U.S. COMMODITY FUTURES TRADING COMMISSION, PLAINTIFF-APPELLEE,

v.

SOUTHERN TRUST METALS, INC., LORELEY OVERSEAS CORPORATION, ROBERT ESCOBIO, DEFENDANTS-APPELLANTS

GILMAN, Circuit Judge: This is a commodities-fraud case. The U.S. Commodity Futures Trading Commission (CFTC) began investigating Southern Trust Metals, Inc., Loreley Overseas Corporation, and Robert Esco-bio (collectively, the Defendants) in response to an investor’s complaint. That complaint also prompted the National Futures Association (NFA)—a private, self-regulatory organization for the futures industry—to open an investigation, which proceeded in tandem with the CFTC’s. The NFA’s investigation ended in a settlement. Afterwards,- the CFTC filed this lawsuit, alleging that the Defendants violated the Commodities Exchange Act (CEA) when they failed to register as futures commission merchants, transacted the purchase and sale of contracts for the future delivery of a commodity (futures) outside of a registered exchange, and promised to invest customers’ money in precious metals (metals) but instead invested the funds in futures.

The district court, after a bench trial, entered judgment for the CFTC on all claims. For the reasons set forth below, we AFFIRM the judgment of the district court except as to the restitution award for the group of investors whose losses were associated solely with the registration violations. As to that portion of the restitution award, we VACATE the judgment and REMAND with instructions to consider other equitable remedies.

I.

BACKGROUND A. Factual background Escobio is the Chief Executive Officer (CEO) and largest shareholder of the Southern Trust Securities Holding Corporation (Holding Corporation).

