Appeals from the United States District Court for the Northern District of Illinois, Eastern Division. Nos. 1:19-CR-00669-1, 2, 4 — Edmond E. Chang , Judge .

ARGUED SEPTEMBER 5, 2024 — DECIDED AUGUST 20, 2025

Before EASTERBROOK, KIRSCH, and KOLAR, Circuit Judges .

KIRSCH, Circuit Judge . Gregg Smith, Michael Nowak, and Chrisopher Jordan were precious metals futures traders who manipulated the market through an unlawful practice called spoofing , meaning they placed deceptive orders they intended to cancel to push the market price a certain direction. At trial, they were all convicted of various crimes in connection with this practice. They appeal their convictions on Page 2multiple grounds. Finding none of their challenges persuasive, we affirm across the board.

Gregg Smith, Michael Nowak, and Christopher Jordan once traded precious metals futures contracts on commodities exchanges operated by the Chicago Mercantile Exchange Group (CME). They each employed a fraudulent scheme, known as spoofing, to game the system and manipulate the prices of the precious metals futures they traded.

Spoofing is possible because of the nature of commodities futures trading. A futures contract is a legally binding agreement to buy or sell a commodity at an agreed -upon price on an agreed-upon future date. Commodities futures traders use an electronic platform known as Globex to access CME -operated exchanges. These traders place bids to buy , or offers to sell, a certain number of futures contracts on Globex at a specified price or level. Trading on Globex is anonymous, and while some traders employ computer algorithms to place orders, others enter their orders manually, as Smith, Nowak, and Jordan did. Globex also permits traders to cancel an order, or an unfilled portion of an order, any time before it is executed.

The price of futures contracts is determined by supply and demand: the price will increase if there is more demand than supply for a product, and vice versa. But a fundamental assumption on CME exchanges is that every order represents a legitimate, bona fide order placed with the intent to trade . Each order visible on Globex therefore impacts the market by conveying an intent to participate in it at a particular price.

Page 3Today, Globex shows every available order, but when Smith, Nowak, and Jordan were traders, it displayed only the ten best bids and the ten best offers at a ny time. And because larger quantity orders will have a greater effect on price than smaller orders will, Globex allow s traders to break up larger orders into a number of smaller ones by placing so -called iceberg orders. In this way, iceberg orders enable traders to conceal the true size of their order. Although these features were designed to mitigate the impact that large orders would have on the market price, they paved the way for fraudulent schemes to manipulate the market— especially spoofing .

A spoofing trader places large orders that he does not intend to execute, driving the price in a more favorable direction by communicating false information that deceives the marketplace about actual supply and demand. This typically involves four steps. First, the trader places an order, often an iceberg order, that he genuinely intends to trade. Second, the trader places a visible spoof order on the other side of the market. The trader never intends to trade this order; rather, it is designed to push the market price to the benefit of the legitimate order. For instance, if a trader wants to buy at a price below the market, he will place a large sell order at a low price (or a series of smaller sell orders at descending prices) to push the market down. Third, the market reacts to the illusion of market activity generated by the spoof order, allowing the trader to execute the genuine order at his desired price. Fourth, the trader cancels the spoof order before it can be filled.

CME rules have long prohibited spoofing . In particular, CME Rule 432 prohibits traders from manipulating or attempting to manipulate 'prices of exchange futures or Page 4options contracts”; employing or attempting to employ “any manipulative device, scheme or artifice to defraud'; and purchasing or selling or offering to purchase or sell 'exchange futures or options contracts or any underlying commodities or securities for the purpose of upsetting the equilibrium of the market or creating a condition in which prices do not or will not r eflect fair market values.' Accordingly, the defendants’ employers have policies prohibiting spoofing, both expressly and implicitly as a form of market manipulation.

Nowak and Smith worked at JPMorgan from 2008 to 2016. Nowak was a managing director who ran the precious metals trading desk, splitting his time between New York and London. Smith was an executive director and sat next to Nowak in the New York office. He joined JPMorgan after it acquired Bear Stearns in 2008. Jordan worked as a precious metals trader in the New York office between 2006 and 2009. After JPMorgan terminated him in 2009, he moved to Credit Suisse, where he worked from March to August 2010.

On multiple occasions, Smith, Nowak, and Jordan each placed orders mirroring the trading pattern of spoofing . That conduct eventually led the government to indict them for various spoofing -related crimes. Smith and Nowak were each charged with attempted price manipulation, 7 U.S.C. § 13(a)(2); wire fraud, 18 U.S.C. § 1343; commodities fraud, 18 U.S.C. § 1348(1); and violating the antispoofing provision of the Dodd-Frank Act , 7 U.S.C. §§ 6c(a)(5)(C) & 13(a)(2). Jordan was charged with wire fraud, 18 U.S.C. § 1343. All three were charged with conspiracy , but none were convicted .

