
546 F.3d 196 (2008)
TEAMSTERS LOCAL 445 FREIGHT DIVISION PENSION, FUND on its own Behalf and on behalf of all those Similarly Situated, Plaintiff-Appellant,
v.
BOMBARDIER INC., Bombardier Capital Inc., Bombardier Capital Mortgage Securitization Corp., Laurent Beaudoin, Brian Peters, Robert Gillespie, Lawrence F. Assell, Defendants-Appellees.
Docket No. 06-3794-cv.
United States Court of Appeals, Second Circuit.
Argued: March 13, 2008.
Decided: October 14, 2008.
*197 Joel P. Laitman (Samuel P. Sporn, Christopher Lometti, Kurt Hunciker, Jay *198 P. Saltzman, Frank R. Schirripa, on the brief), Schoengold Sporn Laitman & Lometti, P.C., New York, NY, for Plaintiff-Appellant.
Patrick M. McGuirk (A. Robert Pietrzak, Isaac S. Greaney, on the brief) Sidley Austin LLP, New York, NY, for Defendants-Appellees.
Before B.D. PARKER, and LIVINGSTON, Circuit Judges, and HALL, District Judge.[1]
B.D. PARKER, Jr., Circuit Judge:
Teamsters Local 445 Freight Division Pension Fund ("Teamsters"), lead plaintiffs in a putative securities class action, appeal from an interlocutory order of the United States District Court for the Southern District of New York (Scheindlin, J.). The district court concluded that Teamsters failed to satisfy the predominance requirement of Rule 23(b)(3), Fed. R. Civ. P, and denied its motion for class certification. We agreed to hear this interlocutory appeal to consider whether the district court applied the correct standard of proofthe preponderance of the evidence standardto this decision. This appeal also raises several ancillary issues: whether the district court made clearly erroneous factual findings in denying class certification; whether it was required to permit a full evidentiary hearing before employing a preponderance of the evidence standard; and whether it was obligated to allow additional class discovery before denying class certification. Finding no error in any of these areas, we affirm.

BACKGROUND
Bombardier, Inc. ("BI") is a Canadian corporation that manufactures and sells a variety of products, including aircraft, recreational vehicles, and locomotives. Bombardier Capital, Inc. ("BCI") is a wholly owned subsidiary of BI that was involved in financing and leasing mobile homes. Bombardier Capital Mortgage Securitization Corporation ("BCM"), a wholly owned subsidiary of BCI, packaged mobile home loans and sold them to the public as "the Certificates," the securities that are the subject of this litigation. $1.85 billion worth of Certificates were sold in seven separate offerings between 1998 and 2001, each secured by a distinct pool of mobile home loan contracts and mortgages. The Certificates were typically traded relatively infrequently and in large amounts by sophisticated institutional investors, such as Teamsters. In May 2002, Teamsters purchased $250,000 par value Series 2000-A Class A-2 Certificates for a total investment of $234,826.
In September 2001, BI, BCI, and BCM discontinued debt offerings secured by mobile home loans. In December 2002, the Series 2000A Certificates were downgraded to below investment grade. That same month, the Toronto Star and other papers reported that the price of BI shares had drastically fallen in 2002 in part due to "questions about [its] financing arm, [BCI]" and the National Post announced that BI "could take a goodwill writeoff of up to $2-billion," in order to "quickly clear up some of the most pressing challenges facing the company's lending unit."[2] In *199 March 2003, the Canadian Press reported that BI and BCI were downgraded to "under review, with negative implications" and that BI "warned of the prospect of major writedowns," and the Hamilton Spectator stated that "[n]on-cash writedowns will likely include [BCI], already written down in 2001."[3]
In February 2005, Teamsters sued. The Complaint alleges that from 1998 to 2001, senior management at BCM, BCI, and BI disregarded underwriting standards, regularly underwrote loans to borrowers who were not creditworthy, and purchased large quantities of facially defective and deficient mobile home loans. The Complaint alleges that these reckless underwriting practices caused escalating delinquency rates, which were systematically underreported. It contends that Certificate prices collapsed following the downgrades and the December 2002 and March 2003 disclosures. The Complaint further alleges that this conduct violated Sections 10(b) and 20(a) of the Securities Exchange Act of 1934, 15 U.S.C. § 78a et seq., and Rule 10b-5 thereunder, 17 C.F.R. § 240.10b-5.
In February 2006, Teamsters moved pursuant to Rule 23(b)(3) for certification of a class of all open market purchasers of the Certificates between February 7, 2000 and February 7, 2005. The appellees opposed principally on the ground that Certificate holders were not a proper Rule 23(b)(3) class because Teamsters could not adequately demonstrate that Certificate prices timely incorporated information material to the strength of the underlying collateral. The district court denied the motion. Teamsters Local 445 Freight Div. Pension Fund v. Bombardier, Inc., No. 05 Civ. 1898(SAS), 2006 WL 2161887 (S.D.N.Y. Aug.1, 2006). It identified the "decisive" question as whether Teamsters could show that class issues predominated over individual issues so that common proof could be used to establish the reliance element of their claim under Section 10(b) and Rule 10b-5. Id. at *4. Teamsters invoked the fraud-on-the-market doctrine as one theory of reliance. Id. at *5; see Basic Inc. v. Levinson, 485 U.S. 224, 242-49, 108 S.Ct. 978, 99 L.Ed.2d 194 (1988).[4] The district court concluded that the fraud-on-the-market presumption was only available if the Certificates were found to have traded in an "efficient" market, one that was "open and developed enough so that it quickly incorporate[d] material information into the price of the *200 security." Id. at *5. According to the district court, if Teamsters could "not avail itself of the presumption that investors relied on defendants' misrepresentations, the requirement that common issues predominate over individual issues [would] not be satisfied, and class certification [would] be denied." Id. at *1.