The Holding Corporation owns Loreley, a British Virgin Islands corporation, which in turn owns Southern Trust, a Florida corporation. Es-cobio formed Southern Trust to provide commodities investment services, and. he serves as its director and CEO. Southern Trust represented that it was able to facilitate customers’ investment in precious metals. Its website and brochure stated that customers “can take physical possession of [their] metals in New York or London.” The company’s brokers told customers much the same story—that the customers were -purchasing metals stored in places like New York, London, and Hong Kong. At least one of Southern Trust’s brokers told customers that Southern Trust charged “storage fees” for the metals. To open a trading account at Southern Trust, customers completed an account-opening form containing language that “[p]hysical precious metals can either be delivered directly to the customer’s designated point of delivery or to a recognized depository, which provides insured nonsegregated storage.” Southern Trust also represented that it could loan customers money to purchase metals. But Southern Trust did not in fact deal in metals; it dealt only in contracts for the future delivery of metals. Such contracts are a type of derivative investment. Southern Trust, however, was not registered with the CFTC as a futures commission merchant and thus could not trade futures on registered exchanges. So Escobio, through Loreley, engaged two foreign brokerages—Berkeley Futures Limited and Hantec Markets Limited—to handle the transactions. Escobio opened trading accounts at Berkeley and Hantec in Loreley’s name, not in the names of Southern Trust’s customers. The accounts were numbered, and Southern Trust maintained records linking its customers to the specific numbered accounts. Opening these accounts required Esco-bio to review documents describing Berkeley’s and Hantec’s investment products. One of Hantee’s' account-opening documents, the “Product Disclosure Statement,” explains that “bullion trading” “operates in the same manner as foreign exchange trading” in that “[w]hat you are actually buying is a [contract” that “derives its value from” a “physical underlying asset” such as “Loco London Gold.” That document’s “Glossary” defines “Loco London Gold” to “meant ] not only that the gold is held in London but also that the price quoted is for delivery there?’ Elsewhere, the document explains that in “bullion trading,” “[Hantec] do[es] not deliver the. physical underlying assets (i.e. gold or silver) to you, and you have no legal right to it.” The Berkeley documents similarly confirm that the account holder intends “to speculate in derivative products.” None of the account-opening documents mention making loans for the purchase of metals. After setting up the trading accounts at Berkeley and Hantec, Southern Trust sent its customers’ money to Loreley, which in turn invested the funds, through Berkeley and Hantec, in futures. Escobio received monthly account' statements showing that all investments were in futures, not metals. Those statements do not reflect any loans to Southern Trust’s customers. Southern Trust never informed its customers that 'their money was being transferred to Loreley, Berkeley, or Hantec. Nor did it inform customers who wished to invest in metals (the group comprising the vast majority of its customers) that their money was instead being invested in futures. Southern Trust still charged those customers interest on fictitious loans, which it falsely told them were made in order to facilitate their investment in metals. After receiving a complaint from one of Southern Trust’s customers, the NFA opened an investigation. Around the same time, Escobio asked Berkeley and Hantec about the nature of Loreley’s investments. Escobio contended at trial that he did so simply to confirm his understanding that Loreley was investing in metals. The CFTC maintained, however, and the district court ultimately concluded, that Esco-bio had done so in anticipation of litigation, and that he had carefully framed his inquiries to elicit responses that would support the defense he later asserted—that he did not know that his customers’ money was being invested <in futures. In response to Escob'io’s inquiry, Han-tec’s CEO said: “I can confirm that you hold accounts with us that only trade Silver Bullion.” Hantec’s CEO clarified at his deposition, however, that “Silver Bullion” is industry lingo for contracts for the future delivery of silver and that he could not have intended any other meaning because trading in “physical metals is not something that Hantec does.” A Berkeley employee similarly responded to, Escobio’s inquiry, writing that “all Loreley accounts with the prefix XILOR were silver bullion accounts” that “only traded in OTC [off-exchange] silver bullion and never traded any futures contracts.” But Berkeley’s CEO testified at his deposition that Berkeley had never delivered metals to any of its customers, including Loreley, nor stored any metals on their behalf. He also testified that, despite Esco-bio’s contrary assertion, he never told Es-cobio that the trades Berkeley handled for Loreley would lead to the storage of metals. None of Southern Trust’s investments led to the delivery of metals. Hantec’s CEO-testified that he told Escobio that Hantec could arrange for the delivery of metals, but that .he did so only in response to a hypothetical question. According to Hantec’s CEO,. Escobio inquired in the abstract about Hantec’s ability ,to arrange delivery: “It’s an inquiry from a-client. Robert [Escobio] did not tell me, T would like to deliver metal? He asked me, ‘If I wanted to deliver a metal, can you arrange it?’ and I said, ‘Let me go find out? ” Hantec’s CEO continued: “I talked to ... one of my contacts at Standard Chartered bank who gave me information and I went back to Robert and explained” that Hantec could arrange delivery. This response was memorialized in a letter to Escobio, stating that “any Gold or Silver you purchase from us is held for your.account and upon full payment we are able to arrange delivery for you when requested.” But the Defendants never asked Hantec to arrange delivery, and no delivery ever occurred. The NFA’s investigation ended in a settlement. Although the NFA’s and the CFTC’s investigators had cooperated with each other, their investigations were independent. The Defendants’ settlement agreement with the NFA therefore does not mention the CFTC or the CFTC’s investigation. As the CFTC’s investigation moved forward, the Defendants continued to produce documents in response to its requests. The Defendants’ lawyers knew at the timé of the NFA settlement that the CFTC might bring its own enforcement action, but they did not suggest to the CFTC or to anyone else that such an action would violate their settlement agreement with the NFA.

B. Procedural background In July 2014, the CFTC filed its complaint, seeking equitable relief and penalties under the CEA. The complaint alleges that the Defendants engaged in two illegal schemes, which we will refer to as the “unregistered-futures scheme” and the “leveraged-metals scheme.” As to the unregistered-futures scheme, the complaint alleges that, even though the Defendants were not registered as futures commission merchants, they accepted money from customers who wished to invest in futures. Because the Defendants were unregistered, moreover, .they could not trade futures on a registered exchange. They therefore sought to trade indirectly, through intermediaries. To that end, the Defendants funneled the customers’ money through Loreley to foreign brokerage firms—Berkeley and Hantec—li-censed to trade futures. Those brokerage firms made the actual investments. As to the leveraged-metals scheme, the complaint alleges that the Defendants accepted money from customers who wished to invest in metals with borrowed ihoney. But instead of issuing loans to those customers and investing their money in metals, the Defendants took the customers’ money and invested it in futures. No loans existed, but the Defendants charged loan interest anyway. At the summary-judgment stage of the case, the parties filed dueling motions.

