
    UNITED STATES of America, Plaintiff-Appellee, v. James BROOKS, Wesley C. Walton, James Patrick Phillips, Defendants-Appellants.
    No. 09-20871.
    United States Court of Appeals, Fifth Circuit.
    May 18, 2012.
    
      Paula Camille Offenhauser, Tony Ray Roberts (argued), James Lee Turner, Asst. U.S. Attys., Houston, TX, for Plaintiff-Appellee.
    Gerald Harris Goldstein (argued), Van Galen Hilley, Cynthia Eva Hujar Orr, Goldstein, Goldstein & Hilley, San Antonio, TX, David Benjamin Gerger (argued), (Courb-Appointed), Gerger & Clarke, Houston, TX, David Adler (argued), Bel-laire, TX, for Defendants-Appellants.
    John Patrick Elwood, Vinson & Elkins, L.L.P., Washington, DC, Barbara Bergman, Albuquerque, NM, for National Ass’n of Criminal Defense Lawyers, Amicus Curiae.
    Before KING, BENAVIDES and DENNIS, Circuit Judges
   BENAVIDES, Circuit Judge:

Defendants-Appellants James Patrick Phillips, Wesley C. Walton, and James Brooks (collectively, the “Defendants-Appellants”) appeal their conviction of and sentencing for false reporting of natural gas trades in violation of the Commodities Exchange Act and the federal wire fraud statute. We AFFIRM.

Factual and PROCEDURAL Background

The Defendants-Appellants are former employees of El Paso Merchant Energy Corporation (“EPME”), a subsidiary of the El Paso Corporation (“El Paso”). The government alleges that the Defendants-Appellants violated the Commodities Exchange Act (“CEA”) and the wire fraud statute by sending false information about natural gas prices to trade magazines that report natural gas prices in indexes, in an effort to affect and manipulate those indexes, which, in turn, would affect the market for natural gas futures and benefit the compan/s financial positions.

Some background on the natural gas industry is necessary for understanding this case. Natural gas is transported throughout North America via a network of pipelines. The gas transportation network is centered around “hubs,” which are geographical locations where major pipeline systems interlink. These hubs act as separate markets, at which supply and demand dictate prices that may differ between the hubs.

Gas trades are divided into different types. Most basically, physical gas is traded, whereby one company agrees to purchase a quantity of gas to be physically delivered to a particular location. In addition to the sale of physical gas, financial trades are made based on gas prices. One particular financial trade, a gas contract for future delivery, is traded on the New York Mercantile Exchange (“NYMEX”). NYMEX contracts are based on the price of gas trading at Henry Hub, Louisiana. Other financial trades, termed “swaps,” are transactions where two traders agree to buy a volume of gas from each other at the same time, but at different prices. In one common format, called a “basis” trade, one party agrees to pay a first-of-the-month index price and the counterparty agrees to pay based on the last day NY-MEX settle. Another common financial transaction is an exchange for physical futures (“EFP”), which is a swap with one end priced off the NYMEX futures market and the other prices off an index plus or minus a differential. Financial trades generally do not result in the transfer of physical gas, but are resolved financially.

The market index prices for physical gas are most prominently published in two privately owned newsletters: Inside FERC Gas Market Report (“Inside FERC”) and Natural Gas Intelligence (“NGI”). Both of these publications publish the natural gas price marketing indicators at the major pipeline hubs and market centers in the United States, and it is undisputed that both publications are highly influential to market price for physical gas. The indexes also are used to determine royalties and public gas contracts, among other things. The publications gather pricing information about the various markets and pipeline hubs by requesting data about physical gas transactions from natural gas traders. After receiving data from the gas traders, and taking a variety of other factors into account, the publications release indexes that purport to represent the price of natural gas at different delivery points. In requesting data, Inside FERC and NGI requested that traders report fixed-price, baseload deals negotiated during bidweek, and it also instructed that basis or EFP trades not be reported.

The Defendants-Appellants were all employees at EPME. EPME traded in both physical and financial transactions of the sort previously mentioned. In 2000, Defendant-Appellant Brooks was EPME’s Senior Vice President for Risk Management, and he was responsible for overseeing physical traders. In 2001, Brooks became the Managing Director for Natural Gas, and he oversaw both physical and basis traders. At the time, EPME was divided into various trading “desks,” which were then split between physical gas trading and finance trading. The desks were based on pipeline network regions. During the time in question, Defendanh-Appel-lant Phillips was a senior physical trader and was manager of the Texas Desk at EPME. Defendant-Appellant Walton was a basis trader on the financial side for both the Texas Desk and the Gulf Coast Region of the Northeast Desk. As a market participant, Inside FERC and NGI would request physical trade information from EPME. EPME would report the information to the trade publications via spreadsheets sent by the physical traders responsible for each of EPME’s desks.

From summer 2002 to fall 2002, El Paso received inquires from various federal agencies and a United States Attorney’s Office grand jury subpoena seeking information on the reports EPME sent to the trade publications. Around that time, El Paso hired Haynes & Boone, a law firm, to conduct an internal investigation into allegations that El Paso employees had submitted false trades to trade publications. Defendants-Appellants Brooks, Walton, and Phillips were interviewed as part of that investigation, and each employee was subsequently terminated. Nonetheless, at least at the beginning of this investigation, El Paso paid the legal fees for both Walton and Brooks.

Starting in March 2003, an Assistant U.S. Attorney began a course of correspondence with El Paso’s legal counsel about El Paso’s payment of legal fees for former employees. El Paso informed the Assistant U.S. Attorney about the company by-laws, according to which EPME was required to indemnify any employee for legal fees if the employee was found not to have engaged in wrongdoing, but EPME was left with discretion about whether to advance payment of legal fees prior to such determination. El Paso stated that, based in part on “the limited results of the Haynes & Boone interviews,” it had decided not to advance legal fees for Brooks, but that it was inclined to advance Walton’s legal fees. El Paso stressed, however, that it would consider the employee’s cooperation with the federal investigation in deciding whether to continue advancing legal fees. After additional correspondence regarding Delaware law and its application to El Paso’s indemnification policy, the government, in response to El Paso’s request for the identities of any individual who was not cooperating, identified Walton, as well as four other employees, who are not defendants here, as non-cooperating employees. Sometime thereafter, El Paso terminated Walton’s legal fees, but it did not inform the government.

Defendant-Appellant Phillips, who had not been discussed in the correspondence, subsequently requested indemnification. On August 12, 2004, El Paso declined Phillips’s request, noting that indemnification was made only after an ultimate determination of the legal proceedings, and that it would not advance his legal fees. El Paso also noted that it was not obliged to advance fees, and that EPME was cooperating with the government and so it would not advance legal fees to “potential subjects or targets of their investigations.”

On September 25, 2006, the government filed a second superseding indictment, charging the Defendants-Appellants with forty-nine counts: specifically, twenty-four counts of false reporting in violation of the CEA, 7 U.S.C. § 13(a)(2), twenty-four counts of wire fraud in violation of 18 U.S.C. § 1343, and one count of conspiracy to commit false reporting and wire fraud in violation of 18 U.S.C. § 371. The government alleged that the Defendants-Appellants were involved in a conspiracy, lasting from about April 2000 through May 2002, whereby the Defendants-Appellants reported false information related to natural gas prices to Inside FERC and NGI to manipulate the index prices reported in those magazines. Specifically, the government alleged that DefendanWAppellant Brooks would direct the physical gas traders at EPME to report false data to the publications, such as trades that did not occur, false prices, or false gas volumes, in a manner that would benefit EPME’s financial positions. Defendant-Appellant Walton, a basis trader on the Texas and Northeast Desks, would allegedly tell the physical traders his financial positions for the upcoming month, such as whether he wanted the index price of gas to increase or decrease in certain areas, so the physical traders could report data manipulating the published indexes in his favor. The second superseding indictment also alleged that Defendant-Appellant Phillips and the other physical gas traders sent fictitious information and reports to Inside FERC and NGI. The government alleged that twenty-four misleading reports were transmitted to these publications, either personally by the Defendants-Appellants or based on their instructions.

The trial lasted from December 4, 2007 to February 7, 2008. During the trial, the government submitted over 1,000 exhibits, including the bidweek surveys sent to Inside FERC and NGI, internal worksheet versions of those surveys, internal EPME emails, EPME trade tickets recording physical and basis deals, summaries of basis positions, and hundreds of taped telephone calls. During trial, the jury heard testimony from fourteen government witnesses, including Matthew O’Loughlin, an expert, and five defense witnesses, including Defendant-Appellant Brooks.

The government’s two primary witnesses were physical traders Dallas Dean and Sharon O’Toole. Dean was a physical trader on the Northeast Desk and O’Toole was a physical trader on the Texas Desk. Both testified about the conspiracy and stated that Defendant-Appellant Brooks instructed them to submit false data to Inside FERC based on information given to them by Defendant-Appellant Walton. O’Toole also testified about Defendant-Appellant Phillips’s involvement in the conspiracy. The government also admitted a large number of incriminating emails between the various traders — often between Phillips and other physical traders — about the content of the reports sent to Inside FERC and NGI or requesting information from basis traders about their financial positions. Similarly, the government played recordings of telephone calls, many recorded on Walton’s line. In some of these conversations, Walton discussed price targets for certain trading regions, the submission of reports that would or had affected published indexes, and whether certain reported trades were too low to be credible. He also thanked the physical traders when the published index prices were favorable to his financial positions.

In one particularly important email chain, various EPME employees, including Brooks, Phillips, and Walton, discussed the reports sent to the publications. Starting this chain, Brooks emailed the physical and financial traders on October 23, 2000, writing:

There has [sic] been several discussions on how IP [Inside FERC ] price should be reported in the month of November. Most of you are aware that we reported only verifiable fixed price transactions to IF for October. It is the opinion of some, that the reason for doing so made no difference, and only eliminated us as an active price setting participant. In an effort to get everyone’s opinion on this, reply as to the following: 1. Report according to our book bias (as in the past). 2. Report verifiable fixed price trades only.

In response, various traders, including Walton and Phillips, chose the first option. Several other traders discussed the options, emailing with Brooks and discussing how Inside FERC had a standardized format for reporting data, but that the “integrity of the data ... is not verified.” Another trader replied that they should “avoid discussing this is on e-mail” due to ongoing investigations, and O’Toole replied, “GOOD point!”

Also testifying for the government was Ronald Clay Sanders, an employee at EPME, who worked as the manager of the risk operations group during the time of the alleged conspiracy. Sanders testified whether the trades reported to Inside FERC or NGI by the physical traders were real and whether they matched any trades in the EPME electronic database. Overall, Sanders testified that only 3.6% of the 6,213 trades reported to Inside FERC and NGI during the course of the conspiracy matched actual trades, and that if the trades reported by the West Desk are excluded — which allegedly stopped participating in the conspiracy in fall 2002 — -only 1.9% of the 5,687 trades match actual trades. Finally, the government presented O’Loughlin, an expert who testified about the effect of EPME’s false reports on the published indexes at Inside FERC and NGI.

The primary defense witness was Defendant-Appellant Brooks. In part, Brooks testified about the incriminating October 2000 email chain where the traders discuss reporting based on “book bias.” Brooks testified that “book bias” did not mean that the physical traders would submit numbers favoring the basis traders’ positions; rather, Brooks stated that the term meant that EPME would report data to the publications based on their perception of where gas was actually trading.

A potential defense witness, Don Guil-bault, invoked his Fifth Amendment privilege against self-incrimination on the day he was scheduled to testify. Guilbault was a physical trader at EPME and he had admitted to submitting false reports to Inside FERC and NGI. According to the Defendants-Appellants, however, Guilbault would have testified that Walton did not provide him with basis positions to shape his reports. Although Guilbault pled guilty prior to the Defendant-Appellants’ trial, he was still awaiting sentencing at the time of the current trial to ensure cooperation. The Defendants-Appellants moved to compel testimony; after a hearing, the district court denied the motion, finding no government misconduct and a valid purpose for the invocation of privilege.

After closing arguments, the jury deliberated for three days. The jury sent several notes during deliberations, one of which asked a question about the phrase “ignorance of the law is no excuse.” Ultimately, the jury found: all Defendants-Appellants guilty of the conspiracy count; Phillips guilty of false reporting and wire fraud on counts 5, 9-10, 14, 19-21, 23-25, 29, 33-34, 38, 43-45, 47-49, and not guilty on all other charged counts; Walton guilty of false reporting and wire fraud on counts 3-5, 9-10, 19-24, 27-29, 33-34, 43-48, and not guilty on all other charged counts; and Brooks guilty on counts 2-5, 8-29, 32-49, and not guilty on all other charged counts.

On December 17, 2009, the district court sentenced the Defendants-Appellants. The district court calculated, for Phillips and Walton, that the proper offense level was thirty-three (with criminal history category 1), with a recommended sentencing range of 135 to 168 months. For Brooks, the district court calculated that the offense level was thirty-five (with a criminal history category 1), with a recommended sentencing range of 168 to 210 months. The district court sentenced Phillips and Walton to 135 months of imprisonment and sentenced Brooks to 168 months of imprisonment.

The Defendants-Appellants filed a timely notice of appeal, and they now assert ten separate grounds for error. They argue that the indictment must be dismissed, and that their convictions and sentences must also be reversed.