Believing that the standard of proof for analyzing Teamsters' evidence of market efficiency "ha[d] not been precisely defined," the district court determined that the preponderance of the evidence standard applied. Id. at *3, 9. It understood this Court's decision in Heerwagen v. Clear Channel Communications, 435 F.3d 219 (2d Cir.2006), to prescribe a binary standard of proof for Rule 23 issues. Teamsters, 2006 WL 2161887, at *4. The district court believed that a plaintiff was required to demonstrate by a "preponderance of the evidence" class certification issues that are "sufficiently independent of the merits to justify weighing the evidence," but to make only "some showing" of issues that are "effectively identical to the merits." Id. (internal quotation marks omitted). Finding that "the availability of a presumption [of reliance] is not a merits issue," the district court applied the preponderance of the evidence standard. Id. at *9.
The district court analyzed Teamsters' evidence of market efficiency according to five of the eight factors set forth in Cammer v. Bloom, 711 F.Supp. 1264 (D.N.J. 1989):(1) the average weekly trading volume of the Certificates, (2) the number of securities analysts following and reporting on them, (3) the extent to which market makers traded in the Certificates, (4) the issuer's eligibility to file an SEC registration Form S-3, and (5) the demonstration of a cause and effect relationship between unexpected, material disclosures and changes in the Certificates' prices. Teamsters, 2006 WL 2161887, at *6-7, 10-12. It found that two factorsthe average weekly trading volume of the Certificates expressed as a percentage of the outstanding shares and the filing of an SEC Form S-3 for each class of the Certificatessupported a finding of market efficiency. Id. at *10-11. However, the district court determined that the other three factors the existence of securities analysts following and reporting on the Certificates, the showing that market makers traded in them, and the demonstration of a causal relationship between the disclosure of material information about the Certificates and their pricesdid not. Id. at *10-12. Based on this analysis and other information available, the district court concluded that Teamsters failed to demonstrate by a preponderance of the evidence that the Certificates traded in an efficient market and therefore could not rely on the fraud-on-the-market presumption. Id. at *12. Because class members would have to prove reliance individually, the court determined that Teamsters could not satisfy Rule 23(b)(3)'s predominance requirement and class certification was denied. Id.
In August 2006, shortly after the district court entered its ruling, and after an eleven-month period of discovery that included a three-month extension, the district court stayed additional discovery. Teamsters then sought, and we granted, leave to appeal the denial of class certification.[5]See Rule 23(f), Fed.R.Civ.P. In December 2006, Teamsters asked the district court to lift the stay and to permit an additional six months of discovery to develop more proof that the Certificates traded in an efficient *201 market.[6] It argued that our decision in Miles v. Merrill Lynch & Co., (In re Initial Pub. Offerings Sec. Litig.), 471 F.3d 24 (2d Cir.2006) ("In re IPO"), which was issued after it had moved for class certification, established for the first time that the preponderance of the evidence standard applied to its Rule 23 evidence.
The district court denied the request. Teamsters Local 445 Freight Div. Pension Fund v. Bombardier, Inc., No. 05 Civ. 1898(SAS), at 8 (S.D.N.Y. Jan. 3, 2007) (order denying discovery request). It observed that the holding of In re IPO "was not wholly unanticipated" and that Heerwagen had already placed Teamsters "on notice that a court would likely apply the preponderance of the evidence test to any disputed issues of fact requiring resolution in order to make a determination as to class certification, unless that issue was `effectively identical' to a merits issue." Id. at 3-4, 6. It noted that Teamsters' request for additional discovery could have been made earlier and that the additional discovery requested was unlikely to cure the deficiencies in the class certification motion. Id. at 5-7.
In accepting Teamsters' appeal, we agreed to consider three questions: (1) whether the "some showing" or "preponderance of the evidence" standard of proof applies to the Rule 23 requirements in securities class actions; (2) whether the district court properly applied the preponderance of the evidence standard to Teamsters' evidence of predominance; and (3) whether the class should be certified because the district court overlooked evidence demonstrating that the Certificates traded in an efficient market, even under a preponderance of the evidence standard.

