P”) undertook to re-evaluate the creditworthiness of Vivendi, S.A. On July 4, 2000, Moody’s noted a “possible downgrade” of a particular senior class of Vivendi, S.A.’s debt might be on the horizon, on account of, inter alia, con-cerns about the considerable amount of debt Vivendi, S.A., would carry after the merger (including extensive prior debts al-ready incurred). S&P also expressed some concern, but tempered its forecast with the expectation- that the company would be able to dispose of several assets and there-by alleviate its debt. Neither Moody’s nor S&P downgraded Vivendi, S.A., at the time. The three-way merger was complete on December 8, 2000, with the surviving entity being Vivendi, formerly a subsidiary of Vivendi, S.A. With the three-way merger, Vivendi became one of the world’s lead-ing media and communications companies, second only to AOL-Time Warner. Among Vivendi’s assets were the world’s largest recorded music company, one of the world’s largest motion picture studios, and businesses in the global telecommunica-tions, television, theme park, publishing, and Internet industries.

Still, Vivendi pressed forth with addi-tional acquisitions. Over the course of the next eighteen months, Vivendi acquired significant stakes, or added to its existing interests, in a number of media and tele-communications companies across the world. To start, within just a few days of the three-way merger’s completion: in De-cember 2000, Vivendi announced its acqui-sition of a 35% interest in Maroc Telecom, the Kingdom of Morocco’s state-owned telecommunications company, for approxi-mately €2.3 billion. In Summer 2001, Vi-vendi acquired publishing company Houghton Mifflin Company (“Houghton Mifflin”), along with its $500 million in net debt, for approximately $2.2 billion. Several months later, on December 17, 2001, Vivendi announced that it would acquire full control of television company USA Networks Corporation (“USA Networks”) for $10.3 billion, approximately $1.6 billion of which Vivendi would finance in cash. That same day, Vivendi announced that it would invest $1.5 billion in satellite television company EchoStar Communications Corporation (“EchoStar”), which was ex-pected to gain access to approximately 15 million homes in the United States when EchoStar acquired DirecTV.

These multi-billion-dollar transactions merely scratched the surface of Vivendi’s buying frenzy. Vivendi also acquired, in whole or in part, MP3.com, GetMusic LLC, RMM Records & Video, MUSI-DISC, Koch Group Recorded Music, Up-roar Inc. and EMusic.com Inc., among other media or telecommunications compa-nies. In total, Vivendi reportedly spent approximately $77 billion on its acquisition spree, with Seagram alone costing roughly $34 billion. According to Plaintiffs, Viven-di’s debts associated with its media and communications operations ballooned from approximately €3 billion in early 2000 to over €21 billion in 2002.

Meanwhile, Vivendi repeatedly ex-pressed its aggressive growth prospects and its secure financial footing. Many of Vivendi’s public statements during its ac-quisition period focused on EBITDA (“Earnings Before Interest, Tax, Depreciation, and Amortization”), an earnings measure that is typically considered a “good example of [a company’s] cash in-come” and ability to service debt. J.A. 2833. On October 30, 2000, the company announced its “objective” to “grow pro for-ma adjusted EBITDA at an approximate 35% compound annual growth rate through 2002.” Special App’x 315. Over the next year, Vivendi repeatedly underscored its “eonfidenc[e] that [it] w[ould] meet [its] very aggressive [EBITDA] growth tar-gets,” id, at 316, and emphasized that its fiscal year 2001 quarterly results met or exceeded its EBITDA growth targets, e.g., id. at 320 (“With three quarters of the ‘aggressive’ incremental EBITDA target for the full year 2001 already achieved in the first half of the year, I can only re-emphasiz[e] our confidence. We will at least meet our stated targets.”); id. at 322 (“EBITDA organic growth is very strong, reaching 36% in the third quarter and 52% year-to-date. It represents the achievement in nine months of close to 100% of the full year 2001 ■ incremental EBITDA growth target.”). Vivendi supplemented these statements with representations that it had “very strong ... results with out-standing growth,” id. at 316, “the highest growth rates in the industry,” id. at 320, “strong operating results,” id. “free opera-tional cash flow [that was] far above [its] objectives,” id. at 328, and “strong free cash flow,” id. at 330.

But the tableau painted by Vivendi’s public statements did not match the tenor of the discussions inside the company. With each acquisition, Vivendi “had to bor-row some money from the banks,” J.A. 2485, and it became “more and more difficult to raise the cash” Vivendi needed to pay for its acquisitions and its accumulat-ing debts, J.A. 2487. Vivendi’s liquidity, or its ability to pay its fixed obligations, be-came increasingly strained. According to one member of Vivendi’s finance department, members of that department be-lieved Vivendi’s liquidity situation was “tense” by the middle of 2001, “dangerous” by late 2001, and “more than dangerous [throughout 2002].” J.A. 2488. The USA Networks and EchoStar transactions at the close of 2001 were particularly alarm-ing to one member of Vivendi’s finance department, who testified that the two deals “would create havoc with the debt level of Vivendi,” whose “cash situation” was already “extremely tense” at the time. Special App’x 366 n.21.

Starting in June 2001, Vivendi’s Trea-surer, Hubert Dupont-L’Hótelain, “clearly raised the issue of a cash problem inside Vivendi” at each one of Vivendi’s Finance Committee meetings. J.A 2512. According to a Vivendi employee present at the meet-ings, Dupont-L’Hotelain repeatedly “ex-pressed concerns over ... the liquidity situation” and discussed Vivendi’s “short-age in cash.” Id. These discussions prompted Vivendi’s Chief Financial Offi-cer, Guillaume Hannezo, to comment on multiple occasions that Vivendi appeared to be “running out of cash” and “nearing bankruptcy.” Id. at 2513.

Hannezo also warned Messier of these conditions. For example, after credit-rat-ing agencies raised concerns with Hannezo in early December 2001 about Vivendi’s contemplated USA Networks and EchoS-tar transactions, Hannezo wrote Messier warning of the “danger” of a downgrade. J.A. 4072. He later penned a memorandum to Messier recounting the “painful and hu-miliating meetings with the ratings agen-cies.” Id. at 3794. In that note, he ex-plained that he did “not want to put up with[] a downgrade, which [he believed] would [lead] to a liquidity crisis.” Id. Hannezo also told Messier that he had “the unpleasant feeling of being in a car whose driver is accelerating in a sharp turn while [he was] the one in the death seat.” Id. “The only thing that I am ask-ing,” Hannezo continued, “is that it doesn’t all end in shame.” Id. at 3794-95. Four days after Hannezo alerted Messier to the “danger” of a downgrade, Vivendi publicly announced its $10.3 billion USA Networks transaction and $1.5 billion EchoStar transaction. In a press conference shortly after the announcement, Vivendi stated that the transactions were “not putting pressure on Vivendi Universal,” and that it anticipated maintaining “a very comforta-ble ... credit rating.” Id. at 4158, 4162.

Around the same time, however, fissures began to appear in Vivendi’s public fagade. Despite Vivendi’s assurances about the fi-nancial soundness of the USA Networks and EchoStar deals, the two transactions prompted Moody’s to change its rating outlook on Vivendi to “negative.” J.A. 4164. The decision, Moody’s explained, came as a result of its concerns over the additional debt incurred by the transactions, in con-junction with other debts previously in-curred by Vivendi and uncertainty about Vivendi’s ability to take steps to reduce its debt. A few weeks later, on January 7, 2002, Vivendi announced the sale of 55 million treasury shares for a total of €3.3 billion. “The proceeds of the sale,” Vivendi explained in a press release, “w[ould] be used mostly to reduce the company’s debt.” J.A. 4117. Vivendi’s stock prices dipped following the announcement of the treasury-share sale.

Despite raising €3.3 billion for Vivendi, the substantial treasury-share sale in Jan-uary 2002 did not prevent Vivendi’s prob-lems from coming to a head several months later. On May 3, 2002, Moody’s downgraded Vivendi’s long-term senior debt rating from Baa2 to Baa3, citing con-cerns about Vivendi’s ability to reduce debt and return its leverage to a point that would justify a Baa2 rating. In response to Moody’s decision, Vivendi stated that the downgrade “ha[d] no impact on Viven-di[’s] ... cash situation,” and that Vivendi “ha[d] every confidence in its ability to meet its operating targets for 2002.” J.A. 4667.

Nonetheless, S&P followed Moody’s suit on May 6, 2002, downgrading Vivendi’s short-term debt from A-2 to A-3. Shortly afterwards, Vivendi issued a press release stating that it “ha[d] no reason to fear .any further deterioration [in its credit rating].” J.A. 4623. Vivendi’s “cash flow situation,” according to the press release, was “com-fortable.” Id. “[E]ven assuming an ex-tremely pessimistic market,” Vivendi would be able to “continue its debt reduction program in all serenity.” Id.

Quietly, Vivendi attempted to slough off some of its less critical holdings for cash. On June 12, 2002, unbeknownst to the public, Vivendi and Deutsche Bank en-tered into a private sale-and-repurchase agreement, under which Vivendi sold a .12.7% stake in its 63%-owned subsidiary Vivendi Environnement and agreed to re-purchase those shares from Deutsche Bank at a later point. On June 17, 2002, while the public remained unaware of Vi-vendi’s deal with Deutsche Bank, Vivendi announced it was considering selling a sig-nificant stake in Vivendi Environnement when market conditions were appropriate. Vivendi’s stock price took a hit on June 21, 2002, after the market learned that Viven-di had already entered a sale-and-repur-chase agreement with respect to some of its shares in Vivendi Environnement. Press reports questioned why Vivendi could not wait until market conditions were appropriate to go through with the sale.

Three days later, on June 24, 2002, Vi-vendi announced the immediate sale, of a 15.6% stake in Vivendi Environnement shares, including the 12.7% stake that was the subject of its repurchase-and-sale agreement with Deutsche Bank. That day-alone, Vivendi’s stock price dropped 23%. Financial commentators remarked that the quick succession of the two Vivendi Envi-ronnement transactions suggested that Vi-vendi “needed a quick cash injection” and “w[as] in a big rush to get that cash.” J.A. 2792. Vivendi parried back on June 26, 2002, stating in a press release that “[o]w-ing to its strong free cash flow,” combined with other factors, Vivendi was “confident of its capacity to meets its anticipated obligations over the next [year].” Special App’x-330. Two days later, however, Viven-di negotiated a new €275 million credit line' from Société Générale.

After the market closed on July 1,' 2002, Moody’s downgraded Vivendi’s long-term senior debt rating again, this time from Baa3 to Bal, landing Vivendi’s long-term senior debt in junk territory. In a press release announcing the downgrade, Moody’s explained that its decision primar-ily reflected growing doubts about Viven-di’s ability to achieve the level of debt reduction befitting of a Baa3 rating and concerns over Vivendi’s ability to refinance liabilities that would become due over the course of the next 12 months. When the market opened the following day, on July 2, 2002, S&P downgraded Vivendi’s long-term debt from BBB to BBB-, just a notch above junk status, and warned that liquidity concerns could prompt further down-grades. Like Moody’s, S&P cited Viven-di’s lack of-transparency about large debt obligations that were fast approaching re-payment deadlines, among other things, as a reason for the-downgrade. After news of both downgrades hit the market on July 2, 2002, Vivendi’s stock price slid approxi-mately 26%. Financial analysts speculated that Vivendi could face a cash shortfall by the end of 2002 because it did not have the means to cover its debt repayments.

Vivendi’s board of directors, meanwhile, hired Goldman Sachs to assess the severity of Vivendi’s financial difficulties. In late June 2002, Goldman Sachs presented its findings to the board and noted that one of four possible scenarios for Vivendi was bankruptcy, as early as September or Oc-tober 2002. The board of directors then zeroed in on Messier as the source of Vivendi’s troubles and sought to oust him from his position as CEO. On July 2, 2002, Messier announced his resignation, and the next day Vivendi’s stock prices tum-bled 22%. Now under new management, Vivendi issued a press release acknowl-edging that the company faced a “short-term liquidity issue.” J.A. 2049. The press release also revealed that by the end of July, Vivendi would have to repay credi-tors €1.8 billion, and €3.8 billion in credit lines would be up for renegotiation. The following week, French regulators began a probe into Vivendi’s financial affairs, while Moody’s and S&P warned of further down-grades.

Additional damaging revelations sur-faced on August 14, 2002, when Vivendi’s new management announced that the com-pany faced refinancing needs of €5.6 bil-lion, had €10 billion more in debt than is typical of a company with a BBB credit rating by S&P, and planned to sell €5 billion worth of assets over the next nine months. That day, S&P further downgrad-ed Vivendi’s long-term debt, and Vivendi’s stock price dropped more than 25%.

II. Procedural History

On January 7, 2003, Plaintiffs filed a Consolidated Class Action Complaint against Vivendi, Messier, and Hannezo (collectively, “Defendants”) in the United States District Court for the Southern Dis-trict of New York (Baer, J.), principally alleging that between October 30, 2000 and August 14, 2002 (the “Class Period”), De-fendants made material misstatements that artificially inflated Vivendi’s stock price, in violation of § 10(b) of the Ex-change Act, 15 U.S.C. § 78j(b), and SEC Rule 10b-5 promulgated thereunder, 17 C.F.R. § 240.10b-5, as well as § 20(a) of the Exchange Act, 15 U.S.C. § 78t(a). In February 2003, Defendants moved to dis-miss, arguing, inter alia,, that Plaintiffs had failed to specify with sufficient partic-ularity the statements Plaintiffs alleged to be false or misleading. By opinion dated November 4, 2003, Judge Baer denied in part and granted in part Defendants’ motion to dismiss, and granted - Plaintiffs leave to amend its Consolidated Class Action Complaint. On November 24, 2003, Plaintiffs filed a First Amended Consoli-dated Class Action Complaint.