Analysis

A. Government Interference with Payment of Legal Fees

The Defendants-Appellants first argue that the government pressured EPME to cut off its payment of legal fees for their attorneys, violating their Fifth and Sixth Amendment rights, and consequently, requiring dismissal of the indictment against them, relying on 2003 correspondence between the Assistant U.S. Attorney and El Paso’s legal counsel. The district court found no such pressure by the government, and the Defendants-Appellants do not show clear error in that determination.

We review a district court’s denial of a motion to dismiss an indictment de novo. United States v. McNealy, 625 F.3d 858, 868 (5th Cir.2010). We review the district court’s underlying factual findings for clear error. Id. “Under the clear error standard, we defer to the findings of the district court unless we are left with a definite and firm conviction that a mistake has been committed.” United States v. Avants, 367 F.3d 433, 441 (5th Cir.2004) (citation and internal quotation omitted).

The record creates no “firm conviction” that the district court erred in finding the government did not coerce El Paso into deciding not to advance the Defendants-Appellants’ legal fees. While the correspondence shows El Paso possessed an intense desire to be seen as cooperative by the government, the government never demanded or suggested to El Paso that it cease paying the legal fees of the Defendants-Appellants. Indeed, rather than create a “firm conviction” that El Paso was coerced into not paying the Defendants-Appellants’ attorney fees, the correspondence shows El Paso, through EPME, exercised its own discretion whether to pay the Defendants-Appellants’ legal fees. The correspondence shows that EPME had the discretion, under its by-laws, not to advance legal fees to its employees. Further, as to Brooks, the correspondence shows El Paso had exercised that discretion prior to the government’s correspondence due to the company’s conclusion that he was involved in wrongdoing.

Nor do Defendants-Appellants fair better in relying on the 2003 Justice Department Memorandum, “Principles of Federal Prosecution of Business Organizations,” also known as the “Thompson Memorandum.” That memorandum provided guidance on how the government should decide whether a corporate entity is cooperating with an investigation, and it suggested that investigators consider whether a corporation was advancing legal fees to culpable agents. Admittedly, that memorandum has been subject to criticism, and the Department of Justice has subsequently revised its policies. Nevertheless, the mere existence of the memorandum could not have compelled El Paso.

This case is distinguishable from the facts that the Second Circuit confronted in United States v. Stein, 541 F.3d 130 (2d Cir.2008). There, the district court found that the government had “forced” KPMG to cease paying legal fees on behalf of the defendants, the payment of which had been KPMG’s long-standing policy, based on threats from the government and the government’s involvement in crafting internal KPMG memos dissuading employees from obtaining counsel. Id. at 147-50. The district court’s factual findings bound the Second Circuit, and on such findings, the Second Circuit held KPMG’s actions were state actions that violated the defendants’ right to counsel of their choice. Id.

Here, as noted above, no such factual findings were made, and reasonably so. Whereas in Stein, where the government specifically threatened to take into account KPMG’s payment of legal fees, referring to the Thompson Memorandum, the correspondence here does not refer to that memorandum and it includes no threat to indict El Paso if it continued to pay fees. Moreover, the governmeiit did not meddle in El Paso’s internal discussion with employees in an attempt to dissuade the retention of counsel. Lastly, whereas KPMG’s long-standing policy of paying legal fees demonstrated that the fees would have been paid but for the government’s actions, EPME’s policy was discretionary, and had been independently exercised to not advance legal fees to Brooks.

Accordingly, the Defendants-Appellants fail to show clear error in the district court’s factual findings, and under those facts, we find that denial of the motion to dismiss the indictment was proper.

B. Applicability and Constitutionality of CEA

The Defendants-Appellants raise a number of challenges to the applicability and constitutionality of the CEA. First, they argue that 7 U.S.C. § 13(a)(2)’s reference to “false ... reports” does not cover the false reports they sent to industry newsletters. Second, they argue that trades of physical natural gas are exempted from the CEA and/or do not meet the Act’s definition of “commodity.” Third, the Defendants-Appellants argue that various terms in § 13(a)(2) are vague, and thus the CEA is unconstitutionally vague as applied to them. Fourth, they argue that the CEA is overbroad. While the Defendant-Appellants’ arguments are sweeping, they are, ultimately, unavailing.

1. “Report”

The Defendants-Appellants first argue that their communications with Inside FERC and NGI do not qualify as “reports” under § 13(a)(2). They state that other portions of the CEA, as well as the CFTC’s regulations promulgated thereunder, distinguish between “statements” and “reports,” and generally use “report” to refer to “a formal record or document the Commission requires regulated futures professionals or traders to file, maintain or provide to the Commission or costumers.”

The CEA states that it shall be unlawful for:

[a]ny person ... knowingly to deliver or cause to be delivered for transmission through the mails or interstate commerce by telegraph, telephone, wireless, or other means of communication false or misleading or knowingly inaccurate reports concerning ... market information or conditions that affect or tend to affect the price of any commodity in interstate commerce ....

7 U.S.C. § 13(a)(2). The term “reports” is not defined in the CEA or CFTC regulations. See 7 U.S.C. § la; 17 C.F.R. § 1.3. Neither the Supreme Court nor any circuit court has considered the definition. Consequently, the applicability of the term “reports” appears to be an issue of first impression.

“In construing the United States Code our task must begin with the words provided by Congress and the plain meaning of those words.” United States v. Valencia, 394 F.3d 352, 355 (5th Cir.2004). Thus, we begin with the plain meaning of “report[ ],” which the dictionary defines as any statement of fact, or at least a detailed statement of fact. See Merriam-Webster, report, available at http://www.merriamwebster.com/dictionary/report (defining report as “a usually detailed account or statement”); Oxford English Dictionary, report, available at http://www.oed.com/ search?searchType=dictionary&q=report (defining report as “[i]nformation provided or conveyed, and related senses,” “[a]n account of a situation, event, etc., brought by one person to another ..., a notification of something observed,” “[a] descriptive account or statement”); see also CBC, Inc. v. Bd. of Governors of Federal Reserve Sys., 855 F.2d 688, 690-91 (10th Cir.1988) (applying dictionary definition of “report” to interpret word in Bank Holding Act). The Defendants-Appellants’ statements to Inside FERC and NGI would satisfy such a definition. They were not expressions of opinion, or casual communications, but were lengthy documents outlining detailed information about natural gas trades, sent to established industry publications with the intent to inform those publications about the state of the natural gas markets.

The Defendants-Appellants argue that “reports,” when used in the CEA, refers only to formal reports required under the statute to be submitted by traders to the CFTC or to customers, and that other portions of the CEA differentiate between “reports” and mere “statements.” While it is true that various parts of the CEA specify reports that are to be kept and submitted, such fact cuts against the Defendants-Appellants. Where the CEA discusses reports to be sent to the CFTC or to customers, the CEA specifies the kind of report. See 7 U.S.C. § 6g (providing “[e]very person registered hereunder ... shall make such reports as are required by the Commission ...” (emphasis added)); 7 U.S.C. § 6i(2) (providing certain trades unlawful “unless such person files ... with ... the Commission such reports regarding any transaction ... as the Commission may by rule ... require” (emphasis added)); 17 C.F.R. § 16.00 (providing “[e]ach reporting market shall submit to the commission ... a report ... showing” specified information); 17 C.F.R. § 17.00 (providing “[e]ach futures commission merchant ... shall submit a report to the Commission ... ”; requiring report to provide specified information). Such specifics would be unnecessary if every use of “report” implied the same type of report. The fact that the CEA specifies the kind of report when discussing reports to be made to the CFTC or to customers implies that when the CEA uses “report,” without such limits, it does so in a more general fashion.

Indeed, reading § 13(a)(2) in the manner suggested by Defendants-Appellants would render other sections of the CEA superfluous. The next two subsections of the CEA make it unlawful for “[a]ny person knowingly to make ... any statement in any application, report, or document required to be filed under this chapter ... which statement was false or misleading with respect to a material fact,” and for “[a]ny person willfully to falsify ... a material fact, make any false ... statements or representations ... to a registered entity, board of trade, of futures associations -” 7 U.S.C. § 13(a)(3), (4) (emphasis added). Similarly, 7 U.S.C. § 6b(a)(2) renders it unlawful for “any person, in or in connection with any order to make ... any contract of sale of any commodity for future delivery ..., (B) willfully to make or cause to be made to the other person any false report or statement or willfully to enter or cause to be entered for the other person any false record.” If § 13(a)(2) was intended to cover only false reports sent to the CFTC or to customers, these other sections would be superfluous.

Moreover, if § 13(a)(2) concerned only false reports submitted to the CFTC, or false reports submitted from traders to customers, there would be no need to limit the provision to communications “in interstate commerce,” and that “affect or tend to affect the price of any commodity.” See 7 U.S.C. § 13(a)(2). These jurisdictional “hooks” would not be needed for Congress to regulate false communications to a government agency, or false communications by federally registered traders. See M’Culloch v. Maryland, 17 U.S. (4 Wheat.) 316, 417, 4 L.Ed. 579 (1819). The fact is apparent when one looks at the CEA’s provisions that specifically deal with false reports to the CEA or customers. Those sections are not limited to communications in interstate commerce or to those that affect commodity prices. Instead, they render all false statements to the CFTC or customers by registered traders unlawful. See 7 U.S.C. §§ 6b(a)(2)(B), 13(a)(3)(4).

Further, the language in § 13(a)(2) indicates that covered “reports” include more than formal communications to the CFTC or customers. As the Northern District of Georgia pointed out, § 13(a)(2) covers reports communicated “through the mails or interstate commerce by telegraph, telephone, wireless or other means of communication.” See CFTC v. Atha, 420 F.Supp.2d 1373, 1380-81 (N.D.Ga.2006). As the section clearly contemplates reports sent by telephone, it is unlikely it is intended to cover only the official reports.

Finally, the CFTC has consistently interpreted § 13(a)(2) to apply to trade reports sent to Insider FERC and/or NGI, like those sent by the Defendants-Appellants. Although not promulgated in notice-and-comment rulemaking, the CFTC has sued various defendants for behavior identical or similar to that at issue here. See CFTC v. Dizona, 594 F.3d 408, 411-13 (5th Cir.2010) (alleging defendants sent false reports to Inside FERC and NGI; affirming district court’s refusal to overturn jury verdict on false reporting because no evidence that reports were false); CFTC v. Reed, 481 F.Supp.2d 1190, 1193 (D.Colo.2007) (alleging defendants sent false trade reports to “industry reporting firm”); Atha, 420 F.Supp.2d at 1377-78 (alleging defendants sent false reports to Insider FERC, NGI, and Gas Daily). The CFTC’s consistent interpretation is afforded at least some deference. See generally Skidmore v. Swift & Co., 323 U.S. 134, 65 S.Ct. 161, 89 L.Ed. 124 (1944).

Accordingly, we find that the Defendant-Appellants’ communications with Inside FERC and NGI qualified as “reports” under 7 U.S.C. § 13(a)(2).

2. Covered Commodities

The Defendants-Appellants next argue that the CEA does not apply to their conduct, making two arguments. First, they argue that natural gas is an exempt commodity under the CEA, and thus, the types of contracts they allegedly falsely reported — natural gas contracts — are exempt. Second, they argue that because the CEA only regulates natural gas futures contracts, which are traded on NY-MEX, any false reporting related to index prices at hubs other than Henry Hub are not covered by the CEA. These arguments will be considered in turn.

a. Exemptions

In 1993, the CFTC issued a final rule which “exempted] from all provisions of the [CEA], [except certain provisions to the extent they prohibit manipulation] ... [contracts for the purchase and sale of ... natural gas, [and] natural gas liquids.” See 58 Fed.Reg. 21,286, 21,294 (1993). Thereafter, 7 U.S.C. § 2(g)-(h) was amended in 2000, as part of the Commodity Futures Modernization Act, to exclude all trades between individual qualified participants that are not “executed or traded on” or “entered into on” a “trading facility,” which, defendants argue, covers the physical natural gas trades. The Defendants-Appellants contend that because natural gas is exempted under both the 1993 CFTC rule and the 2000 amendment to the CEA, their false reporting practices are also exempted from the CEA’s coverage.

The Defendants-Appellants’ argument, however, has been uniformly rejected by the courts that have considered it — this Court included. In United States v. Futch, an unpublished decision, this Court found that the various exemptions only cover actual contracts for natural gas, and do not cover false reports about non-existent contracts. See 278 Fed.Appx. 387, 392 (5th Cir.2008). In reaching this holding, this Court stated that “ § 13(a)(2)’s false reporting offense ... extends to ‘any commodity in interstate commerce’ and is not limited to futures contracts regulated by the CFTC ...[;] ‘false reporting of market information concerning natural gas and attempted manipulation of natural gas price indices does not implicate an agreement, contract or transaction’ and thus does not come under the exceptions in 7 U.S.C. § 2(g)-(h).” See id. (citations and quotations omitted). As in Futch, the charges against the Defendants-Appellants do not arise from their execution of contracts for purchase of natural gas, or contracts entered into outside of a trading facility, but rather, for filing false reports about contracts that they claimed to have executed.

