PATRICK E. HIGGINBOTHAM, Circuit Judge:

In this case, our court returns — not for the first time, and likely not for the last — to events related to the 2010 Deepwater Horizon oil spill. The plaintiffs, all holders of BP securities, bring suit against the company and two of its executives, former CEO Anthony Hayward and former Chief Operating Officer Douglas Suttles.1 They allege that BP made two distinct series of misrepresentations in violation of federal securities law: one series regarding its pre-spill safety procedures, and one regarding the flow rate of the oil after the spill occurred.

The plaintiffs moved to certify two classes; one for the pre-spill misrepresentations, and one for the post-spill misrepresentations. The district court certified the post-spill class, concluding that the plaintiffs had established a model of damages consistent with their liability case and capable of measurement across the class, as required by the Supreme Court's recent decision in Comcast Corp. v. Behrend.2 It refused to certify the pre-spill class, holding that the plaintiffs had not satisfied Comcast's common damages burden.

Both sides petition for review. We affirm.

I.

A.

The events of the 2010 Deepwater Horizon spill are well known to bench and bar and will be only briefly limned here. BP was the co-owner and co-lessee of the Macondo exploratory well, which was located in the Gulf of Mexico, about fifty miles from the Louisiana coast.3 The well was drilled by the Deepwater Horizon offshore drilling vessel. A catastrophic blowout ensued.

During the eighty-seven days of the spill, some five million barrels of oil (approximately 60,000 barrels per day) spilled into the Gulf.

Before the spill, BP was not silent about its safety plans and procedures. The plaintiffs point to three broad categories of pre-spill statements they argue portrayed BP's safety policies as being more advanced on paper than they were in practice:

The alleged misstatements continued, the plaintiffs posit, after the spill occurred; this time, they were about the spill rate:

B.

The plaintiffs, all BP shareholders, brought suit, alleging, inter alia, that BP's alleged misstatements violated section 10(b) of the Securities and Exchange Act of 1934 (the "Exchange Act") and SEC Rule 10b-5.7 After thrice narrowing the case at the motion to dismiss stage,8 the district court turned to whether a class ought to be certified. At first, it said no, reasoning that while the plaintiffs had satisfied most of the requirements of Federal Rule of Civil Procedure 23, they "failed to discharge their burden to establish that damages in this case can be measured on a class-wide basis consistent with their theories of liability,"9 as required by the Supreme Court's decision in Comcast Corp. v. Behrend. Owing to Comcast's recency, however, the district court allowed the plaintiffs another opportunity to move for class certification.

On their second attempt, the "[p]laintiffs modified their proposed subclasses and articulated differing damages methodologies for each."10 The first sub-class involved plaintiffs who had purchased stock before the spill began (the "Pre-Spill" class). Here, the claim was that BP, by making statements suggesting they had made safety and process improvements that they had not actually implemented had "lulled the market into believing that BP was a safer company than it actually was."11 The Pre-Spill plaintiffs' damages theory relied on a "materialization of the risk" claim. In essence, that BP had understated the risk of catastrophe, and when that risk materialized, they could recover its resulting damages. They argued that the economic effects of the spill, as captured by the fall in BP's stock price after the spill occurred, were the "foreseeable consequences of the materially misstated risk (i.e., BP's ability to prevent and effectively respond to serious process safety incidents such as the Macondo spill)."12 Accordingly, plaintiffs seek recovery of the entire fall in stock price caused by materialization of the risk of the spill. The district court rejected this theory, and refused to certify the Pre-Spill class.13

The second sub-class presents purchasers of the stock after the spill started (the "Post-Spill" class). "Plaintiff's theory in the post-explosion time frame is that Defendants misrepresented the internal estimates of the oil spill; that the stock market price failed to fall to the level reflecting the magnitude of the crisis facing BP; that the market learned the truth; and that the stock market price corrected."14 Said differently, because of BP's misstatements, the stock price was higher than it should have been. The damages model, in turn, relied on a theory that the "inflation" in the stock price caused by the misstatements would be exposed by at the fall in the price when certain "corrective events" brought the "true" information to the market's attention. That is, they seek recovery of the difference between a model-driven "true" stock price and the actual stock price. The district court accepted this damages theory as consistent with the liability theory and certified the sub-class.15

Both parties petitioned for review pursuant to Rule 23(f).16 The plaintiffs challenged the district court's refusal to certify the Pre-Spill class, and the defendants appeal the court's certification of the Post-Spill class. We granted both petitions.