The district court granted the CFTC’s motion in part, holding that the-Defendants had conducted off-exchange transactions and had failed to register" as futures commission merchants. It denied the Defendants’ motion in full, rejecting their affirmative defenses that (1) their settlemént with the FTA equitably estopped the CFTC from bringing suit, and (2) they actually delivered metals so as to bring their transactions within an 'exception to the CEA’s registration requirements. The CFTC’s fraud claim then proceeded to trial. After a bench trial, the district court found that the Defendants had engaged in fraud, ordered them to pay restitution in the full amount of the customers’ losses, and imposed fines. The court also permanently enjoined the Defendants from employment in the commodities-trading industry.

On appeal, the Defendants challenge the court’s rulings both on summary judgment and at trial.

II.

ANALYSIS A.

Standard of review On an appeal from a judgment in a bench trial, we review the district court’s conclusions of law de novo. HGI Assocs., Inc. v. Wetmore Printing Co., 427 F. 3d 867, 873 (11th Cir. 2005). We also review de novo the district court’s application of law to facts. United States v. Frank, 599 F. 3d 1221, 1228 (11th Cir. 2010). The district court’s findings of fact, on the other hand, are evaluated under the clear-error standard. HGI, 427 F. 3d at 873. “We will not find clear error unless our review of the record leaves us ‘with the definite and firm conviction that a mistake has been committed.’” Coggin v. Comm’r of Internal Revenue, 71 F. 3d 855, 860 (11th Cir. 1996) (quoting United States v. Gypsum Co., 333 U.S. 364, 395, 68 S.Ct. 525, 92 L.Ed. 746 (1948)).

Finally, when the district court has issued a permanent injunction, we review the scope of the injunction under the abuse-of-discretion standard. Commodity Futures Trading Comm’n v. Wilshire Inv. Mgmt. Corp., 531 F. 3d 1339, 1343 (11th Cir. 2008).

B. Equitable estoppel does not bar the CFTC’s claims. To start with, the Defendants challenge the district court’s summary-judgment ruling that their settlement with the NFÁ does not preclude the CFTC’s claims.

The district court held that equitable estoppel does not apply because (1) the Defendants do not dispute that the NFA is a private, nongovernmental organization through which the commodities-trading industry regulates itself; (2) the CFTC was not a party to the settlement; and (3) settlements with private, nongovernmental organizations do not preclude subsequent claims by government regulators. Although this circuit has not yet addressed whether a settlement between a nongovernmental regulator and a regulated company may preclude subsequent claims by a governmental regulator, the circuits that have addressed the issue have uniformly answered in the negative. See, e.g., Graham v. S.E.C., 222 F. 3d 994, 1007 n.25 (D.C. Cir. 2000) (“Of course, even if the NASD had done something to bind itself, that would not have bound the SEC.”); Jones v. S.E.C., 115 F. 3d 1173, 1179-81 (4th Cir. 1997) (“We have found no statutory, regulatory, or historical reference to support [the] argument that NASD discipline of its members was intended to preclude this disciplinary action by the SEC itself against a securities professional.”).

In Jones, the Securities and Exchange Commission (SEC) brought administrative claims against a securities trader after the trader settled a claim by the National Association of Securities Dealers (NASD). 115 F. 3d at 1180. The Fourth Circuit rejected the trader’s argument that the settlement precluded the SEC’s claims, reasoning that private and public regulators “represent distinct interests” and “bring two separate vantage points' to enforcement efforts—one from the industry itself and the other from the regulator.” Id. This outcome accords with the courts’ general reluctance to apply principles of equitable estoppel to the government. “The Supreme Court has never established that the doctrine of equitable estoppel can be applied against the government and, in fact, has implied that it can not be.” Tovar-Alvarez v. U.S. Atty. Gen., 427 F. 3d 1350, 1353-54 (11th Cir. 2005) (citing Office of Pers. Mgmt. v. Richmond, 496 U.S. 414, 422, 110 S.Ct. 2465, 110 L.Ed.2d 387 (1990)). “[I]t is well settled that the [government may not be estopped on the same terms as any other litigant.” Heckler v. Cmty. Health Servs. of Crawford Cty., 467 U.S. 51, 60, 104 S.Ct. 2218, 81 L.Ed.2d 42 (1984).

This circuit has repeatedly opined that, even assuming that equitable estoppel could apply against the government, “it would require a showing of affirmative misconduct on the government’s part.” To var-Alvarez, 427 F. 3d at 1354; see also Sanz v. U.S. Sec. Ins. Co., 328 F. 3d 1314, 1319-20 (11th Cir. 2003) (“[E]ven if estop-pel is available against the Government, it is warranted only if affirmative and egregious misconduct by government agents exists.”).