This reading has been uniformly adopted by courts, and the Defendants-Appellants do not cite any contrary case law to support their argument. See, e.g., Reed, 481 F.Supp.2d at 1197-98 (holding that false reporting not exempted); Atha, 420 F.Supp.2d at 1379-80 (same); CFTC v. Bradley, 408 F.Supp.2d 1214, 1218-19 (N.D.Okla.2005) (same); United States v. Valencia, No. Civ. A. H-03-024, 2003 WL 23174749, at *10 (S.D.Tex. Aug. 25, 2003) (same), rev’d on other grounds, 394 F.3d 352 (5th Cir.2004); see also CFTC v. Johnson, 408 F.Supp.2d 259, 266-67 (S.D.Tex.2005) (not expressly addressing issue but finding that CEA covers nearly identical false reporting practices). Moreover, other decisions by this Court have implicitly found that the CEA covers false reports about natural gas markets, even if it would not cover the falsely reported contracts (if they existed). See Dizona, 594 F.3d at 418 (dismissing false reporting count for lack of evidence, but assuming CEA covered similar false reporting of natural gas); Valencia, 394 F.3d at 353-57 (assuming but not expressly deciding that the CEA covers false reporting of natural gas); see also 58 Fed.Reg. at 21,291 (approving exemption of natural gas; noting conduct “otherwise subject to the Act would not be exempt for such activity, even if it were connected to their exempted ... (Energy Contract) activity”). In sum, given that we agree with the previously cited decisions that squarely rejected the Defendants-Appellants’ argument, we hold that the exemptions in the CEA and the CFTC do not cover their reporting activities.

b. “Commodity”

The Defendants-Appellants next contend that the false reports they submitted did not concern a “commodity” subject to the CEA. They argue that only natural gas traded at Henry Hub is a commodity under the CEA because only natural gas traded at Henry Hub underlies the natural gas futures contracts traded on NYMEX. Consequently, because the government proved only that their false reports affected or could have affected the price of natural gas generally, and not at Henry Hub, the Defendants-Appellants argue their convictions must be vacated. We do not agree.

The CEA defines “commodity” as “wheat, cotton, rice, corn, oats, barley, rye ..., and all other goods and articles, except onions ..., and all services, rights, and interests ... in which contracts for future delivery are presently or in the future dealt with.” See 7 U.S.C. § la(4). Natural gas is plainly a “good” or “article.” The questions thus turns on whether it is a good “in which contracts for future delivery are presently or in the future dealt with.”

As mentioned above, futures contracts for natural gas are traded on NYMEX, and those futures are derivative of natural gas traded at Henry Hub. Nonetheless, the record shows that natural gas may be moved from any location to Henry Hub through the national pipeline system. Thus, it would be peculiar that natural gas at another hub is not a commodity, but suddenly becomes a commodity solely on the basis that it passes through Henry Hub, and ceases to be a commodity once it moves onto some other locale. While the price of that commodity may fluctuate with its location, and the forces of supply and demand at that location, the actual nature of the “good” does not change.

Although, as discussed above, the Defendants-Appellants conduct did not fall within the regulatory exemption, the existence of that exemption bolsters our reading of the definition of “commodity.” The CFTC exempted from the CEA’s coverage “[c]on-tracts for the purchase or sale of ... natural gas.” See 58 Fed.Reg. at 21,294. Such an exemption would be unnecessary if natural gas was not a commodity under the act.

Case law supports such a reading. Although no court has squarely confronted the question presented by the Defendants-Appellants, neither has any court suggested that natural gas at hubs other than Henry Hub is outside the purview of the CEA. See Futch, 278 Fed.Appx. at 390 (stating “natural gas is a commodity under the Commodity Exchange Act”); Valencia, 394 F.3d at 353 (considering allegations defendant manipulated natural gas market, by reporting false trades, in violation of § 13(a)(2)); United States v. Radley, 659 F.Supp.2d 803, 806 (S.D.Tex.2009) (stating “natural gas” was “the commodity at issue in the case”); Reed, 481 F.Supp.2d at 1196 (finding allegations “Defendant attempted to manipulate the price of natural gas, a commodity that travels in interstate commerce” covered by CEA); Atha, 420 F.Supp.2d at 1377-78 (stating “[njatural gas is a commodity”); Bradley, 408 F.Supp.2d at 1220 (“It is undisputed that natural gas constitutes a ‘commodity’ under the CEA.”); Johnson, 408 F.Supp.2d at 264-65 (finding allegations defendants falsely reported natural gas trades stated a claim under § 13(a)(2)).

Hershey v. Energy Transfer Partners, L.P., 610 F.3d 239 (5th Cir.2010), does not contradict this reading. In that case, the Court considered whether private plaintiffs had a cause of action based on allegations that the defendants were manipulating the price of natural gas at hubs other than Henry Hub. Id. at 243-49. The private plaintiffs’ standing to sue was premised on their holding NYMEX futures contracts. Id. at 240. The CEA, however, provides a right of action for holders of a futures contract for manipulation of that contract or “the price of the commodity underlying such contract.” See 7 U.S.C. § 25(a)(1)(D). Consequently, as the plaintiffs had not alleged manipulation of the Henry Hub natural gas price, which price underlay their security, they had no cause of action against manipulation of the price of natural gas which had no affect on their security. See Hershey, 610 F.3d at 241, 247 (stating “[t]he modifier ‘underlying’ has an important effect on ‘commodity— the ‘underlying commodity’ of a futures contract is a specific good, governed by the terms of the futures contract”; holding “the underlying commodity of a NYMEX natural gas futures contract is not natural gas wherever bought and sold, but the specific natural gas delivered at Henry Hub”). Hershey, however, never questioned whether natural gas was a commodity subject to § 13(a)(2).

Accordingly, we find that natural gas, whether at Henry Hub or at some other location, is a “commodity” within the meaning of the CEA.

3. Vagueness

The Defendants-Appellants next argue § 13(a)(2) is unconstitutionally vague because it fails to give fair notice that the CEA, an act whose primary purpose is to regulate futures and options, covers false reporting of physical trades. In particular, they argue that terms “report,” “false or misleading,” “market information,” “conditions that tend to affect the price of any commodity in interstate commerce,” and “price” are all vague.

“It is a basic principal of due process that an enactment is void for vagueness if its prohibitions are not clearly defined.” Grayned v. City of Rockford, 408 U.S. 104, 108, 92 S.Ct. 2294, 33 L.Ed.2d 222 (1972). “[T]he void-for-vagueness doctrine requires that a penal statute define the criminal offense with sufficient definiteness that ordinary people can understand what conduct is prohibited and in a manner that does not encourage arbitrary and discriminatory enforcement.” Kolender v. Lawson, 461 U.S. 352, 357, 103 S.Ct. 1855, 75 L.Ed.2d 903 (1983). Nonetheless, it is also “well established that vagueness challenges to statutes which do not involve First Amendment freedoms must be examined in light of the facts of the case at hand.” United States v. Mazurie, 419 U.S. 544, 550, 95 S.Ct. 710, 42 L.Ed.2d 706 (1975).

Here, the Defendants-Appellants do not argue that their speech is protected by the First Amendment. Indeed, this Circuit has held that “intentional or reckless falsehood, even political falsehood, enjoys no First Amendment protection[.]” Colson v. Grohman, 174 F.3d 498, 507 (5th Cir.1999) (finding first amendment did not protect defamation and libel made with knowledge of or reckless disregard to falsity).

Consequently, the Defendants-Appellants’ vagueness challenge must be evaluated in light of the proven conduct. As discussed below, the evidence shows the Defendants-Appellants reported knowingly false trades to Inside FERC and NGI, that they did so with the intent that it affect those publications’ reported indexes, and with the intent that it would affect EPME’s financial positions, to their personal benefit. Simply put, it is incredulous to believe that a person of average intelligence could not understand the CEA as potentially applying to that type of conduct. See Futch, 278 Fed.Appx. at 393-95 (holding CEA was not vague in application to false trade reports submitted to Inside FERC).

In particular, “report,” as discussed above, clearly covers the Defendants-Appellants’ emails and faxes to the publications. Similarly, “false and misleading” has a clear and well defined meaning. “[M]arket information” clearly covers reports of quantity and price of trades. See id. at 393 (holding the term “ ‘market information’ is not vague because [defendant’s] false statements about time, place, price, and volume of ... natural gas trades clearly qualified as ‘market information’ under almost any definition of the term”). Similarly, the term “price” is also clear. See Merriam-Webster, price, available at http://www.merriam-webster.com/ dictionary/price (defining “price” as “the amount of money given or set as consideration for the sale of a specified thing”). Even if the Defendants-Appellants are correct that there are a number of prices in natural gas trading, each one of the referenced prices is a “price,” and thus manipulation of it would create a violation of § 13(a)(2). Finally, the term “affect or tend to affect” clearly covers a situation, such as the Defendants-Appellants’, where the false reports served as the basis for the industry publication’s price reports. See Futch, 278 Fed.Appx. at 394 (noting “even if the phrase ‘tends to affect’ were found to be vague in some factual contexts, it is sufficiently clear to have put [defendant] on notice that providing false sales data to Inside FERCs monthly reporting index survey violated the law”).

Accordingly, the CEA is not unconstitutionally vague as applied to the Defendants-Appellants’ conduct.

4. Overbreadth

The Defendants-Appellants also challenge the CEA as being unconstitutionally overbroad. The Defendants-Appellants argue that the CEA, while directed at constitutionally unprotected speech, nevertheless covers constitutionally protected speech because it requires no mens rea proof with regard to the element that the speech “affect or tend to affect” commodity prices.

A statute is overbroad if in “banning unprotected speech,” a “substantial amount of protected speech is prohibited or chilled in the process.” Ashcroft v. Free Speech Coalition, 535 U.S. 234, 237, 122 S.Ct. 1389, 152 L.Ed.2d 403 (2002). Nevertheless, by its express language, the CEA only covers “knowingly ... false or misleading or knowingly inaccurate” speech. Such speech is not constitutionally protected. See Colson v. Grohman, 174 F.3d 498, 507 (5th Cir.1999). Accordingly, the CEA covers no constitutionally protected speech.

C. Jury Instructions

The Defendants-Appellants next argue that the district court’s jury instructions were erroneous on several grounds. We review “preserved error in jury instructions under an abuse of discretion standard and ask whether the court’s charge, as a whole, is a correct statement of the law and whether it clearly instructs jurors as to the principles of the law applicable to the factual issues confronting them.” United States v. Kay, 513 F.3d 432, 446 (5th Cir.2007) (quotation and footnote omitted). Under this standard, district courts “enjoy substantial latitude in formulating a jury charge.” United States v. Davis, 609 F.3d 663, 689 (5th Cir.2010); see also United States v. Williams, 610 F.3d 271, 285 (5th Cir.2010). Similarly, the district court is afforded “great discretion in responding to jury questions.” United States v. Wilcox, 631 F.3d 740, 752 (5th Cir.2011) (quotation marks omitted). However, when a jury instruction “hinges on a question of statutory construction, [our] review is de novo.” United States v. Wright, 634 F.3d 770, 774 (5th Cir.2011).

1. Conspiracy Instructions

First, the Defendants-Appellants argue that the district court incorrectly instructed the jury on the mens rea of conspiracy and conspiracy to commit wire fraud in a response to a jury note. In its jury instructions, based on the Fifth Circuit Pattern Criminal Instructions, the district court instructed that to convict for conspiracy under 18 U.S.C. § 371, the jury must find:

First: That two or more persons made an agreement to commit the crime of false reporting or wire fraud as charged in the indictment;
Second: That the defendant knew the unlawful purpose of the agreement and joined in it willfully, that is, with the intent to further the unlawful purpose; and
Third: That one of the conspirators during the existence of the conspiracy knowingly committed at least one of the overt acts described in the indictment, in order to accomplish some object or purpose of the conspiracy.

The district court also explained that under the first element the jurors need to “agree that the government proved beyond a reasonable doubt that the defendants conspired to commit false reporting; or, all of you must agree that the government proved beyond a reasonable doubt that the defendants conspired to commit wire fraud.” The district court instructed that to convict someone of wire fraud under 18 U.S.C. § 1343, the jury must find:

First: That the defendant knowingly created a scheme or artifice to defraud or to obtain money, property or other things of value by means of material false or fraudulent pretenses, representations or promises as set out in the indictment;
Second: That the defendant acted with a specific intent to defraud;
Third: That the defendant used interstate wire communications facilities or caused another person to use interstate wire communications facilities for the purpose of carrying out the scheme; and
Fourth: That the scheme to defraud employed false material representations.

The district court explained that “ ‘specific intent to defraud’ means an intent to specifically deceive or cheat someone.”

During its deliberations, the jury sent the district court a note asking:

In the second part of Count 1 it states, “that the Defendant knew the unlawful purpose.” Doesn’t this contradict the idea that “ignorance of the law is no excuse.”

After a conference with the parties, the district court replied to the note, writing:

There is no contradiction. The government is not required to prove that a defendant knew the purpose of the agreement was in fact unlawful, that is, in violation of a statute, but the government must prove the defendant knew the purpose of the agreement, and the government must prove that the purpose was in fact unlawful.

The Defendants-Appellants argue that this answer misstates the mens rea required to prove conspiracy and conspiracy to commit wire fraud.