II.

We review the certification or denial of class certification for abuse of discretion within the ambit of the controlling rules of substance and procedure.17 And to properly evaluate the district court's discretion, we briefly review the substantive and procedural law it applied.

A.

Section 10(b) of the Exchange Act and SEC Rule 10b-5 "prohibit making any material misstatement or omission in connection with the purchase or sale of any security."18 Its implicit private right of action has six elements:

It is helpful to focus on three "occurrences" — the misrepresentation, security transaction, and economic loss — and two "relationships," transaction causation, which links the misrepresentation and security transaction, and loss causation, which connects the misrepresentation to the economic loss.

Turning first to transaction causation, "`[t]he traditional (and most direct) way' for a plaintiff to demonstrate [transaction causation] `is by showing that he was aware of a company's statement and engaged in a relevant transaction ... based on that specific misrepresentation.'"20 In Basic Inc. v. Levinson21 the Supreme Court recognized that requiring direct proof of reliance "would place an unnecessarily unrealistic evidentiary burden on the Rule 10b-5 plaintiff who had traded on an impersonal market."22 Instead, if a plaintiff buys shares in a well-developed, impersonal market, she can in certain circumstances rely on a rebuttable presumption of reliance.23 This presumption is based on the "`fraud-on-the-market' theory, which holds that `the market price of shares traded on well-developed markets reflects all publicly available information, and, hence, any material misrepresentations.'"24 This presumption is rebuttable.25

Loss causation is a legal requirement distinct from reliance that demands a causal connection between the misstatement and claimed economic loss.26 Akin to a concept of proximate cause in tort law, its task is to isolate "those economic losses that misrepresentations actually cause," rather than "to provide investors with broad insurance against market losses."27 A plaintiff must prove that the misstatements — not "other intervening causes, such as `changed economic circumstances, changed investor expectations, new industry-specific or firm-specific facts, conditions, or other events'" — were the cause of her claimed economic injury,28 unaided by any presumptions attending efforts to prove transaction causation.29

Congress has not specifically defined "economic loss" for purposes of a securities violation. It has provided an upper cap on damages.30 At the same time, the "out-of-pocket measure," sometimes called the "price inflation" metric, is often used. Under this theory, "a purchaser of securities may recover against a defendant ... only the `difference between the price paid and the "[true]" value of the security ... at the time of the initial purchase by the defrauded buyer.'"31 While our court has not held that this metric is the exclusive way to measure damages in 10b-5 cases, we do insist that cognizable damage must be caused by the misstatements in question. That is, a loss does not constitute an "economic loss" for these purposes unless loss causation can be established.

B.

"To obtain class certification, parties must satisfy [Federal Rule of Civil Procedure] 23(a)'s four threshold requirements, as well as the requirements of Rule 23(b)(1), (2), or (3)."32 All parties agree Rule 23(a)'s requirements have been satisfied. The only dispute here is whether the requisites of Rule 23(b)(3) have been met, "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."33

In Comcast Corp. v. Behrend,34 the Supreme Court turned to damages, commonality, and predomination in a Rule 23(b)(3) class. It is that relationship upon which this case turns. There, the Court held:

In short, in order to certify a class, the damages methodology must be "sound" and must "produce[ ] commonality of damages."36

III.

A.

We begin with the Post-Spill Class.

1.

The plaintiffs' expert, Chad Coffman, purports to calculate damages by using an "out-of-pocket losses" measure. This is a model-driven calculation, which calculates the damages as the difference between the inflated price at which the plaintiffs bought their stock, buoyed by BP's alleged misrepresentations about the magnitude of the spill, and the "true" price, meaning the theoretical price that the BP stock would have traded for had the relevant information been properly disclosed.