The present case is analogous to Jones.

Here, the uncontradicted evidence shows that the NFA, like the NASD, is a private, nongovernmental organization and that the CFTC was not a party to the Defendants’ settlement with' the NFA.

The record, moreover, contains no evidence of affirmative misconduct by the government. So even if equitable estoppel theoretically could apply to the government, it does not apply here. A second, independent ground also exists for affirming the district court’s denial of summary judgment based on the Defendants’ estoppel defense: the record reflects a genuine dispute of material fact regarding the element of reasonable reliance. See Heckler, 467 U.S. at 59, 104 S.Ct. 2218 (noting that “the party claiming the estoppel must have relied on its adversary’s conduct” and that the “reliance must have been reasonable”).

Especially noteworthy is the fact that the settlement agreement makes no mention of the CFTC or its investigation, so the Defendants’, purported reliance lacks a textual basis. The only language in the agreement that even arguably suggests reliance is a clause providing that the agreement “shall resolve and terminate all complaints, investigations and audits relating to [the Defendants].” But interpreting this language to embrace the CFTC’s investigation is unreasonable. For one thing, the notion that the NFA would agree to terminate investigations outside its control—and that the Defendants would accept such an unfulflllable obligation as consideration for their own concessions—defies common sense. Further, a literal interpretation of “all complaints, investigations and audits relating to [the Defendants]” would impose on the Defendants obligations that they surely did not intend, such as the obligation to terminate their own routine, internal accounting audits. Such audits would, after all, be “audits relating to [the Defendants].” The lack of textual support for the Defendants’ estopppl argument creates a genuine dispute concerning the reasonableness of their reliance. At the same time, other evidence creates a genuine dispute about whether there was any reliance at all.

First, the Defendants continued to produce documents in response to requests from the CFTC’s investigators after the settlement. This fact tends to negate any reliance because the Defendants presumably would not have continued cooperating with the CFTC if they had truly believed that their settlement with the NFA had terminated the CFTC’s investigation.

Second, the Defendants’ lawyers, while preparing to defend against that action, never suggested to the CFTC or anyone else that such an action might violate the settlement agreement with the NFA. For these reasons, we find no error in the district court’s denial of the Defendants’ motion for summary judgment based on the affirmative defense of equitable estop-pel.

C. Summary judgment in. favor of the CFTC on its claims for registration violations was appropriate.

We now turn to the merits of this case. The CEA imposes registration requirements on commodities traders and the exchanges where they trade.

Section 6d of the CEA makes it “unlawful for any person to be a futures commission merchant unless ... such person shall have registered [as such] ... with the [CFTC].” 7 U.S.C. § 6d(a)(l).

The statute also requires that all transactions be “conducted on or subject to the rules of a board of trade which has been designated or registered by'the [CFTC].” Id. § 6(a).

Together, these provisions require that only registered traders handle transactions and that they do so on a registered exchange. An exception exists, however, for transactions that result in “actual delivery within 28 days.” Id. § 2(c)(2](D)(ii)(III)(aa).

Actual' delivery means “giving real and immediate possession” of the commodity “to the buyer or the buyer’s agent.” U.S. Commodity Futures Trading Comm’n v. Hunter Wise Commodities, LLC, 749 F. 3d 967, 979 (11th Cir. 2014) (internal quotation marks omitted). “ ‘Actual’ is that which ‘exist[s] in fact’ and is ‘real,’ rather than constructive.” Id. (quoting Black’s Law Dictionary 494 (9th ed. 2009)).

This exception is an affirmative defense on which the commodities trader bears the burden of proof. See Schlemmer v. Buffalo, R & P R Co, 205 U.S.¹, 10, 27 S.Ct. 407, 51 L.Ed. 681 (1907) (explaining-that the “general rule of law is[ ] that a proviso carves special exceptions only out of the body of the act; and those who set up any such exception must establish it”); see also Corning Glass Works v. Brennan, 417 U.S. 188, 196-97, 94 S.Ct. 2223, 41 L.Ed.2d 1 (1974) (“[T]he application of an-exemption under the Fair Labor Standards Act is a matter of affirmative defense on which the employer has the burden of proof.”); Mulhall v. Advance Sec., Inc., 19 F. 3d 586, 590 (11th Cir. 1994) (“[T]he exceptions granted within the EPA constitute affirmative defenses.”).