A conviction for conspiracy under Section 371 requires that the government prove: “(1) an agreement between two or more persons to pursue an unlawful objective; (2) the defendant’s knowledge of the unlawful objective and voluntary agreement to join the conspiracy; and (3) an overt act by one or more of the members of the conspiracy in furtherance of the objective of the conspiracy.” United States v. Coleman, 609 F.3d 699, 704 (5th Cir.2010); see also United States v. Curtis, 635 F.3d 704, 719 n. 53 (5th Cir.2011). Conspiracy actually has two intent elements — intent to further the unlawful purpose and the level of intent required for proving the underlying substantive offense. See 2 Wayne R. LaFave & Austin W. Scott, Jr., Substantive Criminal Law' § 12.2(c)(1) (2003); United States v. Alvarez, 610 F.2d 1250, 1255 (5th Cir.1980) (“Conspiracy is, however, more complex because it involves two elements of intent that shade into each other: each party must have intended to enter into the agreement and the schemers must have had a common intent to commit an unlawful act.”).

The Defendants-Appellants first seem to argue that proving conspiracy always requires proof the defendant knew his conduct was unlawful, regardless of the mens rea of the underlying substantive offense. This argument is inconsistent, however, with the Supreme Court’s opinion in Ingram v. United States, 360 U.S. 672, 79 S.Ct. 1314, 3 L.Ed.2d 1503 (1959). In that decision, the Supreme Court stated that to convict for conspiracy, “[t]here need not, of course, be proof that the conspirators were aware of the criminality of their objective,” but rather, there must only be proof of knowledge of the unlawful conduct. Id. at 678. This holding was reaffirmed in United States v. Feola, 420 U.S. 671, 95 S.Ct. 1255, 43 L.Ed.2d 541 (1975). In Feola, the Supreme Court again stated that the government need not prove anything more than the degree of criminal intent necessary for the substantive offense in order to convict a defendant of conspiracy. Id. at 686-87, 95 S.Ct. 1255. Thus, to the extent that the Defendants-Appellants argue that conspiracy always requires proof that the defendant knew his conduct was unlawful, we reject their argument. See United States v. Blair, 54 F.3d 639, 642-43 (10th Cir.1995) (rejecting same argument and stating that since “ ‘one can violate a criminal statute simply by engaging in the forbidden conduct, a conspiracy to commit that offense is nothing more than an agreement to engage in the prohibited conduct’ ” (quoting Feola, 420 U.S. at 687, 95 S.Ct. 1255)).

More specific to the wire fraud offense, the Defendants-Appellants argue that the answer to the jury’s question was erroneous because it improperly lowered the intent required to prove conspiracy to commit wire fraud. They argue that the response improperly led the jury to believe that the Defendants-Appellants could be convicted even if they lacked specific intent to defraud. This is closer, but again, we do not find the Defendants-Appellants’ argument persuasive.

To prove wire fraud, the government must prove: (1) a scheme or artifice to defraud; (2) material falsehoods; and (3) the use of interstate wires in furtherance of the scheme. See Curtis, 635 F.3d at 718 n. 49; United States v. McMillan, 600 F.3d 434, 447 n. 24 (5th Cir.2010). Violation of the wire-fraud statute requires the specific intent to defraud, i.e., a “conscious knowing intent to defraud.” United States v. Reyes, 239 F.3d 722, 736 (5th Cir.2001). Thus, proving conspiracy to commit wire fraud requires proof that the Defendants-Appellants joined the conspiracy with the specific intent to defraud. See Curtis, 635 F.3d at 719 n. 53. The district court’s response to the jury’s note accurately describes this intent requirement.

The jury note states that as to the conspiracy statute itself, ignorance of the law is no excuse, because “[t]he government is not required to prove that a defendant knew the purpose of the agreement was in fact unlawful, that is, in violation of a statute, but the government must prove the defendant knew the purpose of the agreement.” See Ingram, 360 U.S. at 678, 79 S.Ct. 1314. The note also accurately states that the government must prove that the purpose was in fact unlawful, which requires proof that the Defendants-Appellants acted with the requisite mens rea to commit wire fraud. Coleman, 609 F.3d at 704-06 (analyzing whether elements of target offense also met when determining if conspiracy to commit that offense proven); United States v. Bedford, 536 F.3d 1148, 1155 (10th Cir.2008) (stating government must prove degree of criminal intent necessary to prove underlying crime). Although the district court’s response possibly could have spelled out the relationship between conspiracy and the underlying substantive offenses more clearly, it is not an incorrect statement of the law, particularly in light of the rest of the jury charge. See United States v. Chavis, 772 F.2d 100, 108 (5th Cir.1985) (“The jury charge must ... be considered as a whole, in the full context of the trial.”).

Therefore, we conclude that the district court’s instructions and the note to the jury were an accurate statement of the mens rea required to convict for conspiracy to commit wire fraud.

2. Deliberate Ignorance Instruction

Next, the Defendants-Appellants argue that the district court’s jury instruction on deliberate ignorance impermissibly lowered the mens rea of both offenses. The district used the Pattern Fifth Circuit instruction, and instructed:

You may find that a defendant had knowledge of a fact if you find that the defendant deliberately closed his eyes to what would otherwise have been obvious to him. While knowledge on the part of the defendant cannot be established merely by demonstrating that the defendant was negligent, careless, or foolish, knowledge can be inferred if the defendant deliberately blinded himself to the existence of a fact.

Fifth Circuit Pattern Criminal Jury Instructions, § 1.37. The Defendants-Appellants argue that these instructions were incorrect on two grounds: first, that the evidence did not support the instruction; and second, that the instruction was legally incorrect.

On the first argument, a deliberate ignorance instruction is warranted “when a defendant claims a lack of guilty knowledge and the proof at trial supports an inference of deliberate indifference.” United States v. Moreno, 185 F.3d 465, 476 (5th Cir.1999) (quotation omitted). “The evidence at trial must raise two inferences: (1) the defendant was subjectively aware of a high probability of the existence of the illegal conduct; and (2) the defendant purposely contrived to avoid learning of the illegal conduct.” United States v. Lara-Velasquez, 919 F.2d 946, 951 (5th Cir.1990). In assessing whether evidence sufficiently supports the instruction, we “view the evidence and all reasonable inferences that may be drawn from the evidence in the light most favorable to the [government.” United States v. Mendoza-Medina, 346 F.3d 121, 132 (5th Cir.2003) (quotation omitted); United States v. Gray, 105 F.3d 956, 967 (5th Cir.1997).

The first requirement for using the instruction — the defendant claims a lack of guilty knowledge — is not disputed by the parties. The second requirement— the defendant purposely contrived to avoid learning of the illegal conduct — is satisfied if the evidence at trial raises an inference that: (1) the defendant was subjectively aware of a high probability of the existence of the illegal conduct; and (2) the defendant purposely contrived to avoid learning of the illegal conduct. Lara-Velasquez, 919 F.2d at 951. Here, taking all reasonable inference in the government’s favor, there is more than sufficient evidence to find that the Defendants-Appellants were subjectively aware of a high probably of the existence of illegal conduct and that they purposely contrived to avoid learning of the illegal conduct.

On this first prong, a review of the record shows that there was a great deal of evidence admitted at trial showing that the Defendants-Appellants believed that their conduct was illegal, or were aware of a high probability that it was illegal. For example, testimony at trial revealed that Brooks told co-workers that they would “be toast” if the government looked into their index reporting practices, and later, Brooks ordered traders to delete all copies of the reports that had been sent to the trade publications. Similarly, all of the Defendants-Appellants were involved in the email communication where the traders decided to continue reporting based on “book bias.” In that email exchange, the traders discussed how they should not discuss this topic over email' — ■ an obvious inference from these comments is that the traders were aware them “book bias” method of reporting was likely illegal. Finally, taking a step back, it is simply unbelievable to think that sophisticated gas traders, such as the Defendants-Appellants, did not realize that falsely reporting data to steal money from basis trading partners was, in all likelihood, criminalized under some statute.

On the second prong, the Defendants-Appellants argue that there is no evidence that they “purposefully contrived to avoid learning of illegal conduct.” Specifically, the Defendants-Appellants claim that they did not know the actual instructions sent by the publications, and that they thought they were sending the correct information. There is evidence in the record, however, showing that the Defendants-Appellants purposely avoided learning of the illegal nature of the conduct. For example, both Brooks and Phillips repeatedly ignored the reporting instructions, and they both also had conversations with Kelley Doolan, an editor at Inside FERC, about the reporting requirements. Similarly, other evidence indicated that Walton had been forwarded a spreadsheet with fake trades, and that he was included in the “book bias” email, in which the traders made statements indicating that their reporting practices were not in line with Inside FERCs instructions. Based on this evidence, we hold that it was not an abuse of discretion for the district court to instruct the jury on deliberate ignorance.

Second, the Defendants-Appellants argue that the instruction on deliberate ignorance was an improper statement of the law in light of the Supreme Court’s recent decision in Global-Tech Appliances, Inc. v. SEB S.A., - U.S. -, 131 S.Ct. 2060, 179 L.Ed.2d 1167 (2011). In Global-Tech, the Supreme Court considered willful blindness in the civil context, stating that willful blindness requires proof that: “(1) the defendant [] subjectively believe[d] that there [was] a high probability that a fact exists and (2) the defendant [took] deliberate actions to avoid learning of that fact.” Id. at 2070. The Court continued, stating that willful blindness “surpasses recklessness and negligence,” and that “a willfully blind defendant is one who takes deliberate actions to avoid confirming a high probability of wrongdoing and who can almost be said to have actually known the critical facts.” Id. at 2070-71.

The Fifth Circuit Pattern Instruction meets the standard set forth by the Supreme Court in Global-Tech. The instructions do not have the same failings as the Federal Circuit standard reversed in Global Tech, which allowed for a finding of willful blindness where there is only a “known risk,” and where the defendant did not make an active effort to avoid knowledge. Global-Tech, 131 S.Ct. at 2071. As to Global-Tech’s first prong — the defendant “must subjectively believe that there is a high probability that a fact exists”— the jury instruction provided that the defendant needed to have “deliberately closed his eyes” to a fact that “would otherwise have been obvious to him.” As to the second prong — the defendant “must take deliberate actions to avoid learning of that fact” — the instruction provided that the defendant needed to have “deliberately closed his eyes,” and “deliberately blinded himself to the existence of a fact.” The instruction also stated that merely finding the defendants were “negligent, careless, or foolish” was insufficient. Thus, although this instruction obviously does not use the same language as Global-Tech, the same meaning is conveyed. Accordingly, not only was the deliberate ignorance instruction justified, the instruction itself was legally correct.

3. False Reporting Instruction

The Defendants-Appellants also argue that the jury instructions were in error because the district court incorrectly stated the elements of false reporting under the CEA, 7 U.S.C. § 13(a)(2).

In relevant part, the CEA provides that “[i]t shall be a felony ... for ... [a]ny person ... knowingly to deliver or cause to be delivered for transmission through the mails or interstate commerce by telegraph, telephone, wireless, or other means of communication false or misleading or knowingly inaccurate reports concerning crop or market information or conditions that affect or tend to affect the price of any commodity in interstate commerce....” 7 U.S.C. § 13(a)(2). The district court instructed the jury that to convict it must find that the Defendants-Appellants: (1) “knowingly delivered, or caused to be delivered, for transmission through interstate commerce by telephone or other means of communication a material false or misleading or inaccurate report”; (2) “knew the report was false or misleading or inaccurate”; and (3) “[t]hat the report concerned market information or conditions that affected or tended to affected the price of a commodity in interstate commerce.” The Defendants-Appellants argue that the mens rea of false reporting — knowingly—requires that a defendant must “know” his reports would “affect or tend to affect the price of any commodity in interstate commerce.”

In Valencia, the Court found that “knowingly” in this section of the CEA applies both to the transmission and falsity of the report (elements one and two), but that decision did not reach whether it applied to the final element of the offense. 394 F.3d at 354-56. It is not clear whether “knowingly” applies to all of the elements of the offense. As a matter of natural reading and grammar, there is not an interpretation of the language that clearly makes the most sense. See generally Flores-Figueroa v. United States, 556 U.S. 646, 129 S.Ct. 1886, 173 L.Ed.2d 853 (2009) (applying “ordinary English grammar” to construe statute’s knowledge requirement); see also United States v. Betancourt, 586 F.3d 303, 308-09 (5th Cir.2009) (determining whether mens rea applies to elements of an offense after Flores-Figueroa). The Defendants-Appellants argue that the mens rea should be applied to the final element of the offense based on the Supreme Court’s decision in United States v. X-Citement Video, Inc., 513 U.S. 64, 115 S.Ct. 464, 130 L.Ed.2d 372 (1994). In X-Citement Video, the Supreme Court read the term “knowingly” as applying to each element of a child pornography offense, even though the “most natural grammatical reading” of the statute did not suggest this result. See id. at 68, 115 S.Ct. 464. In reaching this conclusion, the Supreme Court set forth a general rule that a “scienter requirement should apply to each of the statutory elements that criminalize otherwise innocent conduct.” See id. at 72, 115 S.Ct. 464 (citing Staples v. United States, 511 U.S. 600, 619, 114 S.Ct. 1793, 128 L.Ed.2d 608 (1994)); see also Carter v. United States, 530 U.S. 255, 269, 120 S.Ct. 2159, 147 L.Ed.2d 203 (2000) (reaffirming X-Citement Video rule); Valencia, 394 F.3d at 354-56 (applying the X-Citement Video rule to the CEA). Here though, the first two elements of the offense already require that a defendant knowingly transmit a knowingly false statement, largely taking the criminalized conduct out of the realm of innocent activity. See United States v. Butler, 637 F.3d 519, 524 (5th Cir.2011) (stating that Staples and X-Citement Video presumption does not apply where statute “does not entail the risk of subjecting ordinary citizens to criminal prosecution for otherwise innocent conduct”).