After several years of discovery, during which time the case was transferred from Judge Baer to Judge Holwell, Defendants moved for summary judgment on August 15, 2008. Judge Holwell denied that motion on March 31, 2009. On June 2, 2009, De-fendants filed a motion in limine to ex-clude the testimony of Plaintiffs’ expert, Dr. Blaine Nye. On August 18, 2009, Judge Holwell denied Defendants’ motion, with one narrow exception not at issue on ap-peal. Trial was scheduled to begin in the fall of 2009.

On October 5, 2009, a jury trial com-menced on Plaintiffs’ § 10(b) claims against Vivendi, Messier, and Hannezo, as well as Plaintiffs’ § 20(a) control-person claims against Messier and Hannezo. At trial, Plaintiffs introduced into evidence the “Book of Warnings,” a compendium of internal communications and memoranda that Hannezo had written to Messier and other Vivendi employees during the period from 2000 to 2002, warning them of finan-cial difficulties Vivendi was facing at the time. Special App’x 364. As Plaintiffs pointed out to the jury, Hannezo’s commu-nications about Vivendi’s deteriorating fi-nancial health stood in sharp contrast to Vivendi’s rosy public statements. Plaintiffs also presented the testimony of former Vivendi employees, who generally corrobo-rated the bleak internal view presented by the Book of Warnings. Defendants, mean-while, called Messier and Hannezo to testify that Vivendi’s optimistic public state-ments regarding earnings and growth were in fact accurate at the time they were made. Defendants also emphasized that Vi-vendi never actually experienced a full-blown liquidity crisis or defaulted on a loan. According to Defendants, the events that occurred in the summer of 2002 merely reflected a transient hitch, from which the company ultimately rebounded.

The jury began its deliberations in early January 2010. The seventy-two-page final jury verdict form identified fifty-seven al-leged misstatements, some of which were alleged against Vivendi only, and others of which were alleged against Vivendi and Messier and/or Hannezo. Among other things, the final jury verdict form asked the jury to determine whether Plaintiffs had proven the elements of their § 10(b) claim with respect to each of the fifty-seven statements for each Defendant against whom that false statement was alleged. It also asked the jury to deter-mine whether Messier and Hannezo had violated § 20(a).

After fourteen days of deliberation, the jury reached a verdict. The jury found that neither Messier nor Hannezo was liable under § 10(b) or § 20(a) for any of the alleged misstatements. However, it found Vivendi liable under § 10(b) for all fifty-seven alleged misstatements. The district court denied Vivendi’s motions for judgment as a matter of law and for a new trial on February 17, 2011, with one exception: it awarded Vivendi judgment as a matter of law with respect to one statement. See In re Vivendi Universal, S.A. Secs. Litig., 765 F.Supp.2d 512, 545 (S.D.N.Y. 2011). This appeal followed.

DISCUSSION

I. Plaintiffs’ Theory of the Case

Vivendi first challenges Plaintiffs’ theory of the case as well as the way that Plain-tiffs presented that theory at trial. Accord-ing to Vivendi, Plaintiffs were required to prove their case “statement-by-statement.” Vivendi Br. 2. Vivendi suggests that throughout the trial, Plaintiffs did not fo-cus on specifically alleged fraudulent state-ments, but rather, argued generally that the company failed to disclose a liquidity risk (an approach Vivendi refers to as the theory of “unitary omission”). Id. at 35. Vivendi contends that Plaintiffs thus sought to prove that it committed securities fraud with respect to no particular statement at all. Only at the eleventh hour and after the close of evidence at trial, Vivendi continues, did Plaintiffs in fact identify the fifty-seven alleged misstate-ments for which they sought to hold Viven-di hable. The result, according to Vivendi, was that Plaintiffs presented no actionable claim of securities fraud.

Vivendi thus argues that Plaintiffs’ supposed failure to define a specific set of alleged misstatements earlier in the trial had the effect of “eliminating] the foundational element of a claim for securities fraud” under § 10(b) and Rule 10b-5: “a specific false or misleading statement.” Vivendi Br. 41. Under Rule 10b-5, it is unlawful to (1) “make any untrue statement of a material fact,” or (2) “omit to state a material fact necessary in order to make the statements made ... not misleading.” 17 C.F.R. § 240.10b-5(b). Thus, to support a finding of liability, Rule 10b-5 expressly requires an actual statement, one that is either “untrue” outright or “misleading” by virtue of what it omits to state. Absent an actual statement, a complete failure to make a statement—in other words, a “pure omission,” Litwin v. Blackstone Grp., L.P., 634 F.3d 706, 719 (2d Cir. 2011)—“is actionable under the securities laws only when the corporation is subject to a duty to disclose the omitted facts,” Stratte-McClure v. Morgan Stanley, 776 F.3d 94, 101 (2d Cir. 2015) (quoting In re Time Warner Inc. Secs. Litig., 9 F.3d 259, 267 (2d Cir. 1993)); see also Basic Inc. v. Levinson, 485 U.S. 224, 239 n.17, 108 S.Ct. 978, 99 L.Ed.2d 194 (1988). And in and of themselves, “§ 10(b) and Rule 10b-5 do not create an affirmative duty to disclose any and all material information.” Matrixx Initiatives, Inc. v. Siracusano, 563 U.S. 27, 44,131 S.Ct. 1309,179 L.Ed.2d 398 (2011). No such duty .arises “merely because a reasonable investor would very much like to know” that information. In re Time Warner, 9 F.3d at 267.

“Pure omissions,” of course, must be distinguished from “half-truths”—statements that are misleading under the second prong of Rule 10b-5 by virtue of what they omit to disclose. See S.E.C. v. Gabelli, 653 F.3d 49, 57 (2d Cir. 2011), rev’d on other grounds, Gabelli v. S.E.C., — U.S. —, 133 S.Ct. 1216, 185 L.Ed.2d 297 (2013) (“The law is well settled ... that so-called half-truths—literally true statements that create a materially misleading impression—will support claims for securities fraud.” (internal quotation marks omitted)); see also Universal Health Servs., Inc. v. United States, — U.S. —, 136 S.Ct. 1989, 2000 & n.3, 195 L.Ed.2d 348 (2016) (noting that the principle that “half-truths—representations that state the truth only so far as it goes, while omitting critical qualifying information—can be actionable misrepresentations” applies in the “securities law” context (citing Matrixx, 563 U.S. at 44, 131 S.Ct. 1309)). The rule against half-truths, or statements that are misleading by omission, comports with the common-law tort of fraudulent misrepresentation, according to which “a statement that contains only favorable matters and omits all reference to unfavorable matters ié as much a false representation as if all the facts stated were untrue.” Restatement (Second) of Torts, § 529, cmt. a (1977).

It is undisputed that Vivendi had no legal duty to disclose its liquidity risk, such that Plaintiffs could not hold Vivendi liable simply for its silence on the subject. Viven-di therefore contends that Plaintiffs’ pres-entation of the case effectively vitiated the requirement that the Plaintiffs prove Vi-vendi made a false or misleading statement. As a result, Vivendi argues, the jury necessarily held Vivendi liable for failing to disclose something that it had no legal duty to disclose. Simply put, we disagree.

The record does not support Vivendi’s suggestion that Plaintiffs presented their case to the jury on the theory that Vivendi violated § 10(b) by remaining completely silent on the subject of its liquidity risk. To be sure, over the course of the litigation below, Plaintiffs were at times less than precise in articulating their theory of liability, In Plaintiffs’ opening statements, for example, counsel for Plaintiffs remarked at points that Plaintiffs were “going to prove ... that the defendant failed to tell the truth about the growing problems about its liquidity.” Trial Tr. 128 (emphasis add-ed). In isolation, this statement could be taken to suggest that Plaintiffs would at-tempt to prove that Vivendi was liable merely for failing to disclose the compa-ny’s liquidity risk, although, even in iso-lation, it is at least as easy to understand the statement as an accusation that Viven-di had lied about the subject. In context, however, Plaintiffs’ opening statements made clear that the way in which they alleged that Vivendi “failed to tell the truth” was by making affirmative state-ments that were either outright lies or misleading half-truths. See, e.g., id. at 128-29 .(noting, two lines later, that Vivendi “gave reports about how great the compa-ny was doing and, in doing so, ... com-pletely disregarded alarms that Vivendi’s own employees ... were sounding inside Vivendi”).

Indeed, counsel for Plaintiffs went on in that opening statement to ask the jury to “take a look at some examples” of alleged misstatements by Vivendi, Trial Tr. 141, and consider how those statements com-pared to the actual situation inside Vivendi at the time Vivendi made the statements, see Trial Tr. 142-79, Essentially all of the examples provided were, ultimately submit-ted to the jury for consideration. Compare Trial Tr. 142, ivith Special App’x 315 (Statement 3); compare Trial Tr. 152-53, with Special App’x 316 (Statement 5); com-pare Trial Tr. 154-55, with Special App’x 316 (Statement 6); compare Trial Tr. 162, ivith Special App’x 320 (Statement 18); compare Trial Tr. 167, with Special App’x 324 (Statement 32); compare Trial Tr. 167-68, with Special App’x 324 (Statement 33); compare Trial Tr. 169, with Special App’x 324 (Statement 34); compare Trial Tr. 169-70, with Special App’x 324-25 (Statement 35); compare Trial Tr. 171, with Special App’x 326 (Statement 40); compare Trial Tr. 172, ivith Special App’x 327 (Statement 42); compare Trial Tr. 173, with Special App’x 329 (Statement 51); compare Trial Tr. 177, with Special App’x 330 (Statement 55).

It is true that Plaintiffs initially pro-posed to Judge Holwell a jury verdict form that did not include a list of specific al-leged misstatements. In re Vivendi, 765 F.Supp.2d at 577. It is also true that at oral argument on Vivendi’s renewed motion for judgment as a matter of law, which took place after trial, Plaintiffs sug-gested that their initial proposed jury ver-dict form embodied the theory that Viven-di had made “a single unitary omission ... concerning Vivendi’s true liquidity risk” that the Plaintiffs believed “manifested in many different ways and with respect to many different statements,” and thus that might not easily boil down into a discrete set of specific alleged misstatements. J.A. 3693.

At trial, however, Judge Holwell insisted on a more specific approach. After, “re-viewing] the verdict forms used in several [then-]recent securities class actions tried before a jury,” Judge Holwell concluded that Plaintiffs’ proposed jury verdict form was inadequate because “[ujnder the plain language of Rule 10b-5, an ‘omission’ is not a violation unless plaintiffs can point to statements that were made misleading by the omitted facts.” In re Vivendi, 765 F.Supp.2d at 578. Because failing to identify a discrete set of statements in the ver-dict form might thus invite a verdict that would be inconsistent with this language, Judge Holwell “asked [Plaintiffs to pro-pose a[ ] .,. verdict form that identified specific misstatements.” Id. The final jury verdict form thus asked, with respect to each statement and in regard to each De-fendant, whether “plaintiffs [have] proven each element of their Section 10(b) claim.” E.g., Special App’x 243 (emphasis added).

At closing argument after the district court finalized the jury verdict form, coun-sel for Plaintiffs walked through the fifty-seven alleged misstatements, highlighting with respect to each one the evidence that Plaintiffs believed supported a finding of securities fraud.' Repeatedly, counsel for Plaintiffs asked the jury to consider the disparity between Vivendi’s “inside reality” and its “outside message.” See Trial Tr. 7294-365. From opening statements to closing arguments, then, Plaintiffs present-ed to the jury a theory of securities-fraud liability predicated on Vivendi’s state-ments, not its silence.

In any event, “we' review the proof at trial only by reference to th[e] charged theory.” United States ex rel. O’Donnell v. Countrywide Home Loans, Inc., 822 F.3d 650, 663 (2d Cir. 2016)..As in O’Donnell, the record here “shows that the jury was charged only as to a theory of fraud through an affirmative misstatement.” Id. In keeping with the final jury verdict form, Judge Holwell instructed the jury that Plaintiffs had to “prove by a preponderance of the evidence that during the class period ... [Vivendi] made a false or misleading statement or omitted to state a fact which made what was said under the circumstances misleading.” Trial Tr. 7512. Far from charging the jury on what Viven-di terms a “ ‘pure-omission’ theory,” Viven-di Br. 2, Judge Holwell informed the jury that Vivendi was “not required to disclose every piece of material information” it possessed, Trial Tr. -7513. He further expressly distinguished between so-called “pure omissions” and statements that are misleading by virtue of what they omit to disclose. See id. It is simply incorrect, then, to say that Plaintiffs “secured a jury verdict based on ‘proof [of the six elements of a private 10b-5 action] as to no particular statement.” Vivendi Br. 41. In light of the Plaintiffs’ own presentation of their case, it does not appear that they in fact presented a “pure omission” theory, as Vivendi argues. And reviewing the proof at trial with reference to the charged theory, we discern no basis for concluding that the jury verdict was based on a theory other than the one on which the jury was, in fact, instructed.