The Defendants, concede that they were not registered as futures commission merchants and that the trades at issue did not occur on a registered exchange. But they seek, refuge in the exception for transactions resulting in actual delivery. As set forth in the factual background of this opinion, however, there is no basis in the record for the Defendants! contention that actual delivery ever occurred.

The record instead supports the holding of the district court that the Defendants failed to establish their affirmative defense of “actual delivery.” See Hunter Wise Commodities, 749 F. 3d at 979. We therefore find no error in the court’s .grant of summary judgment in favor of the CFTC on its claims that the Defendants engaged in off-exchange transactions and failed,to register as futures commission merchants.

D.

The district court did not err in concluding that the Defendants committed fraud under 7 U.S.C. §§ 6b(a) and 9, and under 17 C.F.R. § 180.1. We next turn to the issue of fraud. For ■our purposes, ,7 U.S.C. § 6b(a), 7 U.S.C. § 9, and 17 C.F.R. § 180.1 are redundant.

Section 6b(a) makes it “unlawful ... for any person ... in connection with .,. any contract of sale of any commodity ... for future delivery ... to cheat or defraud or attempt to cheat or defraud the other person ,.. [or] willfully to make ,.. any false report. or statement ... [or] willfully to deceive or .attempt to deceive the, other person by any means whatsoever.” 7 U.S.C. §§.6b.(a). .Section 9 ;of the same chapter is similar, providing that “[i]t shall be unlawful for any. person ... to use ... in connection with any ... contract of sale of any commodity ... for future, delivery ... any manipulative or deceptive device or contrivance.” Id. § 9(1).

Finally, 17 C.F.R. § 180.1(a) declares.it “unlawful for any person ... in connection with any ,.. contract of sale of any commodity ... or contract for future delivery ... to intentionally or recklessly..... use ... .any manipulative device, scheme, or artifice to defraud; ... [or] [m]ake ... any untrue or misleading statement of a material fact or to omit to state a material fact necessary ... to make the statements made not untrue or misleading; ... [or] [e]ngage ... in any act ... which operates ... as a fraud or deceit upon any person.” The .CFTC must prove the same three elements to establish liability under each of the above provisions: “(1) the making of a misrepresentation, misleading statement, or a deceptive omission; (2) scienter; and (3) materiality.” Commodity Futures Trading Comm’n v. R.J. Fitzgerald & Co., Inc., 310 F. 3d 1321, 1328 (11th Cir. 2002). “Unlike a cause of action for fraud under the common law of [t]orts, ‘reliance’ on the representations is not a requisite element....” Id. at n.6.

1. Misrepresentation, misleading statement, or deceptive omission The district court’s factual findings on the “misrepresentation” element reflect no clear error. With the many references to “physical metals,” “physical possession,” and “storage,” ■ Southern Trust’s brochure, website, brokers, and account-opening documents collectively represented that the company offered investments in metals. Abundant evidence shows, however, that after accepting the customers’ money, Southern Trust sent the funds to Loreley, which in turn sent them to Berkeley and Hantec for investment in futures. The Defendants do not dispute that the accounts at Berkeley and Hantec were in Loreley’s name, not in the names of Southern Trust’s customers.

Moreover, the evidence-shows that Southern Trust never informed its customers that their money was being transferred, to Loreley, Berkeley, or Hantec and, consequently, that the customers did not know that those firms held their money. The district court correctly applied the law to these facts. “Whether a misrepresentation: has been made depends on the ‘overall message’ and the ‘common understanding of-the information • conveyed.’ ” R.J. Fitzgerald, 310 F. 3d at 1328 (quoting Hammond v. Smith Barney Harris Upham & Co., Comm. Fut. L. Rep, (CCH) 36,657 & n.12 (CFTC Mar.¹, 1990)).

We find the case of U.S. Commodity Futures Trading Commission v. Hunter Wise Commodities, LLC, 21 F. Supp. 3d 1317 (S.D. Fla. 2014), squarely on point. The district court in Hunter Wise concluded, after a bench trial, that the defendant “misrepresented facts about the precious metals transactions it oversaw” and provided a deceptive “ ‘overall message’ ” when it “led the retail customers to believe metals were stored on their behalf.” Id. at 1338 (quoting R.J. Fitzgerald, 310 F. 3d at 1328).