While the details of Coffman's Post-Spill model are complex, it is straightforward in principle. Coffman conducted an "event study" of BP's stock price during the Spill. "An event study ... is a statistical regression analysis that examines the effect of an event[, such as the release of information,] on a dependent variable, such as a corporation's stock price."37 Those events are called "corrective disclosures" or "corrective events," which means that the disclosure has partially or entirely corrected a previous misrepresentation.38 Coffman identified six events that he argues showed the public that the amount of oil escaping from the rig was far greater than BP had initially represented.39 He then calculated the stock price decline on those days, "after controlling for market and industry forces." Then, he used a "constant dollar" measure of price inflation, which "appears to equate the amount of a stock-price drop on a given corrective disclosure day ... with the `inflation' caused by a preceding misrepresentation. This `constant dollar' amount of inflation is then carried back to the date of the proceeding misrepresentation, such that any share purchased in the interim is deemed `inflated' by that amount."40

To visualize this approach, imagine a graph, with the x-axis measuring the date (starting when the misstatements were made and ending when after the last corrective event occurred) and the y-axis representing the scale of the price inflation. The inflation starts with some positive number and then — proceeding in a step-function — declines by a certain dollar amount after each corrective event is disclosed, eventually ending with zero. To calculate damages, plaintiffs need only to know the date they bought the shares (measured on the x-axis), and then multiply the price inflation on that date by the total number of shares. Coffman also concludes that his "methodology could be easily updated to remove inflation if a specific disclosure were eliminated, the misstatements occurred later, or confounding information reduced the relevant amount for one of the disclosures." In essence, the model would allow for the removal of one of the purported corrective "steps," reducing the total amount of inflation — and thus economic loss — accordingly.

2.

BP does not challenge Coffman's contention that an out-of-pocket measure of damages would be appropriate in this type of case. Instead, it first focuses on the nature of the Coffman model itself. It argues that he did not actually calculate an "out-of-pocket" measure of damages, as he claimed,41 pointing to a paragraph of his reply report:

BP targets the word "possible," positing that this word indicates that Coffman's methodology "does not satisfy Plaintiff's burden of proving by a preponderance of the evidence that Coffman's methodology calculates damages on a class-wide basis in a matter that is neither speculative nor arbitrary."42

Construing this argument as one stating that Coffman did not put forth the type of the model he claimed he did, we disagree. Read in context, the passage is not so unequivocal as to require us to hold that the district court abused its discretion in certifying the class. Rather, Coffman first notes that determining BP's stock price absent the allegedly deceptive statements would be a "hypothetical exercise." This is correct, of course — as all attempts to narrate what did not materialize in fact necessarily involves hypotheticals. As we read the Coffman report, the reference to the "possible" decline of BP's stock price is an uncontroversial statement that it would be impossible to determine to a certainty what the price of BP stock would have been had the statements in question never been made. Comcast requires a "sound" methodology, not certainty.43 Here, in the next sentence, Coffman stated that he used the corrective disclosure methodology to proxy the inflated stock price, a statement which is consistent with the detailed description of his work in his report, and a methodology often used in these types of cases.44 The isolated use of the word "possible," in the face of evidence indicating that Coffman had, as he said he did, used the "out-of-pocket" damages methodology, does not defeat certification.45

3.

BP's next argument proceeds in two parts. First, that the district court misconstrued Comcast when it "conclude[ed] that it could not consider flaws in the plaintiff's damages methodology because those flaws overlap with a merits inquiry."46 Second, it puts forward a specific application of this argument, proposing that the district court failed to determine whether the corrective events Coffman relies on were tied to the specific misstatements he says they were.

a.

In its order certifying the Post-Spill class, the district court expressed concern over certain aspects of the Coffman model:

BP argues that the district court committed reversible legal error in failing to resolve these concerns over the nexus of corrective events and underlying misstatements at the class certification stage. We disagree.