DISCUSSION
We review for abuse of discretion the district court's denial of class certification. In re IPO, 471 F.3d at 31. While we also apply the abuse-of-discretion standard to the ruling that Teamsters did not meet the predominance requirement of Rule 23(b)(3), we review for clear error the factual findings underlying the ruling, including the determination that the Certificates do not trade in an efficient market. Id. at 40-41. We review de novo any issues of law underlying the Rule 23 ruling, including the question of whether the district court applied the correct standard of proof. Id. We also review for abuse of discretion a district court's decision not to hold an evidentiary hearing and to deny further class discovery.[7]Id.; see also Wills v. Amerada Hess Corp., 379 F.3d 32, 41 (2d Cir.2004); Zappia Middle E. Constr. Co. Ltd. v. Emirate of Abu Dhabi, 215 F.3d 247, 253 (2d Cir.2000).

A. Standard of Proof for Rule 23 Requirements
In determining whether class certification is appropriate, a district court must first ascertain whether the claims meet the preconditions of Rule 23(a) of numerosity, *202 commonality, typicality, and adequacy. It may then consider granting class certification where it "finds that the questions of law or fact common to class members predominate over any questions affecting only individual members, and that a class action is superior to other available methods for fairly and efficiently adjudicating the controversy." Fed.R.Civ.P. 23(b)(3).[8] This appeal addresses a question that weaves through these various requirements of Rule 23: the standard of proof applicable to evidence proffered to meet them.
We addressed this very question shortly after the district court denied Teamsters' motion. In In re IPO, we "readily acknowledge[d]" that our caselaw up until that point "[had] been less than clear." In re IPO, 471 F.3d at 32. We set forth the following standards, among others, to govern class certification:
(1) a district judge may certify a class only after making determinations that each of the Rule 23 requirements has been met; (2) such determinations can be made only if the judge resolves factual disputes relevant to each Rule 23 requirement and finds that whatever underlying facts are relevant to a particular Rule 23 requirement have been established and is persuaded to rule, based on the relevant facts and the applicable legal standard, that the requirement is met; [and] (3) the obligation to make such determinations is not lessened by overlap between a Rule 23 requirement and a merits issue, even a merits issue that is identical with a Rule 23 requirement.
Id. at 41. We disavowed any implication in our earlier decisions that the "some showing" standard may apply to Rule 23 issues and required district courts "to assess all of the relevant evidence admitted at the class certification stage" when determining whether to grant a Rule 23 motion. Id. at 42.
The district court, which did not have the benefit of our decision in In re IPO, understood our decision in Heerwagen, 435 F.3d 219, to set forth two different standards of proof, depending on whether a given Rule 23 issue was "effectively identical to the merits." Teamsters, 2006 WL 2161887, at *4 (internal quotation marks omitted). It found that "[t]he use of a presumption to prove transaction causation is simply a procedural tool that allows a plaintiff to satisfy the predominance requirement of Rule 23(b)(3)." Id. at *9. Because the availability of the fraud-on-the-market presumption did not overlap with the merits, the district court applied the preponderance of the evidence standard to Teamsters' evidence regarding the efficiency of the Certificates' market. Id.
Although we did not use the words "preponderance of the evidence" in In re IPO to describe the standard of proof applicable to Rule 23 issues, we in effect required the application of a cognate standard by directing district courts "to assess all of the relevant evidence admitted at the class certification stage," to "resolve[] factual disputes relevant to each Rule 23 requirement," and "[to] find[] that whatever underlying facts are relevant to a particular Rule 23 requirement have been established," notwithstanding an issue's overlap with the merits. Id. at 41-42. Today, we dispel any remaining confusion and hold that the preponderance of the evidence standard applies to evidence proffered to establish Rule 23's requirements. The district *203 court therefore applied the correct standard.
Teamsters urges a different result for two principal reasons, neither of which is persuasive. It argues first that In re IPO "expressly repudiate[d]" our earlier endorsement of the preponderance of the evidence standard in Heerwagen, and second that we "adopted a middle ground, under which a District Judge is required to make preliminary findings on the class certification issues, but not to apply the preponderance of the evidence standard." Although In re IPO explicitly overruled our prior decisions in In re Visa Check/MasterMoney Antitrust Litig., 280 F.3d 124 (2d Cir.2001), and Caridad v. Metro-North Commuter R.R., 191 F.3d 283 (2d Cir.1999), it only overruled Heerwagen to the extent that the decision supported an application of the "some showing" standard to factual disputes relating to Rule 23 requirements. In re IPO, 471 F.3d at 42. Moreover, In re IPO did not establish any "middle ground" standard of proof. Teamsters makes much of our statement in In re IPO, where we characterized as dictum the statement in Heerwagen that "[c]omplying with Rule 23(b)(3)USFRCPR23's predominance requirement cannot be shown by less than a preponderance of the evidence." In re IPO, 471 F.3d at 37 (quoting Heerwagen, 435 F.3d at 233). This characterization was accurate. Without resolving the issue of the standard of proof actually applied by the district court, Heerwagen narrowly held that if the district court applied the preponderance of the evidence standard, it did not err because the predominance inquiry was sufficiently independent of the merits of the action. Heerwagen, 435 F.3d at 233. The accurate characterization of an endorsement of the preponderance of the evidence standard as dictum does not, however, establish a new, "middle ground" standard of proof. Teamsters similarly overstates the significance of a footnote in In re IPO, where we cast doubt on our comment in Heerwagen that "[i]f plaintiff had a lesser burden, then a motion to certify a Rule 23(b)(3) class would be granted despite the motion judge's belief that it is more likely than not that individual issues would predominate." In re IPO, 471 F.3d at 37 n. 8 (citing Heerwagen, 435 F.3d at 233). Our footnote merely limited what was essentially dictum in Heerwagen by observing that it overstated the adverse implications of applying a standard of proof less stringent than that of preponderance of the evidence.[9]In re IPO, 471 F.3d at 37 n. 8. Neither of the statements in In re IPO can bear the weight that Teamsters would place on them.