Moreover, the court found that the defendant “failed to inform [the retail customers] that the metals it purchased were on a financed basis, it did not own the metals, and the metals, if there were any at all, were not in the retail customers’ names.” Id.; see also U.S. Commodity Futures Trading Comm’n v. Hunter Wise Commodities, LLC, 749 F. 3d 967, 980-82 (11th Cir. 2014) (affirming the district court’s issuance of a preliminary injunction because the CFTC presented aprima facie, case of fraud under 7 U.S.C. § 6b), Southern Trust orchestrated a nearly identical scheme, in. the present case. It misrepresented to customers - the fundamental nature of their investments, telling them that they were investing in metals when ip. fact they were .investing in futures, and charging a fictitious storage fee despite the customers having no metals to, store.

Finally, Southern Trust .failed to tell the customers that it passed..their money through Loreley to Berkeley and Hantec, with the customers having.no knowledge of or relationship with these entities.

The district court therefore did not err in concluding that the CFTC satisfied its burden, under .the preponderance-of-the-evidence standard, to prove the first element necessary to establish fraud.

2. Scienter Regarding the element of scien-ter, Escobio does not dispute that he was the CEO of both Southern Trust and the Holding Corporation, and that he had substantial prior experience in commodities trading. He also does not dispute that he signed the account-opening documents for Loreley’s trading accounts at both Berkeley and Hantec. Those documents, as well as the monthly account statements that Escobio received, make clear that Loreley was investing the customers’ money in futures, not metals. Further, Escobio knew that the accounts at Hantec and Berkeley bore Loreley’s name, not the names of Southern Trust’s customers. Based on these facts, the district court did not clearly err in finding that Escobio knew that he was investing his customers’ money in futures. Nor did the district court clearly err in finding that Escobio knew that Berkeley and Hantec did not make any loans to Southern Trust’s customers, even though Southern Trust charged its cus-, tomers interest on the purported loans. Neither the account-opening documents nor the monthly statements from Berkeley or Hantec reflect any loans from those companies.

Moreover, the Defendants point to no evidence—other than Escobio’s uncorroborated testimony—of any loans from-Berkeley or Hantec, and the district court discounted Escobio’s testimony on that point, as on others, because it determined that he lacked credibility. This circuit applies a “strong rule of deference” in reviewing a district court’s determination of a witness’s credibility at a bench trial. Childrey v. Bennett, 997 F. 2d 880, 834 n.5 (11th Cir. 1993). Given this standard, as well as the numerous conflicts between Escobio’s testimony and the documentary evidence, the court was entitled to find that Escobio lacked credibility and to discount his testimony accordingly.

The district court also correctly applied the law to these facts. “[S]cienter is established if Defendant intended to defraud, manipulate, or deceive, or if Defendant’s conduct represents an extreme departure from the standards of ordinary care.” Commodity Futures Trading Comm’n v. R.J. Fitzgerald & Co., Inc., 310 F. 3d 1321, 1328 (11th Cir. 2002). Adapting “federal securities law” to the commodities-fraud context, this circuit has stated that scienter is shown “when Defendant’s conduct involves ‘highly unreasonable omissions or misrepresentations ... that present a danger of misleading [customers] which is either known to the Defendant or so obvious that Defendant must have been aware of it.’ ” Id. (quoting Ziemba v. Cascade Int’l, Inc., 256 F. 3d 1194, 1202 (11th Cir. 2001)).

The evidence shows that the Defendants either intended to mislead Southern Trust’s customers or made highly unreasonable misrepresentations that posed an obvious danger of misleading them. Esco-bio’s deep involvement in managing the futures-trading accounts at Berkeley and Hantec, as well as his extensive industry experience, support the inference that he knew that he was investing his customers’ money in futures, Hantec’s CEO, at his deposition, put it this way: “Under no circumstance is [it] plausible” that Escobio believed that he was trading in metals. Escobio also surely knew that Berkeley and Hantec had made no loans to Southern Trust’s customers and, therefore, that the customers were being charged interest on loans that did not exist.

The district court thus did not err in concluding that the CFTC had proved scienter.