To shed light on the permissible versus mandated tasks of the district court at this stage of litigation, we look to the thread of two separate lines of recent Supreme Court jurisprudence. The first is Comcast, where the Court emphasized the necessity of establishing, before a class could be certified, congruence between theories of damages and liability. It held that a:

Stated another way, the theory of damages "must be consistent with [the] liability case,"49 and the district court is required to "conduct a rigorous analysis [at the class certification stage] to determine whether that is so."50

The second line of cases turn to the proof required at the class certification stage. In Halliburton I, the Court unanimously held that loss causation need not be proved in order to certify a class,51 later, in Amgen, emphasizing that the plaintiff need not prove an element of its case at the certification whose resolution "is common to the class."52

Recall that the plaintiffs' theory of liability is that BP misrepresented the Spill's flow rate. The theory of damages is that the stock price was inflated as a result of BP's misrepresentations, as revealed by six corrective events. Some of those events are unequivocally connected to the alleged misrepresentations, i.e., a Coast Guard statement several days after the spill reporting that the spill rate estimate was five-fold higher than first anticipated,53 and some are more removed, e.g., BP announcing that its directors were meeting to discuss alternatives to paying a dividend. The district court refused to consider excluding certain corrective events from the plaintiffs' damages model at the certification stage. Our question is: in doing so, was it following Amgen's mandate not to require proof of class-wide elements, or was it violating Comcast's direction that it must determine the mesh of liability and damage theory?

While the counter argument does not lack purchase, we conclude that the district court acted appropriately. As a conceptual matter, the theory of liability is consistent with the theory of damages: the liability stems from BP's flow-rate misstatements, and the loss forming the basis for Plaintiffs' damages model comes from the inflated stock price caused by those misstatements. This situation, then, is not like Comcast, where the plaintiffs' theory of damages was based on four district alleged antitrust distortions, but the theory of liability was based on only one of them.54 There, it was undisputed that the plaintiffs' "methodology ... identifies damages that are not the result of that wrong."55 Under that model, some plaintiffs sought to recover under a theory of damages that corresponded to a theory of liability no longer in the case. This case is different. Here, the dispute is whether the specific corrective events Coffman identified as a measure if stock price inflation are adequately tied to the alleged misstatements. Each plaintiff's theory of damages remains tied to a theory of liability common to all plaintiffs, satisfying the Amgen standard of commonality.

Addressing the corrective events question at the class certification stage raises two problems. First, it is in tension with Halliburton I's holding that no proof of loss causation is required at the class certification stage.56 Recall, loss causation is "a causal connection between the material misrepresentation and the loss;"57 it measures the loss caused by the misstatement. We recognize that other circuits have held that loss causation and damages are not entirely congruent. They have said that loss causation requires plaintiffs to prove that the misstatement was only "a substantial cause of [the] plaintiff's loss," but that to prove damages, plaintiffs must "isolate[ ] and remove[ ]" other contributing forces to the decline in value.58 This makes sense. Plaintiffs must prove that the portion of the price fall that they seek in damages is directly attributable to the misrepresentation, so that they do not recover a windfall. But they do not need to prove it at the certification stage. Halliburton I holds that we do not yet require plaintiffs to prove that the defendant's misrepresentation was a "substantial cause" of loss at this stage;59 it would not make sense to now require them show that the same misrepresentation was the "sole" cause of that very loss.

Second, in Amgen, the Court made clear that questions "common to the class" need not be proved at the class certification stage, so long as they are capable of common resolution.60 Here, the question of whether certain corrective disclosures are linked to the alleged misrepresentations in question is undeniably common to the class, and is "susceptible of a class-wide answer."61 So is the measure of damages which is dependent on the answer to that question, without reference to any individual class members.

We conclude that the district court did not err in refusing to resolve concerns about the inclusion of certain corrective events at the class certification stage.

b.