Second, Teamsters argues that the district court should not have applied the preponderance of the evidence standard without granting it the opportunity to conduct further discovery and a full evidentiary hearing on the issue of the efficiency of the Certificates' market. Teamsters did not request an evidentiary hearing in its motion for class certification, its withdrawn motion for reconsideration, or its motion *204 for leave to appeal to this Court. It nevertheless contends now that "[w]here a district court decides not to hold a `full blown evidentiary hearing,' as is the case here, the prima facie standard should be applied[,]" similar to what is employed when deciding issues of personal jurisdiction without an evidentiary hearing. It relies on our statement in In re IPO that "[t]he Rule 23 requirements are threshold issues, similar in some respects to preliminary issues such as personal or subject matter jurisdiction." Id. at 40.
We find this argument unconvincing. In requiring courts "to assess all of the relevant evidence admitted at the class certification stage," to "resolve[] factual disputes relevant to each Rule 23 requirement," and to "find[] that whatever underlying facts are relevant to a particular Rule 23 requirement have been established," we did not prescribe any particular way of proceeding. Id. at 41-42. To the contrary, we emphasized that district courts retain "ample discretion" to limit discovery and "the extent of the hearing" on Rule 23 issues "in order to assure that a class certification motion does not become a pretext for a partial trial of the merits." Id. at 41; see also Heerwagen, 435 F.3d at 233 (noting that "[t]he amount of discovery" granted on class certification issues "is generally left to the trial court's considerable discretion"). We require only that a court "receive enough evidence, by affidavits, documents, or testimony, to be satisfied that each Rule 23 requirement has been met." In re IPO, 471 F.3d at 41.
For the same reasons, we also deny Teamsters' request to remand to permit additional discovery on class certification issues in the event that the preponderance of the evidence standard is held to apply.[10] Teamsters waited four months after the district court's denial of its class certification motion and stay of discovery, and several months after we granted leave to appeal, to request additional discovery from the district court. Because it did not seek, and we did not grant, leave to appeal the district court's January 2007 decision denying the request, we are not required to consider whether additional discovery is warranted. In any event, we note that the district court's denial of the request did not abuse its broad discretion to direct and manage discovery. Wills, 379 F.3d at 41.

B. Factual Findings
Based on its consideration of five of the eight Cammer factors, the district court found that Teamsters failed to show by a preponderance of the evidence that the Certificates traded in an efficient marketone in which the prices of the Certificates incorporate most public information rapidlyand was therefore unable to rely on the fraud-on-the-market presumption of reliance. Teamsters, 2006 WL 2161887, at *10-12. Teamsters contends that the district court abused its discretion when determining that the Certificates traded in an inefficient market by making clearly erroneous factual findings relating to three Cammer factors: (1) that analysts did not cover or report on the Certificates, (2) that there were no firms making a market in the bonds, and (3) that the empirical data did not demonstrate a causal relationship between unexpected, material information and the Certificates' prices.[11]


*205 1. Analyst Coverage of the Certificates

According to Cammer, the existence of a number of financial analysts who report on a security supports a finding of market efficiency because it permits an inference that financial statements relating to a security are "closely reviewed by investment professionals, who ... in turn make buy/sell recommendations to client investors." Cammer, 711 F.Supp. at 1286; accord In re Xcelera.com Sec. Litig., 430 F.3d 503, 514 (1st Cir.2005) ("Both parties agree that the greater the number of securities analysts following and reporting on a company's stock, the greater the likelihood that information released by a company is being relied upon by investors.").
Teamsters argued to the district court that the "analyst coverage" factor supports a finding that the Certificates traded in an efficient market for two main reasons. First, its expert, Dr. Tavy Ronen, attested that forty-four individual analysts from twenty-eight firms specifically reported on BI during the class period. Ronen Supp. Aff. ¶ 21. She reasoned that "[s]ince the Certificates are backed by loans that were purchased by a division of Bombardier, Inc., and since analysts provided information on BI as a whole, including any material information on its divisions, Certificate investors had a strong base of information to draw upon in determining the price of the Certificates." Id. Ronen also attested that BI and BCI "were integrated in the servicing of the Certificates[,] and had arranged for financing into the Certificates," which meant that "any news affecting their financial health and hence ability to continue supporting/servicing these Certificates would be expected to impact the investors." Ronen Reply Aff. ¶ 22. Second, Ronen pointed to the fact that the three major bond rating agenciesFitch, Moody's Investors Service and Standard & Poor'srated the Certificates, which also helped Certificate prices reflect material information about BI and BCI. Ronen Supp. Aff. ¶ 21.