3. Materiality This brings us to the third and final element—materiality. “A representation or omission is ‘material’ if a reasonable investor would consider it important in deciding whether to make an investment.” Fitzgerald, 310 F. 3d at 1328-29. The Defendants’ briefing on this element addresses only the materiality of their omission that the customers’ money would pass through Loreley to Berkeley and Hantec. If that were the only omission or misrepresentation in this ease, we might need to examine the materiality element more closely. But other misrepresentations found by the district court easily qualify as material. The Defendants, for example, represented that they were investing customers’ money in metals when in fact they were investing it in futures.

Moreover, the Defendants represented that customers owed interest on loans used to purchase metals, but the loans did not exist. A reasonable investor would consider each of these misrepresentations important in deciding whether to invest.

Accordingly, the district court did not err in concluding that these misrepresentations were material. We therefore agree with the district court’s overall conclusion that fraud was established under 7 U.S.C. §§ 6b(a) and 9, and under 17 C.F.R. § 180.1.

E.

The district court did not err in permanently enjoining the Defendants from employment in the commodities-trading industry. Turning now to the propriety of the injunction issued against the Defendants, we note that a district court’s issuance of an injunction is reviewed under the abuse-of-discretion standard. Commodity Futures Trading Comm’n v. Wilshire Inv. Mgmt. Corp., 531 F. 3d 1339, 1347 (11th Cir. 2008) (applying this standard to a permanent injunction issued under the CEA). “[S]o long as [the district court’s] decision does not amount to a clear error of judgment^] we will not reverse even if we would have gone the other way had the choice been ours to make.” S.E.C. v. ETS Payphones, Inc., 408 F. 3d 727, 733 (11th Cir. 2005). “[U]pon a proper showing,” the CEA allows a district court to grant “a permanent or temporary injunction.” 7 U.S.C. § 13a-l(b). ‘“[T]he ultimate test [for an injunction] is whether the defendant’s past conduct indicates that there is a reasonable likelihood of further violations in the future.’ ” Wilshire, 531 F. 3d at 1346 (quoting SEC v. Caterinicchia, 613 F. 2d 102, 105 (5th Cir. 1980)).

This test entails weighing the following six factors: the egregiousness of the defendant’s actions, the isolated or recurrent nature of the infraction, the degree of scienter involved, the sincerity of the defendant’s assurances against future violations, the defendant’s recognition of the wrongful nature of his conduct, and the likelihood that the defendant’s occupation will present opportunities for future violations. SEC v. Camba Air, Inc., 681 F. 2d 1318, 1322 (11th Cir. 1982).

A court need not make a finding on every factor. See Wilshire, 531 F. 3d at 1346-47 (holding that a district court that considered only three of the six factors did not abuse its discretion in issuing an injunction).

Escobio argues that the injunction should be vacated because the district court, in weighing the Carriba Air factors, erred in not concluding that his cooperation with the NFA’s investigation resolved the last three factors in his favor. But the court had discretion in how to interpret Escobio’s cooperation with the NFA. This discretion would have allowed the court, for example, to interpret Escobio’s cooperation not as contrition, but as a self-interested effort to strike a favorable deal with the NFA and, perhaps, to avoid criminal prosecution, Escobio’s denial of wrongdoing at his deposition, at trial, and throughout the NFA’s and the CFTC’s investigations further belies his acceptance of responsibility. The same is true of his attempt to deflect blame onto Berkeley and Hantec, which he claims duped him into' trading futures.

In sum, the court applied the correct legal standard, and its factual findings contain no clear error. We therefore find no fault in its-issuance of a permanent injunction.

F. Restitution is proper only for losses sustained in the leveráged.-metals scheme, not for losses sustained in the unregistered-futures scheme. This-brings us to the final issue in this case—restitution.

The district court awarded restitution-for losses arising from both schemes, First, it awarded $1,543,892 for losses sustained in-the leveragedr-metals scheme, in which the Defendants accepted customers’ money for investment in metals but instead invested the funds in futures.

Second, the court awarded $559,725 for losses sustained in the unregistered-futures scheme, in which the Defendants accepted customers’ money for investment in futures—and actually invested the funds in futures through Loreley’s accounts at Berkeley and Hantec—but failed to register as futures commission.merchants or to conduct the transactions on a registered exchange. The Defendants challenge both awards, arguing that the GFTC failed-to prove, as required by the CEA, that the Defendants’ violations of the-CEA proximately caused their customers’ losses.