BP's next argument is a twist on its first. It argues that several of the corrective events in question actually measure a different type of damages — not stock price inflation stemming from the misrepresentation about the spill rate, but from the consequences of the spill itself.62 We agree that damages stemming from the spill itself are not recoverable under the plaintiffs' theory of liability.63 However, for similar reasons to those we just expressed, the district court did not abuse its discretion in not requiring the plaintiffs to prove — at this stage in the litigation — that all of the corrective events measured the effect of the misrepresentation, rather than the spill itself.

In answering this question, it is useful to focus on the specific nature of the dispute. The plaintiffs say that their corrective events reveal the consequences of the non-disclosure. BP says they do not; but rather reflect the consequences of the spill. The core dispute, then, is about the "fit" between the corrective event and the misstatements. But the tightness of that fit is a question common to the class, for which Amgen did not require proof at the certification stage. To conclude otherwise would vitiate Halliburton I's requirement that loss causation need not be proved at this stage, since proving the quality of the fit at this stage would also require bringing forward the plaintiff's proof of loss causation.

There is one wrinkle. If certain corrective events were later determined to be independent of the misrepresentations, but those corrective events could not be disaggregated from the damages model, the plaintiffs would travel to a place forbidden by Comcast: they would recover damages other than those "resulting from the particular... injury on which [defendant's] liability in this action is premised."64 However, Coffman's methodology allows for the removal of corrective events later found to not "correct" the misrepresentations. The ability to do so, not the actual execution of that correction, is what Comcast requires at this stage.65

c.

BP's final challenge to this class certification is of the same genus. It argues that Coffman's model includes corrective events linked only to pre-explosion misstatements, rather than post-explosion flow rate misstatements.66 This challenge also goes mainly to the "fit" of the corrective events, a question which can be answered with respect to the entire class, and so is not one that needs to be proved at the certification stage.

4.

We conclude that the district court did not abuse its discretion in certifying the Post-Spill class, and AFFIRM.

B.

We now turn to the district court's refusal to certify the Pre-Spill class.

1.

Recall that the Post-Spill damages theory is based on a "out-of-pocket" or "stock price inflation" theory. That is, the theory alleges that the stock price was higher than it would have been, and the damage is the difference between the "true" price and the "paid" price. The Pre-Spill damage theory is different. It is "based on [a] `materialization of the risk' theory," where the "investors are harmed by [ ] corrective events that represent materializations of the risk that was improperly disclosed." Coffman's model posits that "[t]he catastrophic explosion, oil spill, and direct consequences of the Spill reflect the foreseeable consequences of the materially misstated risk.... Thus, under the logic of the theory, the losses suffered by the investors as a result of the materialization of this risk are causally tied to the misrepresentations themselves." Or, said differently, BP allegedly misstated the efficacy of its safety procedures, creating an impression that the risk of a catastrophic failure was lower than it actually was. These statements resulted in an "investor being defrauded into taking a greater risk than disclosed," taking away plaintiffs' "opportunity to decide whether to divest in light of the heightened risk." The Plaintiffs claim that when that risk materialized, in the form of the Spill, and BP's stock price fell as a result, the investor who was defrauded into taking on that heightened risk can recover the bulk of that fall as her damages.67

2.

The question here is not whether the "materialization of the risk" theory can provide a viable measure of damages for a Rule 10b-5 case.68 Rather, it is whether a damages model based on this theory is "susceptible of measurement across the entire class for purposes of Rule 23(b)(3)," as required by Comcast.69 We conclude that the district court did not abuse its discretion in holding that the Pre-Spill damages theory was not capable of class-wide determination. That theory hinges on a determination that each plaintiff would not have bought BP stock at all were it not for the alleged misrepresentations — a determination not derivable as a common question, but rather one requiring individualized inquiry.