Overall, it is not clear whether knowledge applies to the requirement that the false report affect or tend to affect the price of a commodity. However, even assuming that the Defendants-Appellants are correct in their interpretation of the statute, we need not reverse their convictions. Where a trial court misstates or omits an element of an offense, the conviction is reviewed for harmless error. See Neder v. United States, 527 U.S. 1, 9-10, 119 S.Ct. 1827, 144 L.Ed.2d 35 (1999); Pope v. Illinois, 481 U.S. 497, 501-04, 107 S.Ct. 1918, 95 L.Ed.2d 439 (1987); United States v. Bohuchot, 625 F.3d 892, 903 (5th Cir.2010); United States v. Delgado, 256 F.3d 264, 280-81 (5th Cir.2001). Under this plain error standard, the conviction should be affirmed if it is “clear beyond a reasonable doubt that a rational jury would have found the defendant guilty absent the error.” Neder, 527 U.S. at 18, 119 S.Ct. 1827; accord United States v. Skilling, 638 F.3d 480, 481-82 (5th Cir.2011).

Here, there was a great deal of evidence admitted at trial showing that the Defendants-Appellants knew their price reports would or had affected natural gas indexes. For example, according to Dean, Brooks told him that they “gamed the system” and that Dean needed to report trades that would favorably affect the index prices. Additionally, in the October 2000 “book bias” email, Brooks wrote to the other traders that “we reported only verifiable fixed price transactions to IF for October” and “[it] only eliminated us as an active price setting participant.” O’Toole and Dean both also testified that they were instructed by Phillips or Brooks to coordinate their reports with Walton, and that Walton would give them target prices for the indexes. Additionally, there were numerous recorded conversations and emails entered into evidence, during which Walton and Phillips discussed the manner certain reports would or had affected index prices. Moreover, the jury convicted the Defendants-Appellants for wire fraud on every count that it convicted them for false reporting. In doing so, the jury found that the Defendants-Appellants had specific intent to defraud when submitting these false reports, which indicates that the jury also believed that the Defendants-Appellants had knowledge that their reporting would affect index prices.

Given this evidence, it is “clear beyond a reasonable doubt that a rational jury” would have found that the Defendants-Appellants had knowledge that their reports affected or tended to affect the price of natural gas. Accordingly, we decline to decide whether the mens rea applies to the final element of false reporting, because even assuming that it does, the error would be harmless.

4. Cumulative Error

Finally, the Defendants-Appellants argue that the cumulative error of the jury instructions errors requires reversal. “[T]he cumulative error doctrine ... provides that an aggregation of non-reversible errors (i.e., plain errors failing to necessitate reversal and harmless errors) can yield a denial of the constitutional right to a fair trial, which calls for reversal.” United States v. Munoz, 150 F.3d 401, 418 (5th Cir.1998). Beyond the issue of whether the mens rea applied to the final element of the false reporting offense — which we are confident was harmless if it was erroneous — we found no errors in the jury instructions. Therefore, we hold that the cumulative error doctrine does not require reversal.

D. Fundamental and Arguable Ambiguity

The Defendants-Appellants also argue that the questions on the Inside FERC and NGI surveys were fundamentally ambiguous — requiring a judgment of acquittal — or that the district court should have given the jury an arguable ambiguity instruction.

First, the Defendants-Appellants argue that the district court erred by denying their motion for acquittal because they were convicted for answering fundamentally ambiguous questions. Specifically, they argue that there are not universally accepted definitions for the terms “trading location,” “bidweek,” “baseload,” or “fixed price.” This court reviews the district court’s denial of a motion for acquittal de novo. United States v. Bennett, 664 F.3d 997, 1011-12 (5th Cir.2011).

To be fundamentally ambiguous, a “question must lack ‘a meaning about which men of ordinary intellect could agree, nor one which could be used with mutual understanding by a questioner and answerer unless it were defined at the time it were sought and offered as testimony.’ ” United States v. Strohm, 671 F.3d 1173, 1179 (10th Cir.2011) (quoting United States v. Farmer, 137 F.3d 1265, 1269 (10th Cir.1998)); accord United States v. Culliton, 328 F.3d 1074, 1078 (9th Cir.2003). The question must be so vague that it is impossible to have intended to answer it untruthfully. United States v. Richardson, 421 F.3d 17, 33 (1st Cir.2005). Where a question is found to be fundamentally ambiguous, a defendant’s answer to it is insufficient as a matter of law to sustain a conviction. Richardson, 421 F.3d at 33. A question is fundamentally ambiguous, however, in only very “narrow circumstances.” Strohm, 671 F.3d at 1179; United States v. Damrah, 412 F.3d 618, 627 (6th Cir.2005) (stating that doctrine applies only in “exceptional” cases). If a witness “knowingly made a false statement, based on his or her understanding of the question,” the doctrine does not apply, Strohm, 671 F.3d at 1180, and a witness cannot “twist the meaning of a question in his own mind into some totally unrecognizable shape and then hide behind it by alleging its fundamental ambiguity,” Richardson, 421 F.3d at 35 (quotation omitted).

Given the context in which the fundamental ambiguity defense has been applied previously, we hold that it does not apply under the facts of this case. It is completely implausible to think that the Defendants-Appellants reported fabricated trades based on a misinterpretation of the instructions. The fundamental ambiguity defense does not apply where a defendant “twist[s] the meaning of a question in his own mind into some totally unrecognizable shape and then hide[s] behind it by alleging its fundamental ambiguity.” Richardson, 421 F.3d at 35 (quotation omitted); see also Farmer, 137 F.3d at 1269 (stating that a question cannot be isolated from context to engineer ambiguity); United States v. Carey, 152 F.Supp.2d 415, 427 (S.D.N.Y.2001) (defense does not apply where an “answer to an ambiguous question is false under any reasonable interpretation”). There is no reasonable interpretation of the instructions that would allow reporting invented and fabricated trades. Indeed, the Defendants-Appellants are unable to cite any actual trade that was mistakenly reported due to specific ambiguities in the survey instructions.

Additionally, as to the only Defendant-Appellant who testified, Brooks stated at trial that he either (1) did not ever read Inside FERCs instructions, or (2) consciously disregarded the instructions and submitted invented data as a means of reporting “fair market value” (or “book bias”) to make the indexes more accurate, even though he knew the publications only wanted actual trades. In either case, Brooks admits that the instructions did not cause the type of false reporting that occurred. See United States v. Mubayyid, 658 F.3d 35, 63 (1st Cir.2011) (holding that, if the defendant gave a false response based on how he understood the question, his conviction would not be invalidated due to ambiguity in question); Culliton, 328 F.3d at 1079 (“[The defendant] points to no case, and indeed we have found none, that justifies an applicant’s unilateral reinterpretation of questions ... to comport with his own particular goals.”); United States v. Bollin, 264 F.3d 391, 411 (4th Cir.2001) (holding defense not available where defendant testified in a manner that he knew was false, even if question open to multiple interpretations). Accordingly, we hold that the district court did not err in denying the motion for acquittal based on the ambiguity of the terminology in the reporting instructions.

Second, the Defendants-Appellants argue that even if Inside FERCs instructions were not fundamentally ambiguous, the district court abused its discretion by denying a jury instruction on arguable ambiguity. As we noted earlier, “[district courts enjoy substantial latitude in formulating a jury charge, and hence we review all challenges to, and refusals to give, jury instructions for abuse of discretion.” United States v. Camilo, 660 F.3d 914, 925-26 (5th Cir.2011) (quotation omitted). “We consider whether the instruction, taken as a whole, ‘is a correct statement of the law and whether it clearly instructs jurors as to the principles of law applicable to the factual issues confronting them.’ ” United States v. Freeman, 434 F.3d 369, 377 (5th Cir.2005) (quoting United States v. Daniels, 281 F.3d 168, 183 (5th Cir.2002)). It is “reversible error to refuse a charge on a defense theory for which there is an evidentiary foundation and which, if believed by the jury, would be legally sufficient to support a verdict of not guilty.” United States v. Barnett, 197 F.3d 138, 142 (5th Cir.1999) (quotation omitted). An instruction on a defense theory, however, only need be given where “there exists evidence sufficient for a reasonable jury to find in [the defendant’s] favor.” United States v. Mata, 491 F.3d 237, 241 (5th Cir.2007).

During the jury charge conference, the Defendants-Appellants requested that the following jury instruction be given, which was adapted from the Fifth Circuit Pattern Jury Instruction Section 2.69, on perjury:

If you should find that a particular question was ambiguous and that the defendant truthfully answered one reasonable interpretation of the question under the circumstances presented, then such answer would not be false. Similarly, if you should find that the question was clear, but the answer was ambiguous, and one reasonable interpretation of such answer would be truthful, then such answer would not be false.

Fifth Circuit Pattern Criminal Jury Instructions § 2.69. The district court denied this instruction. The Defendants-Appellants argue that their defense revolved around showing that the instructions from Inside FERC were ambiguous and that not allowing the instruction prevented them from presenting their theory to the jury-

A determination of whether a question or statement is arguably ambiguous is generally left to the jury. See, e.g., United States v. Posada Carriles, 541 F.3d 344, 362-63 (5th Cir.2008) (stating that jury resolves ambiguities where they are not fundamental); United States v. Bell, 623 F.2d 1132, 1136 (5th Cir.1980) (same). It is not clear whether an arguable ambiguity instruction is appropriate in cases charging false reporting and wire fraud. In support of their argument, the Defendants-Appellants rely upon a Tenth Circuit case, United States v. Migliaccio, 34 F.3d 1517 (10th Cir.1994), in which the doctrine was applied to a charge of fraud under facts somewhat similar to the current suit. In that case, the Tenth Circuit held that not allowing an arguable ambiguity instruction was reversible error where the defendants were charged with fraudulent billing of medical procedures. Id. at 1520-25. The defendants argued that the terminology was ambiguous and that their answers were truthful under their interpretation of the terms. Id.

Here, in making their argument, the Defendants-Appellants ignore the fact that such an ambiguity instruction is only appropriate in cases where the defendant’s claimed interpretation of the ambiguous terms is reasonable and is supported by the record. Migliaccio, 34 F.3d at 1525. In United States v. Lawrence, the Tenth Circuit discussed Migliaccio and affirmed a district court’s denial of an ambiguity instruction in a wire fraud case. 405 F.3d 888, 896-900 (10th Cir.2005). In doing so, the court stated that an ambiguity instruction “is only necessary where there is evidence supporting the defendant’s interpretation as reasonable.” Id. at 898. Indeed, it is accepted law that a defendant is only entitled to an instruction on a defense theory where there is sufficient evidence such that a reasonable jury could find in his favor on that theory. See United States v. Branch, 91 F.3d 699, 712-13 (5th Cir.1996).

As explained previously, there is no reasonable interpretation of the instructions that allows the reporting of completely fabricated data. This interpretation is divorced from the language of the instructions, and it has no relationship to the allegedly ambiguous terminology. The district court, therefore, appropriately denied the ambiguity instruction. See Lawrence, 405 F.3d at 898; Migliaccio, 34 F.3d at 1525.

E. Evidentiary Rulings

The Defendants-Appellants also appeal several of the district court’s evidentiary rulings. Specifically, the Defendants-Appellants challenge: (1) the district court’s exclusion of their industry practice evidence; (2) the district court’s admission of the testimony of Matthew O’Loughlin, the government’s expert witness; and (3) the district court’s decision not to immunize Don Guilbault, a potential defense witness. We will consider these rulings in turn.

First, the Defendants-Appellants argue that the district court erred by excluding evidence related to industry practice. Specifically, the Defendants-Appellants argue that they were prevented from proving their good faith defense because they were barred from presenting evidence showing that other energy companies were also submitting similarly false data to Inside FERC and NGI.

We review evidentiary rulings for abuse of discretion, subject to harmless error analysis. United States v. Isiwele, 635 F.3d 196, 199 (5th Cir.2011); United States v. Cantu, 167 F.3d 198, 203 (5th Cir.1999). This Court has previously held that it was not an abuse of discretion to exclude evidence offered on a very similar theory. See United States v. Arledge, 553 F.3d 881, 894 (5th Cir.2008) (excluding evidence in fraud case showing that similarly situated third parties committed similar acts because it had little or no bearing on whether defendant acted with fraudulent intent). The industry practice evidence offered here has little or no bearing on whether the Defendants-Appellants acted with fraudulent intent. See United States v. Kahn, 711 F.Supp.2d 9, 12 (D.D.C.2010) (testimony about beliefs of third parties on validity of tax code irrelevant to determination of whether defendant acted in good faith). Indeed, this unrelated information posed a threat of confusing the jury and detracting from relevant information about the conduct of the actual parties. See Fed.R.Evid. 403 (stating “relevant evidence” may be excluded “if its probative value is substantially outweighed by a danger of ... unfair prejudice, confusing the issues, [or] misleading the jury ... ”). Thus, we hold that it was not an abuse of discretion to exclude this testimony.