In short, Plaintiffs presented a case to the jury based on Vivendi’s alleged misstatements, and the jury entered a verdict against Vivendi based on fifty-seven of them. We thus reject Vivendi’s contention that the way in which Plaintiffs tried and proved their case had the effect of vitiating an essential element of their § 10(b) claim: proving that Vivendi made materially false or misleading statements.

II. Materially False or Misleading Statements

Having identified no reversible error stemming from the manner in which Plain-tiffs presented and identified statements at trial, we turn to the statements them-selves. Vivendi contests liability for certain statements on the ground that they were non-actionable opinion, puffery, or for-ward-looking statements. Separately, Vi-vendi also contests liability for all of the statements on the ground that they all rested on an impermissible “liquidity risk theory” of liability. We address these argu-ments in turn.

1. Opinion Statements

Vivendi first argues that certain statements (or sub-statements) are non-actionable statements of opinion. This argument is not preserved for appellate review, as Vivendi failed to contend that certain statements were non-actionable as opinions in its motions for judgment as a matter of law, even after the parties agreed upon the set of statements the jury would consider. See Kirsch v. Fleet Street, Ltd., 148 F.3d 149, 164 (2d Cir. 1998). Recognizing this, Vivendi now tries to excuse its failure to raise this argument below in several ways. Vivendi first points out that it objected to statements as opinions in its motion to dismiss, which it filed in 2003. This argument can be rejected easily. Raising this argument in a motion to dismiss did not sufficiently alert the district court to the existence of the argument more than six years later, when Vi-vendi was required to raise it in its Federal Rule of Civil Procedure 50 motions at trial. See id.

Second, Vivendi suggests that the late submission of the actual statements to the jury prevented Vivendi from challenging certain statements as opinion statements. Even assuming this argument to be other-wise colorable, Vivendi’s own submissions to the district court belie this claim. Specif-ically, Vivendi’s post-trial Rule 50(b) re-newed motion for judgment as a matter of law clearly challenged specific statements on the ground that they were non-actionable for'ward-looking statements; it also (in a footnote) challenged certain statements on the ground that they were inactionable puffery. Given these challenges, Vivendi cannot now argue that the timing of Plain-tiffs’ identification of a specific set of state-ments prevented it from also challenging specific statements on the ground that they were non-actionable opinion,.

Finally, Vivendi contends that intervening authority—by way of Fait v. Regions Fin. Corp,, 655 F.3d 105 (2d Cir. 2011), and Omnicare, Inc. v. Laborers Dist. Council Constr. Indus. Pension Fund, — U.S.—, 135 S.Ct. 1318, 191 L.Ed.2d 253 (2015)—excuses its failure to raise the argument below. This argument, too, lacks merit. To excuse waiver on the grounds of intervening authority, it is not enough to argue that the intervening authority may have sharpened or otherwise elaborated upon an argument. Rather, the intervening authority must have established an argument that was “not known to be available” to the party seeking to excuse waiver at the first opportunity that the party had to raise the argument. Gucci Am., Inc. v. Weixing Li, 768 F.3d 122,135 (2d Cir. 2014) (quoting Hawknet, Ltd. v. Overseas Shipping Agencies, 590 F.3d 87, 92 (2d Cir. 2009)); see also Holzsager v. Valley Hosp., 646 F.2d 792, 796 (2d Cir. 1981). Not so with the decisions Vivendi claims constitute intervening authority.

For purposes of the claim Vivendi makes on appeal, neither Fait nor Omni-care established an argument regarding the actionability of opinion statements that was previously unknown. As both Fait and Omnicare acknowledge, Virginia Bankshares v. Sandberg, 501 U.S. 1083, 1090-98, 111 S.Ct. 2749, 115 L.Ed.2d 929 (1991), addressed the circumstances under which liability may extend to statements of opinion or belief expressed in proxy solicitations. See Fait, 655 F.3d at 110; Omnicare, 135 S.Ct. at 1326-27 & n.2. Fait and Om-nicare merely expanded upon an uncontroversial point already made clear by Virginia Bankshares: that although statements expressing opinions may not be grounds for liability when they are not false or misleading in context to a reasonable investor, such statements are “not beyond the purview” of the federal securities statutes. Fait, 655 F.3d at 110; see also Omni-care, 135 S.Ct. at 1329 (“[I]f a registration statement omits material facts about the issuer’s inquiry into or knowledge concerning a statement of opinion, and if those facts conflict with what a reasonable investor would take from the statement itself, then § 11[ ] ... creates liability. An opinion statement, however, is not necessarily misleading when an issuer knows, but fails to disclose, some fact cutting the other way.”). Indeed, we made similar observations even before Fait or Omnicare. See, e.g., In re Int’l Bus. Machs. Corp. Secs. Litig., 163 F.3d 102, 107 (2d Cir. 1998) (“Statements that are opinions ... are not per se inactionable under the securities laws.”); In re Time Warner, 9 F.3d at 266 (2d Cir. 1993) (noting that “expressions of opinion” are “not beyond the reach of the securities laws” /citing, inter alia, Virginia Bankshares, 501 U.S. at 1088-97, 111 S.Ct. 2749)).

The argument that certain statements are not materially false or misleading be-cause they contain only opinions was therefore known to be available prior to Fait and Omnicare. Of. Gucci Am., Inc., 768 F.3d at 135-36 (concluding that a de-fendant did not “waive its personal juris-diction objection” when, prior to an inter-vening decision, “controlling precedent in this Circuit made it clear that [the defen-dant] ... was properly subject to general personal jurisdiction” (emphasis in origi-nal)); Hawknet, 590 F.3d at 91-92 (con-cluding that a defendant could raise an argument on appeal that the defendant did not raise before the district court because intervening authority “provided [the] de-fendant with a new objection” that, prior to the intervening decision, “would have been directly contrary to controlling prec-edent in this Circuit” (emphasis added)). Although Fait and Omnicare may have provided a stronger basis for such an ob-jection, having a better argument on ap-peal is not tantamount to having a previ-ously unknown argument. As it required not “clairvoyance” but “conscientiousness” on Vivendi’s part to object to certain state-ments on the basis that they were non-actionable opinion statements, Vivendi’s reliance on Fait and Omnicare as inter-vening authority is unavailing. See id. at 92 (“[T]he doctrine of waiver demands consci-entiousness, not clairvoyance, from parties.”). Finding none of Vivendi’s reasons for excusing its failure to raise the opinion argument below convincing, we decline to consider the argument on its merits.

2. Puffery

Vivendi next contends that several state-ments are non-actionable puffery. Vivendi raised this argument only in a footnote in its Rule 50(b) renewed motion for judgment as a matter of law, though the dis-trict court considered,. and rejected, the argument on the merits. Cf. Fortress Bible Church v. Feiner, 694 F.3d 208, 216 n.3 (2d Cir. 2012). Assuming this footnote was sufficient to present the argument to the district court and thus preserve it for ap-pellate review, the statements of which Vi-vendi complains are simply not puffery.

Puffery encompasses “statements [that] are too general to cause a reasonable investor to rely upon them,” ECA, Local 134 IBEW Joint Pension Trust of Chicago v. JP Morgan Chase Co., 553 F.3d 187, 206 (2d Cir. 2009), and thus “cannot have misled a reasonable investor,” San Leandro Emergency Med. Grp. Profit Sharing Plan v. Philip Morris Cos., 75 F.3d 801, 811 (2d Cir. 1996). They are statements that “lack the sort of definite positive 'projections that might require later correction.” Id. (quoting In re Time Warner, 9 F.3d at 259, 267 (2d Cir. 1993)).

The jury reasonably concluded that the statements identified by Vivendi as puffery were actionable. Consider, for example, Vivendi’s June 26, 2001 statement that it “posted RECORD-HIGH NET INCOME, and ha[d] cash available for investing,” Special App’x 318, or its July 23, 2001 representation that “[t]he results produced by Vivendi Universal in the second quarter are well ahead of market consensus,” id. at 319. There was sufficient evidence for the jury to conclude that such statements were not so general that a reasonable investor could not have relied upon them in evaluating whether to purchase Vivendi’s stock. Cf. ECA, Local 13k, 553 F.3d at 205-06 (concluding that “statements such as the assertion[s] that [the defendant company] had ‘risk management processes [that] are highly disciplined and designed to preserve the integrity of the risk management process’; that [the company] ‘set the standard for integrity’; and that [the company] would ‘continue to reposition and strengthen [its] franchises with a focus on financial discipline’ ” constituted puffery (citations omitted)); San Leandro, 75 F.3d at 806, 811 (concluding that “general announcements,” such as the defendant company’s statement that it “ ‘should deliver income growth consistent with [its] historically superior performance’ ” and was “ ‘optimistic about 1993’ ” constituted puffery). We thus reject Viven-di’s argument that certain statements found actionable by the jury are statements of puffery that are non-actionable as a matter of law.

3. Forward-Looking Statements

Vivendi next argues that certain statements fall under the safe-harbor provision for “forward-looking statements” under the PSLRA. See 15 U.S.C. § 78u-5(c). Under that provision a defendant is not liable if (1) “the forward-looking statement is identified and accompanied by meaningful cautionary language,” (2) the forward-looking statement “is immaterial,” or (3) “the plaintiff fails to prove that [the forward-looking statement] was made with actual knowledge that it was false or misleading.” Slayton v. Am. Express Co., 604 F.3d 758, 766 (2d Cir. 2010). Because “[t]he safe harbor is written in the disjunctive,” a forward-looking statement is protected under the safe harbor if any of the three prongs applies. Id.

As an initial matter, Vivendi disputes the district court’s conclusion that “[Plaintiffs challenge the non-forward looking elements of Vivendi’s statements regarding its EBITDA growth, rather than the [forward-looking] elements.” In re Vivendi, 765 F.Supp.2d at 569. “The PSLRA includes several definitions of a forward-looking statement, including ‘a statement containing a projection of ... income (including income loss), earnings (including earnings loss) per share, ... or other financial items’ and ‘a statement of future economic performance, including any such statement contained in a discussion and analysis of financial condition by the management.’” Slayton, 604 F.3d at 766-67 (quoting 15 U.S.C. § 78u-5(i)(l)(A) & (C)). However, “[a] statement may contain some elements that look forward and others that do not,” and “forward-looking elements” may be “severable” from “non-forward-looking” elements. Iowa Pub. Emps.’ Ret. Sys. v. MF Glob., Ltd., 620 F.3d 137, 144 (2d Cir. 2010); see also Makor Issues & Rights, Ltd. v. Tellabs Inc., 513 F.3d 702, 705 (7th Cir. 2008) (“[A] mixed present/future statement is not entitled to the safe harbor with respect to the part of the statement that refers to the present.”).

It is clear that at least some of the statements that Vivendi identifies as forward-looking contain present representations, and that it is these non-forward-looking elements of those statements that Plaintiffs alleged were false or misleading. Consider the February 14, 2001 alleged misstatement, which Vivendi labels as for-ward-looking: “Vivendi Universal enters its first full year of operations with strong growth prospects and a very strong balance sheet. This new company is off to a fast start and we are very confident that we will meet the very aggressive growth targets we have set for ourselves both at the revenues and EBITDA levels.” Special App’x 316. Although some aspects of this statement could conceivably be character-ized as forward-looking, there is nothing prospective about the representation that Vivendi entered 2001 with a “very strong balance sheet,” which Plaintiffs argued at trial was part of what made Vivendi’s Feb-ruary 14, 2001 statement misleading. See Trial Tr. 7297. The safe-harbor provision does not protect this and other present representations—about “very strong 2000 results,” Special App’x 316, or achievement of “ ‘aggressive’ incremental EBITDA tar-gets,” Special App’x 320—embedded with-in statements that Vivendi deems forward-looking.

To the extent that other statements identified by Vivendi as forward-looking are arguably false or misleading with re-spect to their forward-looking elements, we need .not decide whether those state-ments, or elements thereof, are indeed for-ward-looking. Even assuming, arguendo, that they.are, there was sufficient evidence for a reasonable jury to conclude that none of the prongs of the PSLRA safe-harbor provision applies to them.

Contrary to Vivendi’s argument, there was sufficient evidence to support the jury-in concluding that any forward-looking statements were not accompanied by meaningful cautionary language. “To avail themselves of safe harbor protection under the meaningful cautionary language prong, defendants must demonstrate that their cautionary language was not boiler-plate and conveyed substantive information.” Slayton, 604 F.3d at 772. “Vague” disclaimers are inadequate. Id.

Although Vivendi points to a miscellany of disclaimers peppered throughout its re-quired SEC filings in 2001 and 2002, there is sufficient evidence to support the jury’s conclusion that none of them was meaningful. To start, several of the disclaimers highlighted by Vivendi are quite irrelevant to the alleged misstatements at issue. In one, for example, Vivendi warned that fac-tors that “could cause actual results to differ materially from those described in the forward-looking statements” included “inability to identify, develop and achieve success for new products, services and technologies; increased competition and its effect on pricing, spending, third-party re-lationships and revenue; [and] inability to establish and maintain relationships with commerce, advertising, marketing, technol-ogy, and content providers.” J.A. 4167. The considerations mentioned in this disclaimer—success with new products and ser-vices, relationships with competitors and third parties, and marketing and advertis-ing efforts—do not bear even tangentially on Vivendi’s liquidity risk. The jury rea-sonably could have found that this kitchen-sink disclaimer, listing garden-variety business concerns that could affect any company’s financial well-being, was not meaningful cautionary language.