The appellees disputed these arguments. Their expert, Andrew Carron, contended that the activities of analysts who followed BI were irrelevant because the Certificates were not BI debt securities. Carron Aff. ¶ 39. He also argued that Teamsters failed to show that analysts specifically followed the Certificates themselves and criticized Ronen's reliance on rating agency activity. Id. Analyzing the frequency of transactions and average price of transactions in the Certificates on days following three specific instances in which the credit rating of the Certificates was changed, Carron concluded that "[e]ither there [is] insufficient data to determine whether the Certificate prices reflected the credit analyst coverage," or "Certificate prices did not react in a consistent manner, indicating that the market was not efficient." Carron Aff. ¶¶ 42-44, Ex. 11-12.
The district court found that "Teamsters... presented no evidence that analysts specifically followed the Certificates, the value of which is tied to the performance of the underlying mobile homes, and only incidentally to the performance of BI or its subsidiaries." Teamsters, 2006 WL 2161887, at *10. On this ground, the district court determined that a lack of analyst *206 coverage indicated that the market was inefficient. Id. We find no error in this determination. Contrary to Teamsters' claims, the district court did not disregard its evidence on this point. Rather, it acknowledged Ronen's opinion that the forty-four "analysts who followed BI followed the Certificates as well" because "BCI was servicing the collateral for the Certificates, and because BI financially supported BCI." Id. The district court simply found Ronen's account unpersuasive and instead accepted Carron's reasoning that there were no analysts who specifically followed the Certificates. Moreover, although the district court did not address the question of whether the three major bond rating agencies promoted the efficiency of the Certificate market in a manner akin to that of analysts reporting on equities, it was not required to do so in light of the compelling reasons in the record for rejecting such an analogy.[12]

2. Market Makers
Market makers promote the efficiency of a security's market because they "react swiftly to company news and reported financial results by buying or selling stock and driving it to a changed price level." Cammer, 711 F.Supp. at 1287. We begin with the SEC's definition of a "market maker" as
a dealer who, with respect to a particular security, (i) regularly publishes bona fide, competitive bid and offer quotations in a recognized interdealer quotation system; or (ii) furnishes bona fide competitive bid and offer quotations on request; and, (iii) is ready, willing and able to effect transactions in reasonable quantities at his quoted prices with other brokers or dealers.
17 C.F.R. § 240.15c3-1[c]8 (2006).
Teamsters made three main arguments in support of its claim that market makers for the Certificates existed. First, its expert opined that the lead underwriters of each class of the Certificates acted as market makers because the Certificates are analogous to equity IPOs. Ronen Supp. Aff. ¶ 24. Second, based on her analysis of trading records, Ronen concluded that a number of additional firms that were not underwriters also served as market makers. Id. Third, Joseph McAdams, the bond trader for Teamsters' investment advisor, testified that he "[felt] confident" that on any given day during the class period, he could have obtained a quote from any one of a number of broker-dealers. McAdams also testified that between 2002 and 2005, he "was aware of specific bids or offers" for the Certificates, and that he believed that "[t]here were six to seven dealers that ... have been and did continue to be active in the manufactured housing market."
The appellees, relying on Carron's affidavit, disputed the existence of market makers for the Certificates. He attested that a market maker is by definition an entity that "commit[s] to buy (bids) and to *207 sell (offers) the security at specified prices." Carron Aff. ¶ 46. Carron faulted Ronen's study identifying six non-underwriter market makers because it was based on transaction data that did not demonstrate that the firms actually made "active bids/offers." Id.
The district court concluded that Teamsters did not demonstrate that any firm "regularly publish[ed] bids and quotes for the Certificates," or that any firm "would furnish bids and quotes on request and ... would effect transactions for each Certificate." Teamsters, 2006 WL 2161887, at * 11. It also rejected Ronen's argument that the lead underwriter acted as a market maker for the Certificates because the Certificates were analogous to equity IPOs. Id. The district court believed that Teamsters should have, but did not, "independently" show that the Certificate market was efficient. Id.