Second, the Defendants-Appellants challenge the district court’s admission of the government’s expert, Matthew O’Loughlin. The admission of expert evidence is also reviewed “for abuse of discretion; however, evidentiary rulings are subjected to heightened scrutiny in criminal cases.” United States v. John, 597 F.3d 263, 274 (5th Cir.2010). “Federal Rule of Evidence 702 provides that testimony by a qualified expert is admissible if (1) it will assist the trier of fact; (2) it is based upon sufficient facts or data; (3) the testimony is a product of reliable methods; and (4) the witness has applied those principles reliably to the facts.” Id.

The Fifth Circuit has already upheld the admission of O’Loughlin’s expert testimony in nearly identical circumstances. See Valencia, 600 F.3d at 401, 420-29. The Defendants-Appellants’ attempts to distinguish Valencia are unavailing. The Defendants-Appellants argue that here, unlike in Valencia, O’Loughlin expressly “rejected” the publishers’ testimony about their editorial process. Valencia, however, upheld O’Loughlin’s testimony because it was not simply an attack on the credibility of the publishers; his testimony also provided a conclusion grounded in analysis. See 600 F.3d at 427. The Defendants-Appellants do not argue O’Lough-lin’s testimony was not so grounded here, and his disagreement with the publishers did not render his testimony inadmissable. Cf. United States v. Whitted, 11 F.3d 782, 786-87 (8th Cir.1993) (holding experts could not testify about credibility of fact witnesses). Accordingly, the Defendants-Appellants fail to show the district court abused its discretion when it admitted the testimony of O’Loughlin.

Third, Defendant-Appellant Walton argues that the district court erred by failing to order the government to immunize Don Guilbault, a physical gas trader on the same desk as Dean. In particular, Walton argues, first, that the district court should have denied Guilbault’s invocation of his Fifth Amendment right because he had already plead guilty to the relevant crimes and the statute of limitations had expired on any others, and, second, that the district court should have either granted Guil-bault immunity or compelled the government to do so. As Walton shows error on neither ground, his argument fails.

Guilbault worked on El Paso during the relevant times, and, on October 5, 2004, he plead guilty to violating the CEA by submitting false reports to Inside FERC and NGI. At the time of the Defendants-Appellants’ trial, Guilbault had not been sentenced because the government had sought to delay sentencing to ensure Guil-bault’s continued corporation in its prosecutions. On June 2, 2005, Guilbault was interviewed by government agents. According to a summary of the interview, Guilbault stated that, while Brooks told Guilbault to “get with” Walton, Walton told Guilbault that he did not need to show Walton his trades, and that Walton did not otherwise tell Guilbault what to report.

Walton subpoenaed Guilbault to appear at trial, and informed the government of the subpoena the day before Guilbault was to appear. That night, one of the members of the prosecution called Guilbault’s attorney to ask if Guilbault would indeed testify. The next morning at trial, Guil-bault’s attorney informed the court that Guilbault would invoke his Fifth Amendment right against self-incrimination. Gu-ilbault’s attorney told the court that the decision has been Guilbault’s alone to make. Guilbault’s attorney further explained that, while Guilbault had been on a list of possible government witnesses, no decision had been made previously about whether he would be called. Prosecutors then informed the court that they did not intend to call Guilbault because they had concerns about Guilbault’s truthfulness, and pointed to inconsistencies between Gu-ilbault’s 2005 interview and previous statements, as well as other instances that cast doubt on his credibility. Walton thereafter moved to compel Guilbault to testify, to compel the government to grant Guilbault immunity, or to admit a summary of the 2005 interview. The district court denied each request.

“A district court’s decision to exclude a witnesses’s testimony based on an invocation of the witnesses’s Fifth Amendment privilege is reviewed for an abuse of discretion.” United States v. Mares, 402 F.3d 511, 514 (5th Cir.2005). “Although the trial court’s discretion is not unlimited, it must enjoy wide discretion in resolving a self-incrimination claim.” United States v. Van Deveer, 577 F.2d 1016, 1017 (5th Cir.1978) (per curiam). “Generally, an abuse of discretion only occurs where no reasonable person could take the view adopted by the trial court.” Whitehead v. Food Max of Miss., Inc., 332 F.3d 796, 803 (5th Cir.2003) (quotation omitted & emphasis in original).

Here, although Guilbault had plead guilty to violating the CEA, he had not yet been sentenced, and Walton’s questions sought information related to those crimes. The Fifth Amendment right against self-incrimination only extinguishes once “the sentence has been fixed and the judgment of conviction has become final.” Mitchell v. United States, 526 U.S. 314, 326, 119 S.Ct. 1307, 143 L.Ed.2d 424 (1999) (“Where the sentence has not yet been imposed a defendant may have a legitimate fear of adverse consequences from further testimony.”). Accordingly, the dis-triet court did not err in finding Guilbault had a legitimate fear of self-incrimination, and could be excused from testifying.

With regard to immunity, this Court has held that “[district [c]ourts have no inherent power to grant immunity.” United States v. Follin, 979 F.2d 369, 374 (5th Cir.1992). “A district court may not grant immunity simply because a witness has essential exculpatory evidence unavailable from other sources.” Id. (citing United States v. Thevis, 665 F.2d 616, 638-41 (5th Cir.1982)). At most, this Court has left open the possibility that immunity may be necessary to stem government abuse. See Thevis, 665 F.2d at 641. Here, however, the district court found no abuse, and Walton has failed to show error in that determination.

Walton’s sole evidence showing an abuse by the government is the government’s continuances of Guilbault’s sentencing, a single call by a prosecutor to Guilbault after Walton subpoenaed him to testify, and the purported inconsistency in the government’s maintaining Guilbault as a possible witness and its statements on January 24, 2008 that it had concerns about Guilbault’s truthfulness. Guilbault’s attorney, however, informed the court that Gu-ilbault’s decision to invoke the Fifth Amendment was his own. Further, the prosecutor’s call the night before was explained as an inquiry to determine whether the government would need to prepare to cross-examine Guilbault, a task that would be need to be completed that night as Walton only informed the government about the subpoena that day. And the government’s proffer demonstrated a reasonable basis for it to doubt Guilbault’s veracity. In light of such facts, Walton fails to show the district court erred in accepting the prosecution’s, and Guilbault’s attorney’s, view of the facts.

F. Sentencing

Lastly, the Defendants-Appellants raise a number of challenges to the calculation of their Sentencing Guidelines’ sentences. In particular, the Defendants-Appellants challenge the burden of proof born by the government and the calculation of their Guidelines range.

We review the district court’s legal interpretation of the Sentencing Guidelines de novo and factual findings for clear error. See United States v. Murray, 648 F.3d 251, 254 (5th Cir.2011). A factual finding is clearly erroneous only if, based on the entirety of the evidence, the reviewing court is left with the definite and firm conviction that a mistake has been made. United States v. Valdez, 453 F.3d 252, 262 (5th Cir.2006). A factual finding is not clearly erroneous if it is plausible in light of the entire record. Id. Because the Court finds Defendants-Appellants’ arguments unavailing, we affirm the sentence.

1. Burden of Proof

The Defendants-Appellants first argue that the government should have been required to prove the loss caused by their fraud with clear and convincing evidence. The Presentence Report (“PSR”) provided for increases of eighteen and twenty-levels for the Defendants-Appellants due to the calculated loss, which was the largest contributing factor to the Defendants-Appellants’ offense levels. They argue that, because of the significant effect of the loss, due process requires that the government prove the loss by more than a mere preponderance.

“[A]s a general matter, the burden of proof at sentencing is by a preponderance of the evidence.” United States v. Mergerson, 4 F.3d 337, 343 (5th Cir.1993). The Fifth Circuit has stated in dicta, however, that “there may be certain cases where a sentencing fact is a ‘tail that wags the dog of the substantive offense,’ and might arguably require a finding beyond a reasonable doubt.” Id. at 344 (quoting McMillan v. Pennsylvania, 477 U.S. 79, 88, 106 S.Ct. 2411, 91 L.Ed.2d 67 (1986) (rejecting petitioner’s argument that visible possession of firearm enhancement was element of crime required to be proved beyond a reasonable doubt)). Nevertheless the Fifth Circuit has never required such a heightened burden. See id. at 344-45 (finding a preponderance standard was sufficient where life sentence was within range both prior to and after enhancement); United States v. Coleman, 290 Fed.Appx. 684, 685 (5th Cir.2008) (per curiam) (finding sentencing judge did not commit plain error where judge applied preponderance standard to sentencing). Indeed, nearly all of our fellow circuits have rejected the need to apply a heightened standard in light of the advisory nature of the Guidelines.

We need not decide at this time that a heightened burden is never required. While the Defendants-Appellants’ enhancements are significant, accounting for more than fifty percent of their offense levels, and increasing their recommended sentence range from 18-to-24 months to 135-to-168 or 168-to-210 months, this Court has held a similar enhancement did not require a heightened burden of proof. See United States v. Carreon, 11 F.3d 1225, 1240 (5th Cir.1994) (holding enhancement in recommended sentence from six years to twenty years did not require proof beyond a preponderance). Accordingly, we find that a heightened burden or proof, even if required by due process in certain situations, is not appropriate here, and the district court did not err in refusing to apply one.

2. Calculation of Guidelines Range

The Defendants-Appellants assert a number of errors in the calculation of their Sentencing Guidelines. In particular, the Defendants-Appellants challenge the district court’s calculation of loss, its calculation of the number of victims of that loss, and its finding that the Defendant-Appellants obstructed justice.

Turning first to the calculation of loss, “[w]e review de novo the district court’s method for determining loss, while clear error applies to the background factual findings that determine whether or not a particular method is appropriate.” Isiwele, 635 F.3d at 202. “[A] district court need only make a reasonable estimate of loss, and, ‘because the sentencing judge is in a unique position to assess the evidence and estimate the loss ... the court’s loss determination is entitled to appropriate deference.’ ” Murray, 648 F.3d at 254 (ellipsis in original) (quoting United States v. Goss, 549 F.3d 1013 (5th Cir.2008)).

The Defendants-Appellants fail to show that the district court’s method for determining loss was erroneous. The district court, adopting the method used in the PSRs, relied on O’Loughlin’s calculations about the effect of the false reports on the published index prices, and El Paso’s own calculations, in its “Basis Summaries,” about its “exposure” to changes in those index prices. The various losses were then attributed to each Defendant-Appellant based on his responsibility for the various reports. The method provided a “reasonable estimate,” and, indeed, a conservative estimate, of the loss caused by the Defendants-Appellants’ fraudulent scheme. Although the editors of the industry publications used some editorial discretion to determine what index price to publish, and did not rotely publish the volume-weighted average of the reported trades, O’Loughlin demonstrated that the published price and the volume-weighted average of the reported trades was identical eighty percent of the time, and a strong correlation between the two was observable for the remainder of the trades. Admittedly, as Hume observed over 250 years ago, one can never know with certainty that one event is caused by another. Unfortunately for the Defendants-Appellants, the law does not require such absolute certainty.

Nor does the Defendants-Appellants’ challenge to the use of the use of El Paso’s Basis Summaries fare better. As the record shows, the summaries were created so that El Paso could determine its exposure to changes in the various index prices. El Paso entered into a trade to buy or sell natural gas at some price at a certain hub. That contract had value so long as there was some difference between the specified price and the market price for natural gas at the hub at the time of the contract’s execution. For example, a contract to buy a unit of natural gas at $5 next month would gain value if the price of natural gas at the hub increased to $6: the contract would allow the holder to net a $1 profit by buying the gas at $5 and selling it at $6. Conversely, the contract would negatively impact the company if the price of natural gas fell to $4, as the company would be required to spend $5 on the natural gas and then could only sell it at a $1 loss. El Paso’s basis summary charts aggregated these various risks, and thus reflected the inflation or deflation in value of El Paso’s futures contracts.

While the Defendants-Appellants are correct that these charts did not necessarily reflect the flow of cash, they identify no legal authority suggesting that the Sentencing Guidelines are incapable of taking into account the losses and gains described above. The Sentencing Guidelines state that “fair market value of the property unlawfully taken” shall be used to determine the value of loss. See U.S. Sentencing Guidelines Manual § 2B1.1 cmt. n. 2(C)(i) (2001). Here, the Defendants-Appellants’ scheme drove up the market price of their contracts, which necessarily drove down the market price of their counterparties’ contracts. Thus, the basis summaries’ calculation of the increase in the value of El Paso’s futures contracts provides a reasonable basis from which to infer the counterparties’ loss in market value to their contracts.

Moreover, in contrast to the Defendants-Appellants’ protests, the method employed by the district court provided a “realistic, economic approach” to determining the loss caused by their fraud. See United States v. Oils, 429 F.3d 540, 546 (5th Cir.2005) (quotation omitted). Unlike the typical valuation of damages in a securities fraud scheme, where the effect of the fraud must be inferred from the changes in the market price of the security and where, consequently, external forces on that price must be accounted, see, e.g., id. at 546-48, the method employed by the district court directly measured the loss. As described above, the district court relied on the government’s expert’s conclusion that the false trades move the various index prices by definite amounts, and the company’s calculations about the effect of such moves on the value of its assets. With such a method, there is no need to account for external factors that may have also increased or decreased the value of the futures contracts.