Vivendi’s disclaimers with respect to the use of EBITDA were no less oblique. In Vivendi’s October 30, 2000 Form F-4 reg-istration statement filing with the SEC, Vivendi stated that it “considers operating income to be the key indicator of the oper-ational strength and performance of its business.” J.A. 4681. Vivendi continued to state, however, that while “[a]djusted EBITDA should not be considered an al-ternative to operating or net income as an indicator of Vivendi’s performance,” or “an alternative to cash flows from operating activities as a measure of liquidity,” adjust-ed EBITDA was nevertheless a “pertinent comparative measure” to “operating in-come.” Id. (emphasis added). Given the arguable endorsement of the EBITDA measure inherent in this language, suffi-cient evidence supported the jury’s conclusion that such language did not meaning-fully caution against reliance on EBITDA figures as a measure of Vivendi’s performance.

Turning to the “actual knowledge” prong of the PSLRA safe-harbor provision, we conclude that there was sufficient evidence for the jury to find that Vivendi made the statements with actual knowledge that the statements were false or misleading. To take an example, Plain-tiffs presented evidence that Vivendi actually knew that its October 30, 2000 an-nouncement of a 35% EBITDA growth-rate objective was misleading to a reasonable investor. On September 15, 2000, Hannezo circulated an e-mail informing others at Vivendi that “the analysts will not have it easy to track the purchase accounting benefits” in EBITDA figures, J.A. 4169. Much less would a reasonable investor, who is not as well-versed at mak-ing sense of Vivendi’s disclosures as a fi-nancial analyst, be able to discern the im-pact of purchase accounting.

To take another example, Vivendi high-lights as forward-looking the December 19, 2000 statement that Vivendi would be “free of debt in its communications busi-nesses” as of January 1, 2001 and have “free cash flow of more than 2 billion euros for the two coming years.” Special App’x 315. Plaintiffs presented sufficient evi-dence at trial, however, for a jury to find that Vivendi actually knew that this statement conflicted with internal forecasts of debt and free cash flow and thus was misleading. In December 2000, Vivendi was planning to restructure Seagram’s debt, a process that it knew would incur additional short-term debt and require it to pay substantial premiums on that debt. See Trial Tr. 1305-06, 7295. And just two weeks after Vivendi issued the statement, Hannezo stated in an internal communication that he “believe[d] that it [was] wrong to reason in terms of ... free cash flow” because “there [wouldn’t] be any this year.” J.A. 4059. Assuming, arguendo, that some of the statements Vivendi claims are purely forward-looking are indeed so, such evidence was sufficient for a jury to find that Vivendi actually knew that its forward-looking statements were false or misleading. ■

4. Liquidity Risk Theory

In addition to objecting that certain al-leged misstatements are non-actionable opinion, puffery, or forward-looking state-ments, Vivendi lodges a broader attack against the entire set of alleged misstate-ments. To wit, Vivendi repeatedly protests what it terms to be Plaintiffs’ impermissi-ble “liquidity risk theory,” under which all of the fifty-seven statements were allegedly false or misleading with respect to Vi-vendi’s liquidity risk. The nub of Vivendi’s argument appears to be that “liquidity risk” is too “amorphous” and “ephemeral” a concept for any statement to be false or misleading with respect to it, much less all fifty-seven statements at issue here. Viven-di Br. 51, 88.

But, even assuming that this argument has separate purchase from the more specific arguments Vivendi makes as to the actionability of the statements, “liquidity risk” is not so “amorphous” or “ephemeral” a concept as Vivendi would lead us to believe. As Plaintiffs defined it at trial, liquidity is “the ease or difficulty with which a company can timely meet its financial obligations and fund its operations.” Trial Tr. 128; see also Trial Tr. 3481 (Nye testifying that liquidity is “the ability to pay fixed obligations”). Liquidity risk, then, is simply a financial-accounting term for the concept of being “debt rich and cash poor.” Trial Tr. 141. Further, to the extent that liquidity risk is not a perfectly defined concept with rigid outer bounds, that does not necessarily preclude liability for securities fraud. The federal securities laws do not protect against only those false and misleading statements that are false or misleading with respect to very specific material facts. See, e.g,, Suez Equity Inv’rs, L.P. v. Toronto-Dominion Bank, 250 F.3d 87, 97-99 (2d Cir. 2001). (conclud-ing that plaintiffs’ allegations were suffi-cient to state a claim that certain state-ments fraudulently concealed a company executive’s “financial and business prob-lems,” “lack of skill,” and “inability to run the [company]”). The jury found that knowledge of Vivendi’s true liquidity risk at any given time would have been material to a reasonable investor and that the fifty-seven statements were individually false or misleading with respect to this risk. Without opining on whether there are indeed concepts so amorphous or broad that their concealment cannot support an actionable theory under § 10(b) as a mat-ter of law, liquidity risk as defined in this case was not such a concept.

The question, then, is whether there was sufficient evidence to support the jury’s finding that all of the fifty-six statements (excluding the statement on which the district court granted Vivendi judgment as a matter of law) were materially false or misleading with respect to liquidity risk. “The test for whether a statement is materially misleading under Section 10(b)” is not whether the statement is misleading in and of itself, but “whether the defendants’ representations, taken together and in context, would have misled a reasonable investor.” Rombach v. Chang, 355 F.3d 164, 172 n.7 (2d Cir. 2004) (emphasis added) (quoting I. Meyer Pincus & Assocs. v. Oppenheimer & Co., 936 F.2d 759, 761 (2d Cir. 1991)); see also Meyer v. Jinkosolar Holdings Co., Ltd., 761 F.3d 245, 250 (2d Cir. 2014) (“The literal truth of an isolated statement is insufficient; the proper inquiry requires an examination of defendants’ representations, taken together and in context.” (quoting In re Morgan Stanley Info. Fund Secs. Litig., 592 F.3d 347, 366 (2d Cir. 2010))). Whether a misrepresentation is material is “judged according to an objective standard” that turns on “the significance of an omitted or misrepresented fact to a reasonable investor.” Amgen Inc. v. Conn. Ret. Plans & Trust Funds, — U.S. —, 133 S.Ct. 1184, 1191, 1195, 185 L.Ed.2d 308 (2013) (quoting TSC Indus., Inc. v. Northway, Inc., 426 U.S. 438, 445, 96 S.Ct. 2126, 48 L.Ed.2d 757 (1976)).

We conclude that there was sufficient evidence for the jury to find the fifty-six relevant statements materially false or misleading in regards to Vivendi’s true liquidity risk. To be sure, the statements do not each repeat the precise same refrain. Some speak directly to liquidity risk, while others concern components that contributed to Vivendi’s liquidity risk. That individual alleged misstatements may relate to different aspects of a larger problem does not necessarily subvert a finding of fraud, however. It would be perverse if companies could escape liability for securities fraud simply by disseminating a network of interrelated lies, each one slightly distinct from the other, but all collectively aimed at perpetuating a broader, material lie. Where a company seeks fraudulently to hide a particularly large problem with multiple contributing factors, it is quite probable that the company will have to He about a number of related topics in order successfully to conceal the larger issue.

Just so here. Vivendi’s alleged fraud (in the jury’s reasonable estimation) is re-markable in part because the problem that Vivendi sought to conceal from the public was so vast, and touched upon so many aspects of its business, that a few scat-tered misstatements would not have suf-ficed to mask it. Vivendi needed both to systematically misrepresent its ability to satisfy its liquidity demands, and also to assiduously conceal any material facts (of which there were many) that would call into question its abihty to meet its liquidity demands.

Consider, for instance, Vivendi’s state-ments about its self-described “aggressive” EBITDA growth rates, which Vivendi con-sistently advertised as a point of strength. E.g., Special App’x 317 (Statement 9: “[F]or first quarter of 2001, the Company generated very strong EBITDA ... growth with 900 million euros, an increase of 112% or an incremental 475 million eu-ros over the first quarter of the prior year.” (first alteration in original)); id. at 320 (Statement 18: “With three quarters of the ‘aggressive’ incremental EBITDA tar-get for the full year 2001 already achieved in the first half of the year, I can only re-emphasiz[e] our confidence”). As Plaintiffs’ expert testified, high EBITDA suggests high profitability—and by implication, am-ple cash flow available to service debt. But Vivendi’s high EBITDA targets derived in large part from purchase accounting ef-fects (which are just one-time paper ad-justments that cannot readily translate into free cash flow) .rather than profits from a company’s business operations (which reflect actual earnings that may translate into free cash flow). And al-though purchase accounting was the re-quired accounting technique at the time, Plaintiffs submitted evidence that Vivendi emphasized EBITDA growth to the public because financial analysts, to say nothing of the average investor, “w[ould] not have it easy to track the purchase accounting benefits” and the degree to which they contributed to Vivendi’s EBITDA figures. J.A. 4169. Hannezo at one point referred to purchase accounting benefits as “ac-counting magic” and acknowledged that Vivendi met its EBITDA growth targets thanks to purchase accounting benefits. J.A. 4119; see Trial Tr. 1348-50. ■

Further, investors did not digest Viven-di’s statements about EBITDA growth in a vacuum. During the Class Period, Viven-di also made numerous statements about, for example, its cash flow and its debt. Whether misleading or not when made, such statements strongly suggested that Vivendi faced no liquidity risk at the time. Given that Vivendi was in a phase of in-tense buying, moreover, any investor at-tuned to Vivendi’s pattern of behavior would be keen to know whether and how Vivendi was making sufficient profits to translate into cash flow that would cover all of Vivendi’s sundry debt obligations. We find the evidence introduced at trial .sufficient to support the jury’s conclusion that a reasonable investor could find Vi-vendi’s statements about high EBITDA growth misleading for omission to disclose Vivendi’s liquidity risk.

We need not detail the evidence in sup-port of the jury’s verdict with respect to each of the remaining alleged misstate-ments. It suffices to highlight a represen-tative sample of statements:

• On December 19, 2000, Vivendi stat-ed in a press release that, on a Janu-ary 1, 2001 pro forma basis, Vivendi would “be free of debt in its commu-nications businesses, yet ... have a free cash flow of more than 2 billion euros for the two coming years.” Special App’x 315 (Statement 2). Two weeks later, Hannezo expressed to Messier his “belie[f] that it is wrong to reason ... in terms of free cash flow (there won’t be any this year).” J.A. 3952.
• On January 12, 2001, Vivendi stated in a 6-K SEC filing that “[tjhanks to our free net cash flow and the oppor-tunities -to dispose of some holdings, such as our stake in BSkyB, we will have an additional war chest of 10 billion euros for 2001-2002 before the first euro of debt, and without the creation of new shares. That means we will have the resources to pursue the growth of our businesses in an especially healthy and efficient way.” Special App’x 315 (Statement 3). Two days earlier, however, Hannezo [iad informed Messier that it was “wrong to reason ... in terms of free cash flow.” J.A. 3952.
• On June 26, 2001, Vivendi stated in a 6-K SEC filing that it “posted rec-ord-high net income” and had “cash ■ available for investing.” Special App’x 318 (Statement 12) (emphasis omitted). In the same filing, Vivendi also emphasized “the strength of [its] cash flow.” Id. (Statement 13) (em-phasis omitted). In contrast, a Viven-di employee testified that “beginning in June 2001,” Dupont-L’Hótelain “expressed concerns over the cash situation, the liquidity situation,” and noted “the shortage in cash inside Vivendi.” J.A. 2512.
• On September 25, 2001, Vivendi stat-ed that “[f]or the first half [of] 2001, • operating free cash flow was more than 500 million euros (excluding en-vironment),” meaning that “[f]or the first time, cash flow is breaking even after financial costs, taxes and re-stricting costs.” Special App’x 321 (Statement 19). According to a Vi-vendi employee, during this time (“between June and October of 2001”), Dupont-L’Hótelain “often” discussed “the shortage in cash in-side Vivendi,” and Hannezo even not-ed “two or three times” that if Viven-di’s “path ... continue[d], [Vivendi would] be near bankruptcy.” J.A. 2512-13.
• On February 6, 2002, a Reuters arti-cle indicated that Vivendi (through Messier) stated the following: “*Is there any major uncertainty about our level of debt? No. *Are there any hidden off-balance sheet transactions that could cause any particular fears or risks? No_There are no hid-den risks_” Special App’x 324-25 (Statement 35); see also J.A. 4719. Two days later, however, Hannezo informed Messier that “[c]ompared to its peers[,] and particularly if the market begins to disregard EBIT-DA,” Vivendi “has a big problem,” including “free cash flow” difficulties and “overleverage.” Trial Tr. 7346. Hannezo also stated that “although Vivendi’s rival, AOL Time Warner, had impressive cash flows, Vivendi’s was around zero.” Id.
• On June 26, 2002, Vivendi issued a press release stating that “[o]wing to its strong free cash flow, combined with the execution of the disposals program and potential bond issues, [Vivendi] is confident of its capacity to meet its anticipated obligations over the next 12 months.” Special App’x 330 (Statement 56). Two days earlier, on June 24, 2002, Goldman Sachs, in response to a request by Vivendi’s board to analyze Vivendi’s liquidity situation, explained to Vi-vendi’s board that one of four possi-ble scenarios is that Vivendi would have to file for bankruptcy protection as early as September. Soon thereaf-ter, Edgar Bronfman, Jr., whose family was one of Vivendi’s largest shareholders at the time, wrote that Vivendi’s situation was a “matter of the gravest concern” and that Viven-di “must install ... new management right away to take charge of convincing the banks to extend some credit while we sell some of our as-sets to avoid bankruptcy. We have no time. Our board must act tomorrow without fail. Our company may fail, and we have not one minute more to waste.” Trial Tr. 7361.