This finding was not erroneous. The district court considered Teamsters' evidence and found that it failed to show that firms engaged in either of the two activities identified by the SEC as defining a market maker. Id. Although Ronen attested that both underwriters and non-underwriters made a market in the Certificates, according to Carron, the limited trading data on which her conclusion was based did not indicate that the firms actually furnished bids or quotes on request, or were ready, willing, and able to effect transactions in the Certificates. Moreover, although the district court did not mention McAdams' testimony on the issue of market makers, there was no need for it to do so. Nothing in his testimony compelled a finding that there were firms that actually furnished bids and offered quotations on request, or were prepared to effect transactions in the Certificates the way that market makers would have done.[13] Teamsters has not pointed us to evidence that would compel a different finding.[14]

3. Proof of Causation
Evidence that unexpected corporate events or financial releases cause an immediate response in the price of a security has been considered "the most important[] Cammer factor," In re Xcelera.com, 430 F.3d at 512, and "the essence of an efficient market and the foundation for the fraud on the market theory," Cammer, 711 F.Supp. at 1287. Without the demonstration of such a causal relationship, it is difficult to presume that the market will integrate the release of material information about a security into its price. An event study that correlates the disclosures of unanticipated, material information about a security with corresponding fluctuations in price has been considered prima facie evidence of the existence of such a *208 causal relationship. See, e.g., In re Xcelera. com, 430 F.3d at 512-14, 516.[15]
Teamsters proffered an event study prepared by its expert, which purportedly demonstrated that the release of unanticipated, material information in December 2002 and March 2003 was associated with subsequent fluctuations in Certificate prices and "excess" returns. Teamsters, 2006 WL 2161887, at *11; Ronen Supp. Aff. ¶ 27 & Ex. G. Ronen used prices for different classes of Certificates that were reported daily by the Financial Times ("FTIM prices") for the relevant portions of the study. Ronen Supp. Aff. ¶ 27; Ronen Reply Aff. ¶ 15(b). Unlike Certificate transaction prices, FTIM prices and other so-called "matrix" prices, are adjusted daily pursuant to proprietary models to reflect market conditions. Ronen offered the following justification for their use in the study:
[M]anually adjusted prices in the absence of public trading data are a meaningful indicator of market efficiency. Transaction prices for publicly traded instruments mostly incorporate information provided by analysts, who predict prices, earnings, and other pertinent information. Similarly, Bloomberg and other pricing services perform the role of analysts when there are no publicly available prices. Hence, their "indications" constitute a reasonable proxy for transaction prices, and an event study conducted on the basis of these prices is reasonable and meaningful.
Ronen Reply Aff. ¶ 15(b).
The appellees challenged the study on several grounds. First, their expert contended that the study was flawed because it sought to measure the impact of immaterial informationdisclosures about BIon Certificate prices. Carron Aff. ¶ 28. Second, Carron argued that the integrity of the study was impaired because it relied on Bloomberg prices for the Certificates rather than transaction prices. Id. ¶ 30. Contending that Bloomberg prices "are different from transaction prices," and that "[t]here is much greater variation in transaction prices than in Bloomberg prices," he concluded that "[to] conduct an event study using manually adjusted prices is unsound." Id. ¶¶ 30, 33.[16] Third, Carron contended that trading data for the Certificates contradicted the results of the event study because analysis of "all [of] the transactions in every tranche of the Certificates in the period from December 1, 2002 through March 31, 2003," revealed that "[t]he tranches were either not traded or there were no material price declines around the alleged disclosure dates." Id. ¶ 37.
The district court rejected Ronen's event study for two reasons. First, it faulted the purported use of Bloomberg prices, reasoning that
[b]ecause Bloomberg and other proprietary pricing services presuppose that security prices reflect information about the company (or, in this case, the Certificate collateral), these "prices" assume market efficiency. To use prices that assume market efficiency in an event study designed to determine whether or not that market is efficient is circular reasoning. Where Bloomberg prices materially differ from transaction prices, *209 as they do here, event studies must use transaction prices.
Teamsters, 2006 WL 2161887, at *11. Second, the district court criticized the study for measuring "price reactions to news solely concerning the financial health of BI, not its mortgage division," concluding that information about BI itself was not "sufficiently material" to the Certificates' collateral.[17]Id. After rejecting the event study, the district court found that Certificate transaction prices actually "reacted weakly to unexpected downgrades" of the Certificates, which demonstrated market inefficiency. Id. at * 12.
The district court erred when it found that the study used Bloomberg prices. It is clear that the pertinent portion of the event study exclusively used FTIM prices. See Ronen Reply Aff. ¶ 15(b). This error is not material in and of itself. If the district court meant to indicate that its first ground for rejecting the event study was the study's use of FTIM prices, we are uncomfortable with this conclusion. We believe the district court overlooked compelling evidence demonstrating that, notwithstanding material differences between FTIM and transaction prices, FTIM prices may be legitimately used in an event study. Ronen explained that because price changes are the focus of an event study, matrix prices may be used as long as they are shown to be consistent and reliable proxies for transaction prices. Ronen Reply Aff. ¶ 15(a), (e). Appellees never seriously challenged this argument. Ronen also provided well-conceived, empirical studies demonstrating that FTIM prices were consistent and reliable proxies because FTIM, Bloomberg, and transaction prices generally moved in the same direction during the months close to the disclosure dates studied.[18]See Ronen Reply Aff. ¶ 16, 19, Ex. 3-5. In light of this record, we believe it was unsound to conclude that the fact that there were material differences in the values of FTIM and transaction prices prohibited the use of FTIM prices in the study.[19]
The district court's ultimate determination that the event study did not support a finding of market efficiency was not clearly erroneous, however, because of the soundness of the second ground for its rejection of the study: the study's focus on the disclosure of information immaterial to the Certificates, principally news relating to BI. Teamsters, 2006 WL 2161887, at * 11. The disclosures made in December 2002 and March 2003, which were relied on by Teamsters' expert, refer to BI's "goodwill writeoff," the inclusion of BCI in these writedowns, and "the challenges facing [BI's] lending unit." The district court *210 was not compelled, however, to find that these disclosures conveyed material information to Certificate investors. The disclosures may have aptly highlighted the troubles of BI and suggested that BCI would be impacted as a result. None of them, however, connected these problems to the mobile home loans or contracts forming the Certificate collateral or suggested that projected BI writedowns would compromise BI or BCI's ability to extend credit to support the Certificates. Nor does Teamsters' contention that information released before the December 2002 articles primed the market so that the information conveyed in later disclosures was material to the Certificates. Since the district court correctly concluded that the disclosures studied were immaterial, any fluctuations in the Certificates' prices documented by the event study could not reasonably be interpreted to reflect market efficiency. Consequently, the district court did not err in rejecting the study as proof of causation.