Next, the Defendants-Appellants challenge the calculation used to determine the number of victims of their fraud. Each of the Defendants-Appellants received a four-point enhancement to their offense level due to the district court’s finding that their scheme involved fifty or more victims. See U.S. Sentencing Guideline § 2Bl.l(b)(2)(B). In light of the entire record, the district court’s finding is not clearly erroneous. The record includes backup for the Basis Summaries reports that list the details of the various financial trades that went into those calculations. Just one of those backup spreadsheets, showing the trades for a single hub in a single month, shows in excess of fifty counterparties to El Paso’s futures trades — the counterparties who would have seen the value of their contracts artificially lowered by the Defendants-Appellants’ false statements. Accordingly, Defendants-Appellants fail to show error in the district court’s finding that their scheme, which occurred over at least two years and covered multiple hubs, involved more than fifty victims.

Lastly, the Defendants-Appellants challenge the two-point enhancement they received as a result of the district court’s finding that they obstructed justice. In particular, the Defendants-Appellants argue that the district court improperly found that they provided materially false information to the investigating government officials because they mislead the individuals involved in El Paso’s internal investigation. The Defendants-Appellants argue they cannot be found to have obstructed the investigation because, (1) their statements occurred before any government investigation started, (2) their false statements were not made directly to government agents, and (3) their false statements did not actually impede the investigation.

The relevant Sentencing Guidelines allow for an enhancement where:

(A) the defendant willfully obstructed or impeded, or attempted to obstruct or impede, the administration of justice during the course of an investigation, prosecution, or sentencing of the instant offense of conviction, and (B) the obstructive conduct related to (i) the defendant’s offense of conviction and any relevant conduct; or (ii) a closely related offense....

See U.S. Sentencing Guideline § 3C1.1 (2001).

First, with regard to Brooks, the district court found, in addition to his false statements, that in or about May of 2002 he destroyed or ordered another person to destroy material evidence when he ordered an El Paso employee to shred records related to reports to an industry newsletter. As noted in the PSR, and unchallenged by the Defendants-Appellants, such conduct occurred during the course of a state investigation into false reporting at El Paso of which Brooks had knowledge. Brooks’ sole challenge to the district court’s finding of obstruction for his destruction of documents was his conduct was innocent. Looking to the record as a whole, the district court’s finding to the contrary was not implausible. Accordingly, Brooks fails to show such a finding is clearly erroneous, and, in light of such a finding, the district court did not err in providing a two-point enhancement.

With regard to Phillips and Walton, the PSRs found obstruction based on their statements to El Paso’s legal counsel and independent investigators during the company’s investigation arising from inquiries by the CFTC, the Federal Energy Regulatory Commission, and the U.S. Attorney’s Office. The Defendants-Appellants show no error in the district court’s finding that they made their false statements during the course of the investigations. Similarly, they show no error in the district court’s finding the Phillips’s and Walton’s statements were not made in ignorance of the investigations and were not “the result of a spur of the moment decision.” See United States v. Greer, 158 F.3d 228, 235 (5th Cir.1998) (finding obstruction limited to “egregiously wrongful behavior whose execution requires a significant amount of planning and presents an inherently high risk that justice will in fact be obstructed”). Further, although the statements were not made directly to government officials, the district court’s finding that they were made with intent to be communicated to government officials, and thus to impede the investigation into their wrong-doing, was not implausible. See U.S. Sentencing Guidelines Manual § 3C1.1 cmt. n.9 (providing obstruction may be “induced, procured, or willfully caused”); see also United States v. Aguilar, 515 U.S. 593, 601, 115 S.Ct. 2357, 132 L.Ed.2d 520 (1995) (holding, to secure conviction for obstruction of justice charge, government must show defendant “knew that his false statement would be provided to the grand jury”).

Finally, the Defendants-Appellants fail to show error in the district court’s adoption of the PSRs’ finding that their false statements significantly impeded the investigation. False statements which significantly delay an investigation and prosecution, even if not successful in preventing it, may provide a sufficient basis for an obstruction enhancement. See United States v. Phipps, 319 F.3d 177, 191-92 (5th Cir.2003) (holding defendant’s false identification of accomplice, delaying investigation, constituted obstruction). While Defendants-Appellants objected to the PSRs’ finding, they presented no evidence to rebut that finding. See Vital, 68 F.3d at 121. Consequently, the district court could rely on the PSRs, see id., and the Defendants-Appellants fail to show that the district court’s finding was implausible based on the record. Thus, they fail to show error in the obstruction enhancement.

Accordingly, the Defendants-Appellants fail to show any error in their sentences.

Conclusion

For the reasons stated above, Defendants-Appellants’ convictions and sentences are AFFIRMED. 
      
      . In these various futures transactions, the parties discuss financial traders holding ''short” or “long” positions. In a “short” position, a trader benefits from a lower index price, and in a "long” position, the trader benefits from a higher index price.
     
      
      . As will be explained, the parties dispute the extent to which these terms have accepted meanings in the natural gas industry.
     
      
      . Prior to the United States Attorney’s investigation, in 2000, the California Public Utilities Commission started an investigation of El Paso, during which Southern California Edison also requested documents related to EPME's reporting. Moreover, at about the time of the United States Attorney subpoena, El Paso received similar requests for information from the Commodities Futures Trading Commission and the Federal Energy Regulatory Commission.
     
      
      . El Paso and EPME had slightly different policies. El Paso's by-laws required it to both indemnify and to advance legal fees for any of its employees. El Paso would then have the right to seek a refund of payments if the employee was found to have engaged in wrongdoing. EPME was only required to indemnify its employees, however, and the defendants here were all EPME employees.
     
      
      . Phillips subsequently filed a civil suit to force EPME to advance his legal fees, in which he sought discovery. See Phillips v. El Paso Corp., no. 2005-00645 (Texas Dist. Ct. Jan. 5, 2005). The government filed a successful motion to stay that civil suit, pending the criminal investigation.
     
      
      . A number of other members of the alleged conspiracy have already pled guilty to charges of false reporting, wire fraud, or conspiracy.
     
      
      . Mem. from Larry D. Thompson, Deputy Att’y Gen., U.S. Dep't of Justice, Principles of Federal Prosecution of Business Organizations (Jan. 20, 2003), available at http://www. justice.gov/dag/cfti7corporate_guidelmes.htm.
     
      
      . A district court has considered the definition of "report” and found it covers electronic communications such as the Defendants-Appellants'. See CFTC v. Atha, 420 F.Supp.2d 1373, 1380-81 (N.D.Ga.2006) (finding § 13(a)(2) false reporting provision applies to false trade reports sent electronically to Inside FERC).
     
      
      . The Defendants-Appellants provide the court with no reason to believe "report,” first included in the Grain Futures Act of 1922, had a meaning other than that used today. See Grain Futures Act, 42 State 998, 1003 (1922).
     
      
      . Cf. United States v. Radley, 632 F.3d 177, 182-83 (5th Cir.2011) (holding § 2(g)’s “contract, agreement, or transaction” not limited to legally enforceable agreements, but also covers "conducting business,” thus including, and exempting from CEA, defendants’ allegedly manipulative actions; distinguishing Futch, stating falsely reporting trades is not “conducting business”).
     
      
      . Indeed, it is at least open to question whether the CEA requires a commodity to be the subject of a currently existing futures market, or merely that it be such a good for which a futures market could come into being. The CEA defines, as a commodity, all "goods ... in which contracts for future delivery are presently or in the future dealt with.” See § la(4). Assuming only natural gas at Henry Hub was a covered commodity, the Defendants-Appellants present no reason why gas at other hubs could never serve as the basis for other futures markets. See United States v. Reliant Energy Servs., Inc., 420 F.Supp.2d 1043, 1062 (N.D.Cal.2006) (holding "criminal manipulation provision of § [13(a)(2) ] is not limited to futures contracts”; "[rjather, according to the plain meaning of the text, the criminal manipulation provision also applies to 'any commodity in interstate commerce’ ”).
     
      
      . The CFTC gave no indication that it believed the exemption covered only natural gas at Henry Hub.
     
      
      . Moreover, as discussed below, the jury found each violation of the CEA was accompanied by an act of wire fraud, and fraud has long been recognized to be outside the protection of the First Amendment. See United States v. Stevens, — U.S. -, 130 S.Ct. 1577, 1584, 176 L.Ed.2d 435 (2010) (finding "[fjrom 1791 to the present ..., the First Amendment has permitted restrictions upon the content of speech," including "fraud” (quotation and citations omitted)). Here, as discussed below, sufficient evidence was introduced that the Defendants-Appellants possessed a fraudulent intent.
     
      
      . 18 U.S.C. § 371 provides:
      If two or more persons conspire either to commit any offense against the United States, or to defraud the United States, or any agency thereof in any manner or for any purpose, and one or more of such persons do any act to effect the object of the conspiracy, each shall be fined under this title or imprisoned not more than five years, or both.
     
      
      . 18 U.S.C. § 1343 provides:
      Whoever, having devised or intending to devise any scheme or artifice to defraud, or for obtaining money or property by means of false or fraudulent pretenses, representations, or promises, transmits or causes to be transmitted by means of wire, radio, or television communication in interstate or foreign commerce, any writings, signs, signals, pictures, or sounds for the purpose of executing such scheme or artifice, shall be fined under this title or imprisoned not more than 20 years, or both.
     
      
      . Although the two intents are separate, they often functionally collapse into a single intent. United States v. Chagra, 807 F.2d 398, 401 (5th Cir.1986). Thus, oftentimes, it is only necessary for the government to prove the level of intent required for proving the underlying substantive offense. United States v. Feola, 420 U.S. 671, 686, 95 S.Ct. 1255, 43 L.Ed.2d 541 (1975); United States v. Dadi, 235 F.3d 945, 950 (5th Cir.2000).
     
      
      . See also United States v. Ramiscal, 99 F.3d 1148 (9th Cir. Oct. 18, 1996) (unpublished) (rejecting argument that proof of conspiracy always requires proof of knowledge of illegality of conduct); United States v. Jo, 99 F.3d 1147 (9th Cir. Oct. 18, 1996) (unpublished) (same); United States v. Sclamo, 578 F.2d 888, 891 (1st Cir.1978) (rejecting similar argument and stating, "[t]he underlying substantive statute does not require a showing of specific Mens rea; the conspiracy count requires no greater degree of scienter than the substantive count”).
     
      
      . The Defendants-Appellants also argue that the note gave the jury the impression that the maxim "ignorance of the law is no excuse” was officially a jury instruction. Whether or not it was proper for the district court to implicitly adopt this statement, the note accurately stated that this case did not fall within the narrow exception to the traditional rule that "ignorance of the law is no excuse,” as laid out by the Supreme Court. The Supreme Court stated that "the traditional rule that ignorance of the law is no excuse” does not apply only in cases involving highly technical statutes that criminalize otherwise "innocent conduct.” Bryan v. United States, 524 U.S. 184, 194-96, 118 S.Ct. 1939, 141 L.Ed.2d 197 (1998); see also Ratzlaf v. United States, 510 U.S. 135, 149, 114 S.Ct. 655, 126 L.Ed.2d 615 (1994); Cheek v. United States, 498 U.S. 192, 199-200, 111 S.Ct. 604, 112 L.Ed.2d 617 (1991). Although wire fraud is a specific intent crime, it would not fall into this narrow exception to the general rule. See Kay, 513 F.3d at 447-51 (describing narrow exception to traditional rule that ignorance of the law is no excuse). Further, to the extent that the Defendants-Appellants argue that this instruction gave the jury the impression that it could not acquit, even if it found that the Defendants-Appellants believed they were giving accurate answers to the publications, the instruction on specific intent to defraud made clear to the jury that it could not convict unless it found a "conscious knowing intent to defraud.” See United States v. Cavin, 39 F.3d 1299, 1310 (5th Cir.1994) (a finding of intent to defraud and good faith are mutually exclusive). Taken in context with the rest of the instructions, and the remainder of the note, we do not think that the statement regarding "ignorance of the law” was in error.
     
      
      . Although Global-Tech was a civil case, the standard seems to apply equally to criminal deliberate ignorance cases. See United. States v. Ferguson, 676 F.3d 260, 277 n. 16 (2d Cir.2011) (applying standard in criminal case and noting slight differences in terminology); United States v. Butler, 646 F.3d 1038, 1041 (8th Cir.2011) (same).
     
      
      . Although obviously not dispositive, our decision in Valencia has been interpreted by other courts as only requiring knowledge as to the first two elements of the offense. See, e.g., Atha, 420 F.Supp.2d at 1380; CFTC v. Johnson, 408 F.Supp.2d at 267. This Court also adopted that interpretation in Futch, 278 Fed.Appx. at 391, although that is an unpublished and non-precedential decision.
     