The jury’s finding that these (and all of the fifty-six relevant) alleged misstate-ments were materially false or misleading was supported by sufficient evidence. To be clear, we do not foreclose the possibility that in a different case, a set of alleged misstatements will cover such varied and sundry territory that a single theory of fraud will not adequately encompass all of the statements. We merely conclude that, on the facts of this case, there is sufficient evidence to support the jury’s finding that a reasonable investor could find each of the alleged misstatements false or mislead-ing in context with respect to Vivendi’s liquidity risk, and that this risk was not so amorphous, in this case, to be categorically inactionable for purposes of a theory of liability.

III. Expert Testimony

Vivendi next asserts that the district court abused its discretion in admitting the testimony of Plaintiffs’ expert, Dr. Nye, on loss causation and damages. Under Federal Rule of Evidence 702, which governs the admissibility of expert testimony, an expert with “specialized knowledge [that] will help the trier of fact” may testify so long as that testimony is “based on sufficient facts or data” and “is the product of reliable principles and methods” that the witness has “reliably applied ... to the facts of the case.” The proponent of the expert testimony bears the burden of establishing these admissibility requirements, and the district court acts as a “gatekeeper” to ensure that the “expert’s testimony both rests on a reliable foundation and is relevant to the task at hand.” United States v. Williams, 506 F.3d 151, 160 (2d Cir. 2007) (quoting Daubert v. Merrell Dow Pharms., Inc., 509 U.S. 579, 597, 113 S.Ct. 2786, 125 L.Ed.2d 469 (1993)).

“The district court has broad discretion to carry out this gatekeeping function,” and “[i]ts inquiry is necessarily a ‘flexible one.’ ” In re Pfizer Inc. Secs. Litig., 819 F.3d 642, 658 (2d Cir. 2016) (quoting Daubert, 509 U.S. at 594, 113 S.Ct. 2786). “We therefore review both the district court’s ‘ultimate reliability determination’ and its decision about ‘how to determine reliability’ for abuse of discretion.” Id. (quoting Kumho Tire Co. v. Carmichael, 526 U.S. 137, 142, 119 S.Ct. 1167, 143 L.Ed.2d 238 (1999)).

Consistent with what has now become “standard operating procedure in federal securities litigation,” Nye performed an event study to determine whether, and the extent to which, Vivendi’s stock price was artificially high (ie., inflated) during the Class Period due to the market’s misap-prehension of Vivendi’s true liquidity risk. United States v. Gushlak, 728 F.3d 184, 201 (2d Cir. 2013); see also FindWhat Inv’r Grp. v. FindWhat.com, 658 F.3d 1282, 1313 n.31 (11th Cir. 2011) (“The methodology of event studies has been sus-tained by many circuits.”). In a typical' event study, an expert “disentangle[s] the effects of two types of information on stock prices—information that is specific to the firm under question ... and information that is likely to affect stock prices market-wide.” Mark L. Mitchell & Jeffry M. Net-ter, The Role of Financial Economics in Securities Fraud Cases: Applications at the Securities & Exchange Commission, 49 Bus. Law. 646, 556-57 (1994). The ex-pert then identifies which “information ... caused notable changes in the price of [a company’s] securities]” and the magnitude of those changes. J.A. 853; see also In re Pfizer Inc., 819 F.3d at 649. Thus, an event study can help an expert determine whether, and the extent to which, the release of certain information caused a stock price to fall. See id. at 649-50. This, in turn, allows an expert to make inferences about the degree to which the company’s stock price may have been artificially inflated on the basis of the market’s misconception as to the truth prior to the release of that infor-mation. See id.

The first step for Nye was to identify changes in Vivendi’s stock price during the Class Period that could not be attributed to general market dynamics, but were unique to Vivendi, called “residual re-turns.” J.A. 856. Nye began by analyzing the normally observed correlation between Vivendi’s stock price and market- and in-dustry-wide trends over the course of a benchmark “control period.” Identifying this correlation made it “possible [for Nye] to predict,” for each day of the Class Peri-od, the “predicted return” on Vivendi’s stock, ie., “what the i-eturn of [Vivendi’s] security should [have] be[en]” on the basis of the normally observed correlation. In re Pfizer, 819 F.3d at 649 (quoting Daniel R. Fischel, Use of Modern Finance Theory in Securities Fraud Cases Involving Actively Traded Securities, 38 Bus. Law. 1, 18 (1982)); see also J.A. 856. Nye then calcu-lated, for each day of the Class Period, the “actual return” on Vivendi’s stock, ie., the amount that the company’s stock price ac-tually changed. Id. The residual return on any given day, then, was simply the difference between the actual return and the predicted return.

Thus, because the residual returns equal the predicted returns subtracted from the actual returns, they factored out the market- and industry-wide effects cap-tured by predicted returns. In other words, the residual returns Nye calculat-ed, as he explained it, isolated the varia-tions in Vivendi’s stock price that were specific to Vivendi, rather than reflective of fluctuations affecting the entire market or the industry in which Vivendi operated. A positive residual return on any given day generally implied that good news about Vivendi emerged, and that the stock price went up accordingly. On the flipside, a negative residual return on any given day generally implied that negative infor-mation about Vivendi issued that day.

After identifying the residual returns that were statistically significant, Nye then attempted to isolate the residual returns that could be attributed to information re-lated to Vivendi’s liquidity risk, rather than other information related to Vivendi but unrelated to liquidity. To do this, Nye reviewed more than 16,000 documents to determine whether the information re-leased in .the market about Vivendi on any particular day had to do with Vivendi’s liquidity risk. His analysis yielded a list of days on which there was either a positive or negative residual return associated with information bearing on Vivendi’s liquidity risk.

The final relevant list included nine “negative” residual return days and one “positive” residual return day. As Nye tes-tified, the nine negative-return days were days on which negative news about Viven-di’s liquidity risk came out and resulted in inflation dissipating from Vivendi’s stock price. The one positive-return day, mean-while, was a day on which positive news pertaining to Vivendi’s liquidity came out and inflation in Vivendi’s stock price in-creased. The sum"of the nine negative-return days, offset by the one positive-retúrn day, came to €22.52. This amount, Nye concluded, was the maximum loss that investors suffered due to the market’s lack of knowledge about Vivendi’s true liquidity risk, which is to say the maximum artificial inflation that entered Vivendi’s stock price and subsequently dissipated as the market found out' about the truth.

Inflation reached its highest point, Nye believed,. around December 13, 2001. As far as the market knew at that time, Vi-vendi had doubled down on statements about Vivendi’s growth projections, but in-side the company, Vivendi employees viewed the company’s liquidity situation as dangerous and Hannezo was telling Messier that a credit-downgrade would lead to a liquidity crisis. Thus, in Nye’s opinion, De-cember 13, 2001 was when “the discrepan-cy between what the market knew and what Vivendi knew was at its widest.” Trial Tr. 3577.

If what goes up must come down, as the saying goes, then (Nye assumed) what came down must have gone up. In other words, the artificial inflation that dissipated from Vivendi’s stock price must have entered into the price in the first place. See Glickenhaus & Co. v. Household Int'l, Inc., 787 F.3d 408, 415 (7th Cir. 2015) (“The best way to determine the impact of a false statement is to observe what happens when the truth is finally disclosed and use that to work backward, on the assumption that the lie’s positive effect on the share price is equal to the additive inverse of the truth’s negative effect.”).

A key question was how that inflation entered the stock or, more aptly, when. Given that the maximum amount of inflation in the stock was €22.52, one approach to determining how inflated the stock price was throughout the Class Period would have been to say that all €22.52 of inflation entered into Vivendi’s stock price from the very beginning of that period, on October 30, 2000, and remained at that level until the date of the first negative residual re-turn, January 7, 2002. There is an obvious downside to this approach, however. Namely, the full amount of the inflation reflects the value of the truth about Viven-di’s liquidity problem at the apex of that problem. But the magnitude of Vivendi’s liquidity risk—and by extension, the amount of liquidity-related inflation in Vi-vendi’s stock—presumably had not reached its peak at the start of the Class Period. Rather, it grew over time as Viven-di’s liquidity situation worsened, and as the distance between the truth and the deception thus widened. Ascribing the full value amount of loss to the very first alleged misstatement would therefore tend to overstate the degree to which Vivendi’s stock was inflated due to the market’s lack of knowledge about Vivendi’s true liquidity risk, at least toward the beginning of the Class Period. Such an approach might thus lead to an inflated recovery for class mem-bers who purchased the stock earlier in the Class Period.

A better method, Nye reasoned, would be to model inflation as increasing over time—that is, as the magnitude of Viven-di’s liquidity risk grew—and reaching its maximum point on December 13. But pre-cisely because the market was not privy to the full extent of Vivendi’s liquidity risk, or so Plaintiffs alleged, the scope of that li-quidity risk had no direct measure. With-out a direct measure, Nye turned to poten-tial proxy measures. He examined three quantitative proxies for the magnitude of Vivendi’s true liquidity risk at any given time and considered how well each one might approximate the inflation trajectory over the relevant period. Observing that all three “followed similar paths over time, and matched qualitative descriptions of [Vivendi’s] accelerating debt and liquidity problems over time,” Nye selected as a proxy the most conservative of the proxy candidates: the increasing degree to which purchase accounting benefits contributed to Vivendi’s EBITDA figures. J.A. 864-65. Because Vivendi reported EBITDA fig-ures on a quarterly basis, Nye’s model of inflation showed inflation increasing step-wise on such a basis.

It is important to emphasize that, al-though Nye calculated the artificial inflation in Vivendi’s stock that was due to the market’s misapprehension about Vivendi’s true liquidity risk, his analysis did not purport to prove that that misapprehension was caused by Vivendi’s alleged fraud. Artificial inflation is not necessarily fraud-induced, for a falsehood can exist in the market (and thereby cause artificial inflation) for reasons unrelated to fraudulent conduct. See Glickenhaus, 787 F.3d at 418. Nye did not measure inflation actually caused by Vivendi’s alleged fraud nor “as-sume[] that [Vivendi’s] share price was inflated due to misrepresentations,” Id.

It was up to the jury to determine how much, if any, of the artificial inflation iden-tified by Nye was caused, by Vivendi’s alleged fraud (and thus by the various statements Vivendi released in the rele-vant period), by assessing the alleged mis-statements and their connection to the misconception in question. Nye’s analysis merely operated on the assumption that Plaintiffs would be able to prove at trial all the necessary elements to succeed on their private 10b-5 action.

Because Nye determined the amount of artificial inflation due to the market’s lack of information about Vivendi’s true liquidity risk, without reference to whether that inflation was a result of Vivendi’s alleged misstatements, Nye’s testimony did not depend on the specific identification of the fifty-seven alleged misstatements that Plaintiffs later identified at the close of trial. By design, then, Nye’s testimony did not exhibit any obvious correlation be-tween the inflation increases identified by Nye and the timing of the fifty-seven statements. Though fifteen of the fifty-seven statements issued on days where, under Nye’s model, inflation increased, such correlation was not something Nye himself sought to prove. And to the degree that the remaining forty-two statements were not associated with an immediate increase in inflation, under Nye’s model, that would not obviously affect Nye’s own testimony.

Nevertheless, according to Vivendi, the fact that these forty-two statements did not directly correlate with specific increas-es in inflation made Nye’s testimony unre-liable. Vivendi asserts that the securities laws require an alleged misstatement to have a “price impact,” and that no such impact exists with respect to these forty-two statements. Vivendi Br. 72. To salvage Nye’s testimony from this supposed legal deficiency, Vivendi continues, the district court had to fabricate an erroneous inflation “maintenance” theory. That theory, as Vivendi frames it, posits that statements that merely maintain inflation already ex-tant in a company’s stock price, but do not add to that inflation, nonetheless affect a company’s stock price. Vivendi urges us to hold that this purportedly newfangled the-ory violates the securities laws, and that because Nye’s testimony necessarily rests on the theory, the district court abused its discretion in admitting it.