Moreover, the district court's additional determination that the empirical data actually supported a finding of market inefficiency because "[t]here were no material price drops in the Certificates after they were downgraded below investment grade in December 2002 and February 2003" and because "transaction prices ... reacted weakly to unexpected downgrades" was well grounded in the record. Id. at * 12. Teamsters' contentions to the contrary that BI and BCI historically provided direct financial support to the Certificate collateral so as to preclude any Certificate price declines in reaction to downgrades and that there were nevertheless "precipitous price reactions a few days later when there was news of further anticipated substantial BI and BCI manufactured housing asset write-downs"are unsupported by the record.

4. Finding of Market Inefficiency
After analyzing the Cammer factors, the district court concluded that three of themthe absence of market makers for the Certificates, the lack of analysts following the Certificates, and the absence of proof that unanticipated, material information caused changes in the Certificates' pricesas well as the infrequency of trades in the Certificates "all tend to establish the inefficiency of the Certificate market" and prevent Teamsters from relying on the fraud-on-the-market presumption. Id. Teamsters challenges this conclusion on the ground that the district court ignored fundamental differences in the way stocks and bonds are traded.
We are mindful of one court's observation "that a comparison between equity and bond markets is a comparison between the proverbial apple and orange" and that
denying [the] application of fraud on the market to the bond market because it does not operate in the same way as a national exchange or trade in the same volume, frequency, or manner as equity on those exchanges is throwing out oranges because they are not apples.
In re Enron, 529 F.Supp.2d. at 755, 768. We conclude, however, that the district court properly used the Cammer factors as an "analytical tool," Unger v. Amedisys Inc., 401 F.3d 316, 325 (5th Cir.2005), and made no clear error in determining that Teamsters failed to show by a preponderance of the evidence that the Certificates traded in an efficient market. In view of this conclusion, we do not have occasion to address the nettlesome question of whether, for the purposes of determining the applicability of the fraud-on-the-market doctrine, an adjusted set of Cammer factors or even a different analytical approach altogether is better suited to analyze market *211 efficiency in securities cases arising from the sale of debt instruments.

CONCLUSION
The decision of the district court is affirmed.
NOTES
[1]  The Honorable Janet C. Hall, of the United States District Court for the District of Connecticut, sitting by designation.
[2]  Steve Maich, Scapegoat CEOs Bury a Bad Year: TD, Bell Clear the Decks, Nat'l Post, Dec. 27, 2002; Allan Swift, Turbulent Year for Quebec Inc. Changes Called Healthy, Toronto Star, Dec. 27, 2002; see also Bombardier Faces Bumpy Year: Quebec Hit Especially Hard By Painful Corporate Squeeze, The Halifax Daily News, Dec. 26, 2002; Quebec-Based Companies Undergo Shakeups: Restless Stockholders Put Pressure on Top for Change, Calgary Herald, Dec. 26, 2002; Allan Swift, Bombardier Faces Bumpy Year, Windsor Star, Dec. 26, 2002.
[3]  Allan Swift, Bombardier Shares Take Hit After Warning, Hamilton Spectator, Mar. 5, 2003; Allan Swift, New Bombardier CEO Tellier Slashes Profit Expectations, Warns of Write-Offs, The Canadian Press, Mar. 4, 2003.
[4]  The Basic Inc. v. Levinson fraud-on-the-market theory involves two rebuttable presumptions that permit a finding of class-wide reliance with respect to a Rule 10b-5 claim: "that (1) misrepresentations by an issuer affect the price of securities traded in the open market, and (2) investors rely on the market price of securities as an accurate measure of their intrinsic value." Hevesi v. Citigroup Inc., 366 F.3d 70, 77 (2d Cir.2004).

It is "based on the hypothesis that, in an open and developed securities market, the price of a company's stock is determined by the available material information regarding the company and its business" and that "[m]isleading statements will therefore defraud purchasers of stock even if the purchasers do not directly rely on the misstatements." Basic, 485 U.S. at 241-242, 108 S.Ct. 978 (internal quotation marks omitted). The theory is premised on the existence of an informationally efficient market, in which "market professionals generally consider most publicly announced material statements about companies, thereby affecting stock prices." Id. at 246 n. 24, 108 S.Ct. 978.
[5]  After we granted leave to appeal, Teamsters withdrew a motion for reconsideration that it had previously filed before the district court.
[6]  Teamsters intended to renew its class certification motion and sought to subpoena the Trustee of the Certificates at issue, the holders of the Certificates during a five-year period, thirty or more additional broker-dealers and/or institutional purchasers of the Certificates, and unidentified analysts.