      
      . See also United States v. Velte, 331 F.3d 673, 680 (9th Cir.2003) (holding mens rea did not apply to "without authority” language in statute because setting a fire in a national park not generally considered an innocent act); United States v. Quarrell, 310 F.3d 664, 672 (10th Cir.2002) (statute prohibiting excavating for artifacts on federal lands did not require knowledge that one was on federal land because "[o]ne would anticipate that excavating for archaeological resources on another person’s land, whether private or public, would not be viewed as an innocent act”); United States v. Sablan, 92 F.3d 865, 868 (9th Cir.1996) (federal statute barring unauthorized computer access did not require knowledge access would cause damage because unauthorized access not an innocent act).
     
      
      . The Defendants-Appellants also briefly challenge the district court’s denial of a good faith instruction and an instruction that failure to follow Inside FERC’s instructions, standing alone, is not a crime. As to the good faith instruction, the district court did not abuse its discretion in denying it. “The district court will not abuse its discretion when it denies a proffered instruction unless this instruction (1) was a correct statement of the law, (2) was not substantially covered in the charge as a whole, and (3) concerned an important point in the trial such that the failure to instruct the jury on the issue seriously impaired the defendant’s ability to present a given defense.’’ United States v. Jobe, 101 F.3d 1046, 1059 (5th Cir.1996) (citation and quotation marks omitted). A district court may “refuse to submit an instruction regarding a good faith defense if the defense is substantially covered by the charge given and the defendant has had the opportunity to argue good faith to the jury." United States v. Upton, 91 F.3d 677, 683 (5th Cir.1996) (quotation omitted). Here, the Defendants-Appellants were permitted to argue that they acted in good faith and had no intent to defraud, and the jury instructions accurately conveyed the specific intent required to both commit fraud and conspiracy. See United States v. Storm, 36 F.3d 1289, 1294-95 (5th Cir.1994) (refusing to find error where “defense of good faith was substantially covered by charge to the jury” on the terms " ‘knowingly’ and ‘willfully’ ”).
      Second, the Defendants-Appellants proposed instruction that a failure to follow Inside FERC's instructions, by itself, is not evidence of a crime, is confusing and the instruction likely would have misled the jury. Further, the instruction seems to be inaccurate, given that a failure to follow Inside FERC’s instructions alone, with the proper intent, could constitute false reporting or wire fraud. Thus, denying this instruction was also not an abuse of discretion. See Jobe, 101 F.3d at 1059.
     
      
      
        . At oral argument and in their briefing, the Defendants-Appellants stale that Inside FERC survey question, given the ambiguous terms, functionally was: “What undefined type of trades that may or may not call for delivery of gas for an unspecified time did you conduct during some time frame and that occurred in an area without geographic boundaries.” However, even based on the Defendants-Appellants' characterization of the instructions, they gave false responses because the question only requests trades that were actually conducted.
     
      
      . See United States v. Munoz, 233 F.3d 1117, 1130-32 (9th Cir.2000) (stating that ambiguity instruction not appropriate in fraud case due to broad nature of statute).
     
      
      . Because the arguable ambiguity instruction is not supported by the record, we decline to decide whether such an instruction is ever appropriate in cases charging fraud or false reporting.
     
      
      . Additionally, it is not an abuse of discretion for a district court to deny a proposed jury instruction where the defense theory was adequately presented to the jury. See United States v. Gray, 751 F.2d 733, 736-37 (5th Cir.1985). For example, in the case of a proposed good faith defense, we have held that denial of a specific instruction is not an abuse of discretion where the content of the defense is raised during argument and the jury is accurately instructed on specific intent to defraud. See United States v. Bilotto, 245 Fed.Appx. 410, 413-14 (5th Cir.2007) (per curiam); United States v. Manges, 110 F.3d 1162, 1177 (5th Cir.1997); Daniel, 957 F.2d at 170; United States v. St. Gelais, 952 F.2d 90, 94 (5th Cir.1992); Gray, 751 F.2d at 736-37. Here, even though the district court denied the specific instruction on ambiguity, the Defendants-Appellants were permitted to present this argument to the juiy, and in fact, Phillips’s lawyer discussed how the ambiguous terms negated the intent elements of the charged offenses during closing arguments at length. Further, the district court accurately instructed the jury on how both offenses require knowledge of the falsity of the statement, which prevented the jury from convicting if it found that the Defendants-Appellants actually believed that they were complying with the instructions. Thus, the district court’s charge “enabled the jury to recognize and understand the defense theory, [to] test it against the evidence presented at trial, and then [to] make a definitive decision whether, based on that evidence and in light of the defense theory, the defendant was guilty or not guilty.” Gray, 751 F.2d at 736-37 (quotation omitted).
     
      
      . The Defendants-Appellants’ half-hearted attack on O’Loughlin’s qualification is also unavailing. The Defendants-Appellants, along with failing to raise this objection to the district court, cite no authority to show that work in the relevant field is a necessary qualification for expert testimony. Presumably, their failure stems from the fact that any such authority would contradict the terms of Rule 702, which allows an expert to be qualified by “knowledge, skill experience, training or education.” See Fed.R.Evid. 702 (emphasis added).
     
      
      . Walton’s citation to out-of-circuit precedent to argue that government misconduct is not a necessary prerequisite is unavailing in light of Thevis. See Thevis, 665 F.2d at 639-41 (declining to follow Gov’t of Virgin Islands v. Smith, 615 F.2d 964, 974 (3d Cir.1980)). Moreover, even if this Court could consider such authority, Walton fails to show immunity was justified under it. Walton fails to show that Guilbault's exclusion skewed the evidence in the government’s favor. Although Guilbault could have testified that Walton never asked him to send false trades, such testimony hardly contradicts O'Toole’s and Dean’s testimony that Walton provided them with his positions. See United States v. Straub, 538 F.3d 1147, 1156-57 (9th Cir.2008) (finding exculpatory evidence must "directly contradict[ ]” admitted evidence to warrant immunity). Further, in cross-examination of O’Toole, Walton introduced his theory that he did not always provide the traders with his positions, and that he did not ask to review their submissions to the publications. See United States v. Ebbers, 458 F.3d 110, 119 (2d Cir.2006) (finding exculpatory evidence must not be "cumulative”). Guilbault's testimony would not have been materially more exculpatory.
     
      
      . Waltons' argument, made only in passing and citing no support, that the interview memorandum should have been introduced as evidence is also unavailing. The memorandum is hearsay. See United States v. Moore, 651 F.3d 30, 83 (D.C.Cir.2011) (finding witness's prior confessions hearsay under Federal Rule of Evidence 804(b)(3)). Guil-bault’s invocation of the Fifth Amendment rendered him unavailable. See id. However, none of the exceptions to hearsay apply. The portion of the statement Walton sought to introduce was not against Guilbault’s interest because it was exculpatory. See Fed.R.Evid. 804(b)(3). And the fact that it was contradicted by an earlier statement by Guilbault tends to show it does not “ha[ve] equivalent circumstantial guarantees of trustworthiness.” See Fed.R.Evid. 807; Moore, 651 F.3d at 83 (finding witness's prior contradictions rendered hearsay statements untrustworthy). Accordingly, Walton showed no error in the district court’s decision to exclude the interview summary.
     
      
      . The calculated loss resulted in a twenty-level increase for Brooks, increasing his offense level from fifteen to thirty-five, and resulted in an eighteen-level increase for Walton and Phillips, increasing their offense levels from fifteen to thirty-three.
     
      
      . See United States v. Villareal-Amarillas, 562 F.3d 892, 894-98 & n. 3 (8th Cir.2009) (holding sentencing factors may be proven by preponderance; finding dicta in United States v. Archuleta, 412 F.3d 1003, 1007 (8th Cir.2005), expressing otherwise was erroneous); United States v. Fisher, 502 F.3d 293, 308 (3d Cir.2007) (holding preponderance sole standard of proof in sentencing; stating "because the Guidelines are now advisory and district judges are empowered to discharge their duties fully in the first instance, it is a logical impossibility for the ‘tail to wag the dog,’ as could occur when the Guidelines were mandatory”); United States v. Brika, 487 F.3d 450, 460-62 (6th Cir.2007) (holding preponderance standard applies, even where judge sentenced defendant for conduct underlying charge on which jury hung); United States v. Reuter, 463 F.3d 792, 793 (7th Cir.2006) (finding tail-wagging-dog concern rendered "academic” after Booker)-, but see United States v. Staten, 466 F.3d 708, 717-20 (9th Cir.2006) (finding due process required proof by clear and convincing evidence where enhancement increased offense level fifteen levels and effectively doubled defendant’s sentence; holding United States v. Booker, 543 U.S. 220, 125 S.Ct. 738, 160 L.Ed.2d 621 (2005), which rendered Sentencing Guidelines advisory, did not require departure from earlier precedent).
     
      
      . See also United States v. Vittek, 228 Fed.Appx. 469, 475-76 & n. 23 (5th Cir.2007) (per curiam) (finding increase in recommend sentencing range from 51-to-63 months to sentence of 168 months did not require heightened standard of proof).
     
      
      . The estimate did not include any loss caused to counterparties who purchased natural gas from El Paso at index price, or those parties who did not contract with El Paso, but nevertheless payed an inflated price for natural gas due to Defendants-Appellants actions.
     
      
      . Indeed, the PSRs excluded gains where the published index prices was different than the volume weighted average would have dictated.
     
      
      . See David Hume, An Enquiry Concerning Human Understanding (1748).
     
      
      . Moreover, loss may be measured not only by the actual loss caused by a defendants’ actions, but by the loss the defendants intended to cause. See U.S. Sentencing Guidelines Manual § 2B1.1 cmt. n.2(A) (2001). Loss is the "greater of the actual loss or intended loss.” See id. Thus, even if the Court were to conclude O'Loughlin's testimony was insufficient to demonstrate the actual influence the VWA had on the published indexes, such difference was a fair approximation of the change the Defendants-Appellants intended to have on the published indexes.
     
      
      . As discussed above, these transactions rarely resulted in the actual transfer of physical gas, but were instead resolved financially.
     
      
      . This also explains why trades that specified the price to be paid as the published index price did not create this type of risk: any variations in the market price would be reflected in the price at which El Paso would have to buy or sell.
     
      
      . Although it is difficult to believe that the value of these contracts were not converted to cash, or some other asset, at any point during the Defendants-Appellants’ two-year scheme.
     
      
      . This can be seen from the example above. If El Paso has a contract to buy gas at $5, then the counterparty has a contract to sell gas at $5. If the Defendants-Appellants could fraudulent raise the market price to $6, their contract would be worth $1, while the counterparty’s contract would have a negative value of $1. In essence, the Defendants-Appellants would have stolen $1 from their counterparty by fraudulently shifting the market value of the trade. Further, if the coun-terparty was hedged, it would merely shift the loss to yet another third party.
     
      
      . The Guidelines provide a non-exhaustive list of examples of such conduct, including "destroying or concealing or directing or procuring another to destroy or conceal evidence that is material to an official investigation or judicial proceeding,” and "providing a materially false statement to a law enforcement officer that significantly obstructed or impeded the official investigation or prosecution of the instant offense.” See id. at cmt. n.4 (d), (g). The Guidelines further provide examples of non-covered conduct, such as "making false statements, not under oath, to law enforcement officers, unless Application Note 3(g) above applies,” and "providing incomplete or misleading information, not amounting to a material falsehood in respect to a presentence investigation.” See id. at cmt. n. 5(b), (c). A 2006 amendment to the Guidelines allows consideration of pre-investigation conduct. See United States v. Alexander, 602 F.3d 639, 642 n. 3 (5th Cir.2010).
     
      
      . The district court adopted the factual findings of the PSR. "[I]f no relevant affidavits or other evidence is submitted to rebut the information contained in the [presentence report], the court is free to adopt its findings without further inquiry or explanation.” United States v. Vital, 68 F.3d 114, 121 (5th Cir.1995).
     
      
      .While the pre-2007 Guidelines required conduct to occur during the course of an investigation into the conduct at issue, they did not require the investigation to be led by the federal government, or to be a criminal investigation, so long as it was led by government officials. See United States v. Fiore, 381 F.3d 89, 94 (2d Cir.2004) (finding 'SEC civil investigation into conduct giving rise to later criminal charge sufficient to render obstructive conduct relevant for sentencing enhancement); United States v. McGovern, 329 F.3d 247, 252 (1st Cir.2003) (finding Medicaid & Medicare civil investigation sufficient to allow for obstruction enhancement); see also United States v. Upchurch, 88 Fed.Appx. 794, 795-96 (5th Cir.2004) (per curiam) (finding state investigation into conduct at issue sufficient to trigger obstruction enhancement). While the Defendants-Appellants assert the earlier investigation was into wash trading, the record indicates the investigation also covered false reporting, and, accordingly, the district court’s conclusion was not implausible.
     
      
      . The PSR also found Brooks obstructed the investigation based on his statements to El Paso’s legal counsel and internal investigation. Nonetheless, because the district court’s finding of obstruction was supported by Brooks’s destruction of evidence, the Court does not address Brooks’s false statements.
     
      
      . The Defendants-Appellants’ additional purported error, that the district court erroneously treated the guidelines as presumptively reasonable, see Gall v. United States, 552 U.S. 38, 50, 128 S.Ct. 586, 169 L.Ed.2d 445 (2007), is without any support in the record. Indeed, the district court's statement of reasons indicates that it made "an individualized assessment based on the facts presented.” See id.
      
     