We begin with an assessment of Vivendi’s argument that a statement must be associated with an increase in inflation to be actionable, before turning to what relevance, if any, such an argument had to the district court’s decision to admit Nye’s testimony. The “price impact” requirement to which Vivendi refers arises in the context of “transaction causation,” or “reliance,” the element of a private § 10(b) action that asks whether there is “a proper ‘connection between a defendant’s misrepresentation and a plaintiffs injury,’” or, framed more specifically, whether the fraud affected “the investor’s decision to engage in the transaction.” Erica P. John Fund, Inc. v. Halliburton Co., 563 U.S. 804, 810,131 S.Ct. 2179-12,180 L.Ed.2d 24 (2011) (“Halliburton I”) (quoting Basic, 485 U.S. at 243,108 S.Ct. 978). “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 a common stock—based on that specific misrepresentation.” Id. at 810, 131 S.Ct. 2179. But because “limiting proof of reliance [to the traditional method] “would place an unnecessarily unrealistic evidentiary burden on the Rule 10b-5 plaintiff who has traded on an impersonal market,’ ” id. (quoting Basic, 485 U.S. at 245,108 S.Ct. 978), the Supreme Court has established a rebuttable presumption of reliance under which courts may “assume ... that an investor relies on public misstatements whenever he ‘buys or sells stock at the price set by the market,’ ” id, (quoting Basic, 485 U.S. at 244, 247, 108 S.Ct. 978).

“Price impact” simply concerns “whether the alleged misrepresentations affected the market price in the first place.” Id. at 814, 131 S.Ct. 2179. If they do not affect the stock price, then there is “no grounding for any contention that investors indirectly relied on those misrepresentations through their reliance on the integrity of the market price.” Amgen, 133 S.Ct. at 1199. Defendants can therefore attempt to rebut the presumption of reliance by introducing “evidence that the misrepresentation did not in fact affect the stock price.” Halliburton Co. v. Erica P. John Fund, Inc., — U.S.—, 134 S.Ct. 2398, 2414,189 L.Ed.2d 339 (2014) (“Halliburton II”).

In distinguishing between inflation intro-duction and inflation maintenance, Vivendi contends that statements that introduce new inflation actually affect a company’s stock price, while statements that merely maintain inflation have no impact. And the reason they have no “price impact” is be-cause the “preexisting inflation would have persisted” had the defendant who made those inflation-maintaining statements “simply remained silent” as was the defen-dant’s right in the absence of a duty to disclose. Vivendi Reply Br. 33. Thus, Vi-vendi’s objection to the idea that a statement may cause inflation by maintaining it (rather than by increasing it) rests on two premises: that the maintained inflation would have remained if Vivendi had simply remained silent; and that Vivendi had the option of remaining silent even though it in fact chose to speak. Both premises are problematic.

First, contrary to Vivendi’s implication to the contrary, it is not necessarily the case that preexisting inflation indeed re-mains in a company’s stock price in the face of that company’s silence, either in a circumstance where the stock is inflated because the market arrived at a miscon-ception on its own or a case in which inflation may itself be traced to a prior fraudulent statement. Perhaps, in the face of silence, inflation could have remained unchanged. But it also could have plum-meted rapidly, or gradually, as the truth came out on its own, no longer hidden by a misstatement’s perpetuation of the miscon-ception. Alternately, inflation (or, really, the market’s continued belief in the mis-conception) could have dissipated gradually because the defendant’s silence in the face of escalating concerns on a particular subject would have all but amounted to an admission. The important point is that the defendant’s alleged misstatement, in a sce-nario where, as here, the defendant does not remain silent, prevents the market from discovering which of these scenarios, among other relevant scenarios, would have materialized had the defendant said nothing at all. In light of the dubiousness of the premise that inflation would have continued in the face of silence, it becomes evident that Vivendi has framed the effect of a given affirmative material misstatement in the context of preexisting inflation improperly. It is far more coherent to con-clude that such a misstatement does not simply maintain the inflation, but indeed “prevents [the] preexisting inflation in a stock price from dissipating.” FindWhat, 658 F.3d at 1317 (holding that “defen-dants whose fraud prevents preexisting in-flation in a stock price from dissipating are just as liable as defendants whose fraud introduces inflation into the stock price in the first instance”).

In short, it is hardly obvious that had Vivendi remained silent, the market would indeed have maintained its rosy perception of Vivendi’s liquidity state. Even were that not so, however, Vivendi’s attack on the so-called inflation-maintenance theory suffers from a greater deficiency: in suggesting that, had it remained silent, the misconception-induced (whether or not fraud-in-duced) inflation would have persisted in the market price, Vivendi assumes it is even relevant what would have happened had it chosen not to speak. Yet in framing the argument this way, Vivendi misunder-stands the nature of the obligations a com-pany takes upon itself at the moment it chooses, even without obligation, to speak. It is well-established precedent in this Cir-cuit that “once a company speaks on an issue or topic, there is a duty to tell the whole truth,” “[e]ven when there is no existing independent duty to disclose infor-mation” on the issue or topic. Meyer v. Jinkosolar Holdings Co., Ltd., 761 F.3d 245, 250 (2d Cir. 2014); see also Caiola v. Citibank, N.A., N.Y., 295 F.3d 312, 331 (2d Cir. 2002) (“[T]he lack of an independent duty [to disclose] is not ... a defense to ... liability[,] because upon choosing to speak, one must speak truthfully about material issues.”). That is because, at the moment the company chooses to speak, it takes upon itself the obligation to speak truthfully, and it is the breach of that obligation which forms the basis for the § 10(b) claim. Framed as such, it becomes clear that, once a company chooses to speak, the proper question for purposes of our inquiry into price impact is not what might have happened had a company re-mained silent, but what would have hap-pened if it had spoken truthfully. And there is little need to speculate what would have happened to the inflation in Vivendi’s stock price had it released to the public not a rosy picture of its liquidity state, but the misgivings its executives were sharing behind the scenes.

Vivendi’s -argument thus rests on erro-neous principles that, once dispelled, make clear that it is hardly illogical or inconsis-tent with precedent to find that a statement may cause inflation not simply by adding it to a stock, but by maintaining it. Were this not the case, companies could eschew securities-fraud liability whenever they actively perpetuate (i.e., though affir-mative misstatements) inflation that is al-ready extant in their stock price, as long as they cannot be found liable for whatever originally introduced the inflation. Indeed, under Vivendi’s approach, companies (like Vivendi) would have every- incentive to maintain inflation that already exists in their stock price by making false or mis-leading statements. After all, the alterna-tives would only operate to the company’s detriment: remaining silent, as already noted, could allow the inflation to dissipate, and making true statements on the issue would ensure that the inflation dissipates immediately.

A hypothetical helps illustrate the point. Suppose an automobile manufacturer widely praised for selling the world’s safest cars plans to release a new model (“Model V”) in the near future. The market be-lieves that Model V, like all of the compa-ny’s previous models, is safe, or has no reason to think otherwise. In fact, the automobile manufacturer knows that Mod-el V has failed crash test after crash test; it is, in short, simply unfit to be on the road. To protect its stock price, however, the automobile manufacturer informs the market, as per routine industry practice, that Model V has passed all safety tests. When the truth eventually reaches the market, the automobile manufacturer’s stock price bottoms out.

In addition to potentially being liable for any number of things if Model V indeed makes it to the market, the automobile manufacturer has almost certainly commit-ted securities fraud. And the question of the automobile manufacturer’s liability for securities fraud does not turn on whether inflation moved incrementally upwards when the company represented to the mar-ket that the new model passed all safety tests. Nor does it rest on whether the market originally arrived at a misconception about the model’s safety on its own, or whether the company led the market to that misconception in the first place. “We decline to erect a per se rule that, once a market is already misinformed about a particular truth, corporations are free to knowingly and intentionally reinforce ma-terial misconceptions by repeating false-hoods with impunity.” FindWhat, 658 F.3d at 1317. “Defendants who commit fraud to prop up an already inflated stock price do not get an automatic free pass under the securities laws.” Id.

In rejecting Vivendi’s position that an alleged misstatement must be associated with an increase in inflation to have a “price impact,” we join in the Seventh and Eleventh Circuits’ conclusion that “theo-ries of ‘inflation maintenance’ and ‘inflation introduction’ are not separate legal catego-ries.” Glickenhaus, 787 F.3d at 418; FindWhat, 658 F.3d at 1316 (“There is no reason to draw any legal distinction be-tween fraudulent statements that wrong-fully prolong the presence of inflation in a stock price and fraudulent statements that initially introduce that inflation.” (emphas-es added)). Put differently, we agree with the Seventh and Eleventh Circuits that securities-fraud defendants cannot avoid li-ability for an alleged misstatement merely because the misstatement is not associated with an uptick in inflation.

All of that said, it is unclear how Vivendi’s “price impact” argument, even were it valid, bears on the question here: whether the district court abused its discretion in concluding that Nye’s testimony “rest[ed] on a reliable foundation and [was] relevant to the task at hand.” Williams, 506 F.3d at 160 (quoting Daubert, 509 U.S. at 597, 113 S.Ct. 2786). Nye’s model measured “ ‘actual inflation’—inflation due to investors not knowing the truth” about Vivendi’s liquidity risk. Glickenhaus, 787 F.3d at 418. And it identified the amount of inflation due to investors not knowing the truth “even if no false statement [was] ever model,] because investors might not know the truth for reasons other than false statements.” Id. at 417. This method of measuring actual inflation, without reference to the timing or nature of a defendant’s alleged misstatements, is commonly employed by experts who provide testimo-ny on loss causation and/or damages in securities-fraud cases. See, e.g., In re Pfizer, 819 F.3d at 649-52; Glickenhaus, 787 F.3d at 415-19; FindWhat, 658 F.3d at 1313-14.

Here, Nye’s testimony is relevant as to loss causation because the total amount of actual inflation that Nye identified is the maximum amount of loss potentially caused by Vivendi’s alleged misstatements; Nye’s testimony is also relevant as to dam-ages because Nye’s model of inflation over the course of the Class Period provides a means for calculating each Plaintiffs dam-ages. See Gushlak, 728 F.3d at 197 (ex-plaining that an investor’s damages are generally “equal to ‘the artificial inflation when the shares were purchased minus the artificial inflation when the shares were sold.’ ” (quoting Michael Barclay & Frank C. Torchio, A Comparison of Trading Models Used for Calculating Aggregate Damages in Securities Litigation, 64 L. & Contemp. Probs. 105,106 (2001))).

Vivendi’s “price impact” argument, if successful, would at most imply that Plaintiffs could not establish reliance with respect to some of the fifty-six relevant misstatements. But that would not render Nye’s testimony wholly irrelevant to loss causation or damages; nor would it transform Nye’s calculation of actual inflation into the product of unreliable principles or methods. See In re Pfizer, 819 F.3d at 661 (“The dispositive question [under Rule 702] is whether the testimony will assist the trier of fact ... not whether the testimony satisfies the plaintiffs burden on the ultimate issue at trial.” (quoting Ambrosini v. Labarraque, 101 F.3d 129, 135 (D.C. Cir. 1996))). Thus, even if Vivendi’s “price impact” argument were correct, it would not justify concluding that Nye’s testimony is sufficiently unreliable or unhelpful to the jury that the district court’s admission of that testimony constituted an abuse of discretion.

In any event, we do not accept Vivendi’s position that the “price impact” requirement inherent in the reliance element of a private § 10(b) action means that an al-leged misstatement must be associated with an increase in inflation to have any effect on a company’s stock price. A forti-ori Nye’s testimony did not have to show such an association for each alleged mis-statement in order to “rest[ ] on a reliable foundation and [be] relevant to the task at hand.” Williams, 506 F.3d at 160 (quoting Daubert, 509 U.S. at 597, 113 S.Ct. 2786). As Vivendi has identified no other convinc-ing reason why Nye’s testimony fails to satisfy these basic requirements, we con-clude that the district court did not abuse its discretion in admitting it.

IV. Loss Causation

Finally, we address Vivendi’s challenge to the sufficiency of the evidence to support loss causation. “Loss causation ⅛ the causal link between the alleged misconduct and the economic harm ultimately suffered by the plaintiff.’ ” Lentell v. Merrill Lynch & Co., 396 F.3d 161, 172 (2d Cir. 2005) (quoting Emergent Capital Inv. Mgmt, LLC v. Stonepath Grp., Inc., 343 F.3d 189, 197 (2d Cir. 2003)). In some respects, loss causation resembles the tort-law concept of proximate cause, which generally requires that a plaintiffs injury be the “ ‘foreseeable consequence’ ” of the defendant’s conduct. Emergent Capital, 343 F.3d at 197 (quoting Castellano v. Young & Rubicam, Inc., 257 F.3d 171, 186 (2d Cir. 2001)). But this traditional foreseeability test is “imperfect” in the § 10(b) con-text, for “it cannot ordinarily be said” that the alleged misstatements themselves, “as opposed to the underlying circumstance that is concealed or misstated” “cause[]” investors’ loss. See Lentell, 396 F.3d at 173. We thus clarified in Lentell that to establish loss causation, a plaintiff must show that “the loss [was a] foreseeable” result of the defendant’s conduct (ie., the fraud), “and that the loss [was] caused by the materialization of the ... risk” con-cealed by the defendant’s alleged fraud. Id.

Put more simply, proof of loss causation requires demonstrating that “the subject of the fraudulent statement or omission was the cause of the actual loss suffered.” Suez Equity, 250 F.3d at 95 (emphasis added). If “the relationship between the plaintiffs investment loss and the information misstated or concealed by the defendant ... is sufficiently direct, loss causation is established.” Lentell, 396 F.3d at 174. “[B]ut if the connection is attenuated, or if the plaintiff fails to ‘demonstrate a causal connection between the content of the alleged misstatements or omissions and the harm actually suffered,’ a fraud claim will not lie.” Id. (quoting Emergent Capital, 343 F.3d at 199).