Consider the following scenario: The true risk of a major spill was 2%, but BP's statements had improperly represented the risk as 0.5%. Further imagine two different plaintiff-investors. The first is a low-risk pension fund, whose investment policy forbids investing in companies for whom the risk of a catastrophic event is greater than 1%. The second is a high-risk fund whose risk threshold is higher than 2%. Both plaintiffs invested in BP based on BP's statements representing the risk as 0.5%. In this hypothetical, BP's misstatements caused the low risk pension fund to make an investment forbidden under its policy. It would not have bought BP stock at all had it known the true risk of a catastrophe. This is the type of plaintiff the materialization-of-the-risk theory is designed to compensate. By contrast, the high-risk fund still might have purchased the stock, even had it known the "true" risk, though presumably at a lower price that accounted for the increased risk. For the second type of plaintiff, full materiali-zation-of-the-risk damages would prove a windfall.

The loss causation element requires a clear causal link between the misrepresentation and the economic loss, ensuring in a Rule 10b-5 case ensures that investors are protected only "against those economic losses that misrepresentations actually cause."70 The securities laws do not provide "broad insurance against market losses."71 For the first plaintiff, who would not have purchased the stock absent the misrepresented risk, the decline in the stock's value when the risk actually materialized may well be causally linked to the misrepresentation, in which case that full stock price decline following the materialization of the catastrophic event could constitute a valid economic loss. The second plaintiff, by contrast, might have purchased the stock even assuming the true risk. Although she would be entitled to damages based on the inflated price she paid, she cannot be compensated for the materialization of a risk she may have been willing to take.

The problem is that the Coffman model here does not provide any mechanism for separating these two classes of plaintiffs. And because it lacks the ability to do so, it cannot provide an adequate measure of class-wide damages under Comcast.72

In response, the plaintiffs point to the fraud-on-the-market presumptions set out in Basic. They argue that "if the[y] ... prove the prerequisites of fraud on the market — which they have done — it is presumed that the Pre-Spill Class relied on BP's misrepresentations in purchasing the [stock] and the misrepresentations were a cause-in-fact of their losses."73 This is half true. The first statement, arguing that the fraud-on-the-market presumption applies if the plaintiffs show four basic facts, is correct.74 The second statement is not correct. The fraud-on-the-market theory does not provide any presumptions with regard to loss causation — whether the misstatement caused the loss.75 And here, where the economic loss depends on the posture of the plaintiff vis-à-vis risk tolerance, that loss causation, and thus damage, cannot be presumed nor can it be found class-wide.

Moreover, the fraud-on-the-market presumption is rebuttable,76 and plaintiffs' own model may well have rebutted it. Under Basic, courts presume reliance because (a) all information in an efficient market is priced into a security and (b) investors typically make investment decisions based upon price and price alone.77 That is, if an investor makes investment decisions based upon price, he or she necessarily buys any particular stock in reliance upon all of the information or misinformation incorporated into its price. But plaintiffs' own model asserts that they relied on something other than price: risk. By claiming that class members may have divested themselves of BP stock if they had known about the true risk of an accident in the Gulf — as distinguished from that risk's impact on BP's stock price — the plaintiffs are arguing that their investment decisions were based substantially upon factors other than price. The plaintiff's argument thus undercuts one of the rationales for the Basic presumption of reliance.

To summarize, plaintiffs' materialization-of-the-risk theory cannot support class certification for two reasons. Unlike the stock inflation model, the materialization-of-the-risk model cannot be applied uniformly across the class, as Comcast requires, because it lumps together those who would have bought the stock at the heightened risk with those who would not have. It also presumes substantial reliance on factors other than price, a theory not supported by Basic and the rationale for fraud-on-the-market theory.

For these reasons, we AFFIRM the district court's decision not to certify the Pre-Spill class.

3.

Finally, the plaintiffs argue that the district court erred in denying their motion to file a renewed motion for class certification, using a different theory of damages.

As an initial note, we likely lack jurisdiction to review this denial. Rule 23(f) vests us with interlocutory jurisdiction only over "an order granting or denying class-action certification."78 An order denying leave to file an amended motion for class certification does not fall into that narrow category.79 Even we were to conclude otherwise, we cannot conclude that the district court abused its discretion in refusing — after issuing two through and well-reasoned opinions — to give the plaintiffs a third bite at the apple.80

IV.

We AFFIRM the judgment of the district court.