[7]  Teamsters contends that we should review the denial of its request for an evidentiary hearing de novo because "this issue is inextricably linked to the District Court's application of the higher `preponderance of the evidence' standard" to its evidence of predominance. We disagree. See In re IPO, 471 F.3d at 41 (explaining that in determining class certification, "a district judge has ample discretion to circumscribe both the extent of discovery concerning Rule 23 requirements and the extent of a hearing to determine whether such requirements are met").
[8]  Revisions to Rule 23(b)(3) that went into effect after the district court's denial of the class certification motion superficially altered the rule's text without substantively changing the predominance requirement.
[9]  We explained that the statement was not necessarily correct because

[i]f a standard lower than preponderance were permitted, a judge could rule that predominance is shown by that lesser standard without going further and ruling that individual issues have been shown to predominate. The evidence might be in equipose, or the judge might simply not have considered whether the defendant's contrary evidence is persuasive. The situation is somewhat similar to a judge ruling that the plaintiff is not entitled to summary judgment on undisputed facts without ruling that the defendant is entitled to summary judgment.
In re IPO, 471 F.3d at 37 n. 8.
[10]  Teamsters makes this request on the ground that it signaled to the district court that it had "moved for class certification reasonably believing that its partial record of Certificate efficiency would be adjudged against the lesser `some showing' standard."
[11]  Teamsters does not contest the district court's consideration of the Cammer factors, but only the determination that the factors weigh in favor of a finding of Certificate market inefficiency. The Cammer factors have been routinely applied by district courts considering the efficiency of equity markets. At least one court has applied them to bond markets with a recognition of the differences between the manner in which debt bonds and equity securities trade. In re Enron Corp. Sec., 529 F.Supp.2d 644, 748 (S.D.Tex.2006). This Court has not adopted a test for the market efficiency of stocks or bonds, and we do not do so here.
[12]  While a favorable rating by one of the three major bond rating agencies may "make[] it easier to sell the security to investors, who rely upon [the rating agency's] analysis and evaluation," Am. Sav. Bank, FSB v. UBS PaineWebber, Inc. (In re Fitch, Inc.), 330 F.3d 104, 106 (2d Cir.2003), there are reasons why a district court may conclude that rating agencies less directly impact the price of bonds in comparison to analysts who follow an equity, directly relate information to buyers, and engage in the act of selling. See Randall S. Thomas & James F. Cotter, Measuring Securities Market Efficiency in the Regulatory Setting, 63-SUM Law & Contemp. Probs. 105, 113-14 (2000) (concluding that rating agencies are not analogous to "sell-side equity analysts" who follow equities, publish their research and earnings estimates, and "provid[e] a valuable conduit for information to pass from companies to investors").
[13]  McAdams' expression of general confidence that he could have obtained a quote from several broker-dealers during the class period and that he believed there were firms that were "active" in mobile home-backed securities does not show that firms actually furnished bids and offered quotations on request, or were ready, willing, and able to effect transactions in the Certificates. He failed to identify any of the firms that purportedly made specific bids or offers for the Certificates during the class period and only testified to obtaining an actual bid or quote after the close of the class period.
[14]  Teamsters argues that the district court erred when it found that the absence of firms that "regularly publish[ed]" bids and quotes for the Certificates favored a finding of market inefficiency because bond markets differ from equity markets in that no entities regularly publish bond bids and quotes. We need not address this argument here, where the district court based its market maker finding on considerably more than the absence of the regular publication of bids and quotes for the Certificates.
[15]  An event study may be rejected, however, if it is methodologically unsound or unreliable. See, e.g., Bell v. Ascendant Solutions, Inc., 422 F.3d 307, 316 (5th Cir.2005).
[16]  Carron also argued that Bloomberg prices for the Certificates "did not change for many consecutive days," which "indicate[d] conclusively that either Bloomberg prices are not reliable and/or the market for the Certificates is not efficient." Carron Aff. ¶ 30.
[17]  The district court reasoned that "[t]he news analyzed in event studies must relate to the underlying financial health of the Certificatesnews relating to BI generally is not sufficiently material to the financial health of the mobile home installment sales contracts and mortgage loans that constitute the Certificates' collateral." Teamsters, 2006 WL 2161887, at *11.
[18]  Ronen further demonstrated that Carron's own study attempting to show that Bloomberg prices were not reliable proxies was flawed; that he overstated differences in the movement of FTIM and transaction prices during the relevant periods; and that he erred when he concluded that "Bloomberg prices and transaction prices often moved in different directions." See Carron Aff. Ex. 6a-c; Ronen Reply Aff ¶ 17-19, Ex. 4-5.
[19]  The district court also incorrectly characterized one of Carron's findings by stating that "[a]fter analyzing both Bloomberg prices and transaction prices for the Certificates, Carron concludes that Bloomberg prices experienced greater variation over time than transaction prices." Teamsters, 2006 WL 2161887, at * 11. This finding reversed Carron's actual conclusion, see Carron Aff. ¶ 33, but is not, in and of itself, a material error.