Homing in on the phrase “materialization of risk” from Lentell, Vivendi con-tends that the loss that Plaintiffs sought to establish here was not a materialization of the risk concealed by Vivendi’s alleged misstatements. According to Vivendi, the risk that it allegedly concealed (ie., the risk of a liquidity crisis) must have materi-alized into a more significant problem (ie., an actual liquidity crisis) in order for Plaintiffs to show that Vivendi’s alleged fraud caused them loss. Since it is undis-puted that Vivendi’s liquidity risk “never materialized” into “an objective event such as bankruptcy, default, or insolvency,” Vi-vendi asserts that Plaintiffs cannot estab-lish loss causation. See Vivendi Br. 83-84 (emphasis omitted). We disagree.

Vivendi fails to appreciate that to show loss causation, it is enough that the loss caused by the alleged fraud results from the “relevant truth ... leakpng] out.” Dura Pharm., Inc. v. Broudo, 544 U.S. 336, 342, 125 S.Ct. 1627, 161 L.Ed.2d 577 (2005); cf. also id. at 344, 125 S.Ct. 1627 (“[T]he Restatement of Torts, in setting forth the judicial consensus [on what a party must show to demonstrate loss], says that a person who ‘misrepresents the financial condition of a corporation in order to sell its stock’ becomes liable to a relying purchaser ‘for the loss’ the purchaser sustains ‘when the facts ... become generally knowri and ‘as a result’ share value ‘depreciated.’ ” (emphasis added and all but first alteration in original) (quoting Restatement. (Second) of Torts § 548A, cmt. 6 (1977))). Although we have previously stated that a plaintiff can establish loss causation either by showing a “materialization of risk” or by identifying a “corrective disclosure” that reveals the truth behind the alleged fraud, see Carpenters Pension Trust Fund of St. Louis v. Barclays PLC, 750 F.3d 227, 233 (2d Cir. 2014); Omnicom, 597 F.3d at 513, our past holdings do not suggest that “corrective disclosure” and “materialization of risk” create fundamentally different pathways for proving loss causation, such that a specific corrective disclosure is the only method by which a plaintiff may prove losses resulting from the revelation of the truth. Indeed, Lentell itself understood “materialization of risk” as reflective of the principle that “to establish loss causation, [plaintiffs must show that a] ... misstatement or omission concealed something from the market that, when disclosed, negatively affected the val-ue of the security.” Lentell, 396 F.3d at 173 (emphases added). Whether the truth comes out by way of a corrective disclo-sure describing the precise fraud inherent in the alleged misstatements, or through events constructively disclosing the fraud, does not alter the basic loss-causation cal-culus.

That “corrective disclosure” and “mate-rialization of risk” are not wholly distinct theories of loss causation highlights the flaws of Vivendi’s position. Vivendi’s con-ception of loss causation would have the effect of insulating companies from securities-fraud liability whenever the thing con-cealed in a material misstatement never ripens from a mere risk to an out-and-out disaster—unless a specific corrective dis-closure issues.

A simple hypothetical helps bring into stark relief why Vivendi cannot be right that the Plaintiffs, short of pointing to explicit corrective disclosures, had to point to an event, such as a bankruptcy, to dem-onstrate loss causation in this case. Sup-pose that a company knows that it faces tremendous risk of bankruptcy, yet fraud-ulently informs the market that there is no risk of bankruptcy. Soon, the risk becomes too great to ignore, and a series of events indicating. that the company is on the verge of bankruptcy takes place: a major bank backs out of a potential loan agreement with the company; a large deal with another firm falls through after the other firm does due diligence into the company; the company rapidly sells off an abnormally large amount of its assets in an effort to raise capital; and so on. The company’s stock price sinks, indeed becomes all but valueless.

The company in this hypothetical lied about its risk of bankruptcy—a lie that was separate and distinct from any lie about whether the company actually filed for bankruptcy—and events revealing the truth about the company’s risk of bank-ruptcy caused investors to lose money. Yet, Vivendi would have us believe that, absent a specific corrective disclosure, the actual filing of bankruptcy is the necessary “materialization of risk” that must occur in order for the company to have caused in-vestors any loss under § 10(b). But whether the company caused loss to investors under § 10(b) does not turn on whether the company actually files- Chapter 11 at some poipt or manages to steer clear of bankruptcy at the last minute. “Fraud de-pends on.the state of events when a statement is made, not on what happens later.” Schleicher v. Wendt, 618 F.3d 679, 684 (7th Cir. 2010); see also Pommer v. Medtest Corp., 961 F.2d 620 (7th Cir. 1992) (“The securities, laws approach matters from an ex ante perspective: just as a statement true when made does not become fraudu-lent because things unexpectedly go wrong, so a statement materially false when made does not become acceptable because it happens to come true. Good fortune ... does not make the falsehood any the less material.” (citations omitted)).

Here, although no specific corrective disclosure ever exposed the precise extent of Vivendi’s alleged fraud, Plaintiffs’ theory of: loss causation nevertheless rested on the revelation of the truth. According to Plaintiffs, Vivendi’s alleged misstatements concealed its liquidity risk, and a series of events in the first half of 2002 made the truth about that liquidity risk come to light. According to Nye’s testimony on loss causation and damages, those events took place on nine days, when the following, news reached the market: (1) January 7, 2002 news that Vivendi sold 55 million of its treasury shares; (2) May 3, 2002 news that Moody’s downgraded Vi-vendi’s long-term senior debt to a notch above junk status; (3) June 21, 2002 news that Vivendi sold a stake in its subsidiary Vivendi Environnement, despite earlier statements that it would wait to sell; (4) June 24, 2002 news just three days later that Vivendi sold an even larger stake in Vivendi Environnement; (5) July 2, 2002 news that Moody’s downgraded Vivendi’s long-term senior debt to junk status, fol-lowed by S&P’s downgrade of Vivendi’s short-term senior debt; (6) July 3, 2002 news that Vivendi acknowledged its short-term liquidity problems and its €1.8 billion in obligations that were due that very month; (7) July 10, 2002 news that rating agencies cautioned that further down-grades were possible, and that French au-thorities had raided Vivendi’s Paris head-quarters to investigate possible securities fraud; (8) July 15, 2002 news that a mem-ber of Vivendi’s board of directors was urging Vivendi quickly to sell Canal+, which was not generating earnings as ex-pected; and (9) August 14, 2002 news that Vivendi planned to sell €10 billion in assets over the following two years, €5 billion of which it hoped to sell within just nine months.

There was ample evidence to support the jury’s finding of a “sufficiently direct” “relationship between the ... loss [that Plaintiffs suffered on these nine days] and the information misstated or concealed by [Vivendi].” Lentell, 396 F.3d at 174. To take just one example—Vivendi’s January 7, 2002 sale of 55 million treasury shares— Nye testified at trial that a treasury-share sale of such magnitude indicated to the market that Vivendi “need[ed] cash badly,” and that “academic economic literature ... inform[ed] [this] view.” J.A. 2768. Vivendi’s own witness, the company’s credit-rating liaison at the time of the transaction, testi-fied to the effect that there was “no question” that the sale implied to the market that Vivendi needed cash. J.A. 2770-71. This and other evidence presented at trial were sufficient for the jury to conclude that the nine events identified by Nye revealed the truth about Vivendi’s liquidity risk, and that concealment of “the subject” of Vivendi’s alleged misstatements—its li-quidity risk—was therefore “the cause of the actual loss suffered” by Plaintiffs. Suez Equity, 250 F.3d at 95 (emphasis added).

V. Plaintiffs’ Cross-Appeal

Plaintiffs set forth two additional con-tentions on cross-appeal, challenging prior judgments of the district court. Neither has merit.

Plaintiffs first maintain that, at the class certification stage, the district court improperly excluded certain foreign shareholders from the class based on a concern that some foreign courts may not give preclusive effect to a class judgment. We review a district court’s conclusions as to.whether the requirements of Federal Rule of Civil Procedure 23 were met, and in turn whether class certification was appropriate, for abuse of discretion. Gallego v. Northland Grp. Inc., 814 F.3d 123, 129 (2d Cir. 2016); In re Initial Public Offerings Secs. Litig., 471 F.3d 24, 31-32 (2d Cir. 2006). “That standard of review is deferential: the district court is empowered to make a decision—of its choosing— that falls within a range of permissible decisions, and we will only find ‘abuse’ when the district court’s decision rests on an error of law or a clearly erroneous factual finding, or its decision cannot be located within the range of permissible decisions.” Gallego, 814 F.3d at 129 (internal quotation marks omitted).

As an initial matter, the district court did not abuse its discretion when, in assessing whether the class action would be “superior to other available methods for fairly and efficiently adjudicating [a] controversy,” Fed. R. Civ. P. 23(b)(3), it considered whether a class judgment would be given preclusive effect in foreign courts. Concerns about foreign recognition of our judgments are reasonably related to supe-riority. As Judge Friendly recognized in Bersch v. Drexel Firestone, Inc., “if defen-dants prevail against a class[,] they are entitled to a victory no less broad than a defeat would have been,” and so the risk that a foreign court will not grant preclu-sive effect to a class judgment may, as it did in Bersch, counsel against the inclusion of some foreign claimants. 519 F,2d 974, 996-97 (2d Cir. 1975), abrogated in part on other grounds, Morrison v. Nat’l Austl. Bank Ltd., 561 U.S. 247, 130 S.Ct. 2869, 177 L.Ed.2d 535 (2010). It was therefore within the district court’s discretion to take that risk into account.

With respect to the district court’s ultimate determination to exclude some foreign shareholders on superiority grounds, it was Plaintiffs’ burden to establish, by a preponderance of the evidence, that its proposed class met the requirements of Rule 23. See In re Am. Int’l Grp., Inc. Secs. Litig., 689 F.3d 229, 237-38 (2d Cir. 2012); Myers v. Hertz Corp., 624 F.3d 537, 547 (2d Cir. 2010). We recognize that assessing superiority is a fact-specific inquiry, and we do not opine on how likely it must be that a foreign court will recognize a class judgment in order for Rule 23’s superiority requirement to be met. Here, however, Plaintiffs do not identify any evidence that they presented to the district court which suggested that foreign courts in the countries at issue would grant pre-clusive effect to a class judgment. The district court accordingly did not abuse its discretion in concluding that, except for shareholders from a few countries, Plaintiffs had not demonstrated superiority.

Plaintiffs’ second contention is that, after trial, the district court incorrectly dismissed claims by American purchasers of ordinary shares under Morrison v. Nat’l Austl. Bank Ltd., 561 U.S. 247, 130 S.Ct. 2869, 177 L.Ed.2d 535 (2010). Plaintiffs contend that (1) Vivendi forfeited any Morrison-based defense because it did not bring its motion to dismiss the claims until after trial, and (2) in any event, the district court should not have dismissed these claims because the purchasers incurred “irrevocable liability” within the United States, and thus were covered by § 10(b). We review the district court’s decision de novo. In re Air Cargo Shipping Sews. Antitrust Litig., 697 F.3d 154, 157 (2d Cir. 2012).

Vivendi did not forfeit its Morrison argument because, prior to Morrison, its motion was foreclosed by controlling precedent in this Circuit, and parties are not required to raise arguments “directly contrary to controlling precedent” to avoid waiving them. Hawknet, 590 F.3d at 92 (2d Cir. 2009); see also Holzsager, 646 F.2d at 796 (“[A] party cannot be deemed to have waived objections or defenses which were not known to be available at the time they could have first been made, especially when it does raise the objections as soon as their cognizability is made apparent.”). Here, before the Supreme Court decided Morrison in June 2010 (less than a month before Vivendi filed its motion), this Circuit’s conduct and effects tests were the “north star of [its] § 10(b) jurisprudence.” Morrison, 561 U.S. at 257, 130 S.Ct. 2869. In Morrison, the Supreme Court struck down those tests and made clear that § 10(b) applies only to “transactions in securities listed on domestic exchanges, and domestic transactions in other securities,” id. at 267, 130 S.Ct. 2869, thereby-providing, for the first time, a legal basis for Vivendi’s argument that the claims of American purchasers of ordinary shares were not covered by § 10(b). Vivendi ac-cordingly did not forfeit its right to seek dismissal of those claims under Morrison.

Plaintiffs also maintain that under this Court’s decision in Absolute Activist Value Master Fund Ltd. v. Ficeto, American purchasers of ordinary shares, and specifically those who acquired shares in the course of the three-way merger between Vivendi, S.A., Canal+, and Seagram, are protected by § 10(b) because they incurred “irrevocable liability” while present in the United States, 677 F.3d 60, 67 (2d Cir. 2012). We disagree. In Absolute Activist, we used the concept of “irrevocable liability” to determine what constitutes a “domestic purchase or sale” under Morrison. Id. at 67-68. We reasoned that when the “parties” to a transaction incur irrevocable liability in the United States, defined as “becoming] bound to effectuate the transaction” or “entering into a binding contract to purchase or sell securities,” the transaction is domestic and § 10(b) applies. Id. at 67. To the extent that Plaintiffs rely on the merger as the transaction at issue, the location of the Americans who acquired ordinary shares as a result of the merger, who Plaintiffs admit were not parties to it, is not relevant to the question of whether the merger qualifies as a “domestic purchase or sale.” Plaintiffs do not otherwise point to any evidence that the parties to the merger incurred irrevocable liability in the United States. The district court therefore appropriately determined that American purchasers of ordinary shares were not protected by § 10(b) under Morrison.

CONCLUSION

We have considered Vivendi’s remaining arguments, as well as Plaintiffs’ remaining cross-appeal arguments, and find them to be without merit. The partial judgment of the district court is therefore AF-FIRMED. 
      
      . Judge Richard J. Holwell presided over the trial. After he stepped down from the bench in 2012, the case was assigned to Judge Shira Scheindlin, who entered the order of partial final judgment from which Vivendi appeals.
     
      
      . Credit ratings are generally divided into "investment-grade” and “non-investment-grade,” the latter of which is sometimes re-ferred to as “speculative-grade” or "junk.” Moody's credit rating of Baa3 is its lowest rating in the investment-grade category, which is to say its lowest rating above junk status. See generally Moody’s Investment Ser-vice, Rating Symbols and Definitions (2016), https://www.moodys.com/sites/products/About MoodysRatingsAttachments/MoodysRating SymbolsandDefinitions.pdf.
     
      
      . For short-term debt, S&P’s A-3 rating is its lowest rating in the investment-grade catego-ry. See generally S&P Global, S&P Global Ratings Definitions (2016), https://www. standardandpoors.com/en_US/web/gues1/ article/-/yiew/sourceld/504352. .
     
      
      . For long-term debt, S&P’s BBB rating is its . second-lowest rating in the investment-grade category. See S&P Global, supra note 4.
     
      
      . Section 20(a) of the Exchange Act imposes “derivative liability on parties controlling per-sons who commit Exchange Act violations." Tongue v. Sanofi, 816 F.3d 199, 209 n.12 (2d Cir.2016). Accordingly, Plaintiffs only alleged § 20(a) claims against Messier and Hannezo.
     
      
      . Plaintiffs do not appeal this determination.
     
      
      . For instance, “a duty to disclose under [§ ] 10(b) [or Rule 10b—5] can derive from statutes or regulations that obligate a party to speak.” Stratte-McClure, 776 F.3d at 102.
     
      
      . Because a "pure omission” theory is rela- . tively uncommon in securities litigation, and also not strictly within the letter of Rule 1 Ob-5, courts often, to some confusion, use the term "omission” when referring to statements that fall under the second prong of Rule 10b-5. See, e.g., Ganino v, Citizens Utils. Co., 228 F.3d 154, 161 (2d Cir. 2000).
     
      
      . Specifically, when Judge Holwell solicited proposed verdict forms from both sides to-wards the close of evidence but before closing statements, Plaintiffs requested that the pro-posed verdict form not list specific state-ments, on the ground that including "numerous alleged subsidiary statements” would "break[] up” and "[f]ragment[ ] [Plaintiffs’ claim in [a] way [that] risks confusing and misleading the jury.” J.A. 1686. Plaintiffs wanted, instead, a straightforward verdict form that asked the jury simply to determine, with respect to each Defendant (Vivendi, Messier, and Hannezo), whether that Defen-dant "knowingly or recklessly ma[d]e materially misleading statements or omissions that " concealed liquidity risks at the company dur-ing the Class Period.” E.g., J.A. 1690.
     
      
      . Vivendi also argues that Plaintiffs’ suppos-edly belated identification of a specific set of statements violated the PSLRA’s requirement that "securities-fraud plaintiffs ... ‘specify each statement alleged to have been mislead-ing’ and ‘why the statement is misleading.’ ” Vivendi Br. 38 (emphasis in quoting source) (quoting 15 U.S.C. § 78u-4(b)(l)). This argument appears to assume what it seeks to prove: that the PSLRA’s so-called "specificity requirement,” as Vivendi terms it, Vivendi Br. 40, confines securities-fraud plaintiffs to the particular alleged misstatements identified in their complaint. We identify no such requirement in the PSLRA, which sets out certain pleading standards so as to prevent securities-fraud plaintiffs from filing costly securities class-action suits on the basis of a barely formed hunch, but nowhere binds such plain-tiffs to the precise set of alleged misstate-ments identified in their complaint through-out the entire course of litigation.
      Further, many, if not most, of the fifty-seven alleged misstatements were identified in Plain-tiffs' First Amended Consolidated Class Action Complaint, which Plaintiffs filed in November 2003. As for the remaining alleged misstate-ments included on the final jury verdict form, when the parties were engaged in discovery in 2007, Defendants submitted multiple sets of interrogatories asking Plaintiffs to "[i]deii-tify and describe each false statement, mis-leading statement and/or omission of material fact on which you are suing in this Consoli-dated Action.” B.g., J.A. 1944; J.A. 2055. De-fendants described Plaintiffs.' interrogatory re-sponses as "enormously detailed” documents that reflected the “great care” with which Plaintiffs "identif[ied] ... statements that they even conceivably thought that they m[ight] intend to pursue.” Trial Tr. 6673. And al-though a small handful of the alleged mis-statements on the final jury verdict form did not appear in the First Amended Consolidated Class Action Complaint or Plaintiffs’ interrog-atory responses, they were nonetheless de-tailed in Plaintiffs’ expert reports, which Vi-vendi received during discovery. See id. at 6737-38. We thus agree with the district court that Vivendi was “aware long before trial” both "that [Pjlaintiffs believed the fifty-seven [alleged misjstatements ... were misleading” and "why [P]laintiffs believed each of [those] statements was misleading.” In re Vivendi, 765 F.Supp.2d at 579.
     
      
      . Vivendi argues that these statements should not have been submitted to the jury, but does not contend on appeal that the district court was wrong to view the question whether a given statement was inactionable puffery as a fact one. Thus, we assume this to be the case, and we review the jury’s verdict in this regard for sufficiency of the evidence. See Gronowski v. Spencer, 424 F.3d 285, 291 (2d Cir. 2005) (“In reviewing the sufficiency of the evidence in support of a jury's verdict, we examine the evidence in the light most favorable to the party in whose favor the jury decided, drawing all reasonable inferences in the winning party's favor.”).
     
      
      . We consider here only Vivendi’s argu-ments that: (1) any forward-looking state-ments were accompanied by meaningful cau-tionary language, and (2) Plaintiffs failed to show that Vivendi made such statements with actual knowledge that they were false or mis-leading. To the extent that Vivendi contends that the statements are not material because they did not increase price inflation, we ad-dress that argument infra, in Part III.
     
      
      . The district court instructed the jury to determine whether any forward-looking statements were accompanied by meaningful cautionary language. It further noted in its opinion denying Vivendi’s renewed motion for judgment as a matter of law that "it was for the jury to determine whether the cautionary language accompanying any of the statements ... was sufficiently ‘meaningful.’ ” In re Vivendi, 765 F.Supp.2d at 567 n.45. Vivendi does not argue on appeal that the meaningfulness of the cautionary language in question was not a factual question (whether or not the district court could have or should have resolved it as a matter of law). As with puffery, we therefore treat the meaningfulness of the cautionary language here as a question of fact that the district court appropriately put to the jury to consider, and review the sufficiency of the evidence in support of the jury's determination.
     
      
      . Vivendi suggests in its reply brief that, in assessing whether there was sufficient evi-dence fpr any reasonable jury to find liability as to these purportedly forward-looking state-ments, we must defer to the impaneled jury’s answers, in special interrogatories, that Vi-vendi acted recklessly in making each of the fifty-seven statements. Our hands tied by these interrogatory -responses, the argument goes, we should limit our inquiry to whether there was sufficient evidence to find the state-ments not to be forward-looking, as plainly they cannot have been made with actual knowledge.
      As an initial matter, Vivendi does not clearly make such an argument, predicated on the special interrogatories, in its opening brief. See Vivendi Br. 56. Thus, the argument is waived. See JP Morgan Chase Bank v, Altos Homos de Mexico, S.A. de C.V., 412 F.3d 418, 428 (2d Cir. 2005) ("[Ajrguments not made in an appellant's opening brief are waived even if the appellant pursued those arguments in the district court_”).
      It is also without merit. As the Eleventh Circuit has observed, there is a fundamental distinction between an argument that the ac-tual jury’s verdict is internally inconsistent (and thus that the court should order a new trial), and an argument that the district court should grant a party judgment as a matter of law on the basis that there is insufficient evidence in the record to support any reasonable jury’s verdict against the movant. See Hubbard v, BankAtlantic Bancorp, Inc., 688 F.3d 713, 716 (11th Cir, 2012) ("When a court considers a motion for judgment as a matter of law—even after the jury has ren-dered a verdict—only the sufficiency of the evidence matters. The jury's findings are irrel-evant,” (citation omitted)); cf. United States v. Jespersen, 65 F.3d 993, 998 (2d Cir, 1995) (“[Wjhen reviewing the sufficiency of the evi-dence, the Supreme Court has made it clear that jury verdicts are not to be reviewed for consistency.”).
      A consistency challenge argues that the jury verdict itself is flawed—and we generally ask in assessing such a claim whether the jury’s findings are "ineluctably inconsistent,” an in-quiry that may require some examination of the record. Cash v. County of Erie, 654 F,3d 324, 343 (2d Cir. 2011) (quoting Munafo v, Metro. Transp. Auth., 381 F.3d 99, 105 (2d Cir. 2004)), Since the jury itself is capable of correcting such an inconsistency at the judge's behest, a party must raise a consisten-cy challenge before the district court dis-charges the jury, See id. at 342. Because suc-cess as to such a claim does not suggest that no reasonable jury could have found for the prevailing party, only that the verdict itself could not be reconciled internally, the remedy is not a directed verdict, but a new trial. See id. at 342.
      In contrast, a motion for judgment as a matter of law is not based on the jury’s ver-dict, but on the record established at trial. Such a motion must be made before the jury even renders a verdict (and can be granted at such a time in rare circumstances), and then renewed thereafter. See Chaney v. City of Or-lando, 483 F,3d 1221, 1228 (11th Cir. 2007) ("The fact that Rule 50(b) uses the word ‘re-new[ed]’ makes clear that a Rule 50(b) motion should be decided in the same way it would have been decided prior to the jury's verdict, and that the jury's particular findings are not germane to the legal analysis.”). And success on such a motion- results not in a new trial, but in a directed verdict in favor of the mov-ant—and thus reflects the court's assessment not that the jury has erred, but that the evi-dence could not support any jury in reaching a verdict against the movant. For these rea-sons, a judge, assessing a motion for judgment as a matter of law, looks only to the evidence in the record; she is not bound by a jury's answers in special interrogatories.
      To the degree that Vivendi indeed means to malee a consistency (rather than a sufficiency) challenge, that argument (as well as Vivendi’s argument that the findings of liability as to Vivendi, Messier, and Hannezo were inconsis-tent) was not timely made. See In re Vivendi, 765 F.Supp.2d at 550-52 (finding Vivendi waived any challenge to the verdict on consis-tency grounds by failing to timely object to the verdict); see also Anderson Grp., LLC v. City of Saratoga Springs, 805 F,3d 34, 46-47 (2d Cir. 2015). As to the sufficiency argument that is before us, we consider all the evidence in the record, and are not bound by the jury’s determination in special interrogatories that Vivendi acted recklessly in making the state-ments,
     
      
      . Hannezo qualified this statement at trial, testifying that it referred to his view that Vivendi would not have enough free cash flow “when it comes to buying things like Direct TV or EchoStar or Yahoo.” J.A. 2540-41.
     
      
      . Indeed, this broader attack echoes specific points made throughout the other challenges in this section. For instance, Vivendi argues that the amorphousness of "liquidity risk” necessarily rendered statements regarding or concealing such a risk inactionable opinions, See Vivendi Br. 51.
     
      
      
        . Nye holds an M.B.A. and a Ph.D. in fi-nance from Stanford University. He also owns an economic consulting group that frequently provides expert reports in securities litigation.
     
      
      . As the Seventh Circuit has explained:
      [T]here are two senses of “inflation.” One is "actual inflation”—¡just the difference be-tween the stock price and what the price would have been if the truth had been known; this is what the expert’s model measures. The other is "fraud-induced in-flation”—the difference between the stock price and what the price would have been if the defendants had spoken truthfully; this is what the jury determined using the model plus its findings regarding false statements. Before the first false statement is made, there is "actual inflation” in the stock price but no "fraud-induced inflation" because although the stock is overpriced, misrepre-sentations are not the cause.
      
        Glickenhaus, 787 F.3d at 418.
     
      
      . To be clear, we do not hold that all state-ments unassociated with an increase in inflation necessarily have a "price impact.” We merely hold that such statements do not, as Vivendi argues, categorically lack a "price impact.” Thus, we do not address whether there may be other reasons, not raised by Vivendi here, why some statements unassoci-ated with an increase in inflation do not affect a company’s stock price,
     
      
      . The only evidence that Plaintiffs identify is Vivendi’s suggestion in a prior brief that Can-ada typically grants preclusive effect to class judgments when there are a significant num-ber of Canadian class members. Plaintiffs do not contend that they informed the district court of this alleged admission, however, nor was the district court obligated to search the record for evidence that it was Plaintiffs’ bur-den to produce.
     