Page 5Smith and Nowak were tried together. They did not meaningfully contest that their trading activity resembled the four -step pattern of spoofing. Rather, they argued that their trading was fully consistent with innocent behavior and that the government could not prove the requisite intent. During a three-week trial, t he government presented substantial evidence to the contrary. Below, we summarize the evidence relevant to this appeal.

Kumar Venkataraman, a finance expert, explained how Smith’s and Nowak’s trading patterns and resultant fill ratios aligned with the typical spoofing pattern. In a set of 100 trading episodes identified, Smith's spoof orders had a fill ratio (meaning the percentage of contracts filled) of 0.18%, compared to a 79.11% fill ratio for his genuine orders. Nowak's fill ratios were similar: 0.22% for his spoof orders and 90.11% for his genuine orders. The defendants’ broader trading showed this pattern , as well. De spite an abysmal fill ratio on the spoof orders, Venkataraman testified that Smith and Nowak used this strategy “again and again.” He concluded that Smith and Nowak’s trading strategy was “inconsistent with a design” to fill the genuine orders and was instead “designed” to “push the price” of the market and execute the order on the other side. There was no “economically rational” reason for their patten if they intended to trade the spoof orders , Venkataraman said. But because the market perceived the orders as genuine, they achieved the intended “shock to the market” and successfully moved the price on the other side.

The government also presented the testimony of CME investigator Brian Wika and three of Nowak and Smith’s former coworkers who admitted to spoofing and cooperated with Page 6authorities. John Edmonds sat next to Smith and Nowak at JPMorgan's New York office. He testified that he witnessed Smith and Nowak spoof regularly, at least several times per day, and that they in fact taught him how to spoof. According to Edmonds, Smith once told him that they spoofed because “size moves the market” and would complain “[t]hey’re fucking hitting me' when spoof orders he placed with the intent to cancel were executed. After a meeting where JPMorgan compliance officials warned traders to stop spoofing because regulators were looking into it, Edwards heard Smith say to another coworker , “There goes the business.” Edmonds also reviewed the trading episodes offered by the government and confirmed that they matched his own spoofing pattern. Based on his own experience at JPMorgan, he was unaware of any legitimate nonspoofing explanation for this trading.

Christian Trunz worked “side by side” with Smith, who m he described as his mentor. Trunz admitted that he engaged in spoofing to deceive other market participants. He testified that he witnessed Smith spoof “all the time” using the same strategy. Trunz sent a chat to another JPMorgan salesperson that Smith was “bidding up on the futures trying to get some off,' and once saw Smith become 'angry' and 'throw his glasses against the screen' when his spoof order was executed. He further testified that Nowak spoofed while they worked 'back to back' at JPMorgan. And while coaching Trunz ahead of a compliance review, Nowak once warned, 'Remember, every order we placed, we intended to trade.'

Corey Flaum sat along side Smith at Bear Stearns before it was acquired by JPMorgan in 2008. Flaum also confessed to spoofing and testified that he saw Smith spoof at least several Page 7times per week. Flaum testified that Smith's trading episodes were 'carbon copies' of his own spoofing pattern.

At various points, Edmonds, Trunz, and Flaum each defined spoofing in broad strokes and described its purposes and impact on the market to explain why they spoofed. They were also shown charts depicting specific trading episodes and opined that Smith and Nowak lacked an intent to trade and had been spoofing in those instances . The district court offered to give a jury instruction that the witnesses would be serving in a dual role, at times offering an opinion rather than their personal observations about a particular order . Smith and Nowak declined the instruction. The government also submitted various chats between the defendants and other coworkers discussing the legitimate orders they sought to execute, accompanied by data showing that they simultaneously placed and quickly canceled large orders on the other side of the market.

CME investigator Wika explained what spoofing is, how traders typically achieve it, how CME investigators identify it, and why CME rules prohibit it. When asked about his credentials, Wika stated that he had worked in CME’s investigations group for 14 year s and had been a manager for three or four. Wika testified that the CME began investigating Smith after it received a complaint from a market participant. When discussing the results of his investigation, Wika said that Smith’s high cancellation rates were 'indicative of spoofing activity—indicative of lack of intent to trade those orders.” He prepared an investigative report concluding that Smith had spoofed and identifying specific trading episodes as representative examples of Smith's spoofing behavior. Over the defendants’ objection, the court admitted the report into Page 8evidence as a business record under Federal Rule of Evidence 803(6).

After deliberating for a week, the jury announced that it was deadlocked. Although the defendants sought a mistrial, the court granted the government’s request for the standard supplemental jury instruction under United States v. Silvern , 484 F.2d 879 (7th Cir. 1973) (en banc). Consistent with that decision and the Seventh Circuit pattern instructions, the court instructed the jurors to 'make every reasonable effort to reach a verdict” and discuss their “ differences with an open mind,' but cautioned them not to 'surrender [their] honest beliefs about the weight or effect of evidence.” The next day, the jury sent a note expressing “concerns over comments made by a juror” that suggested that the juror had “made early decisions regarding the verdict for the defendants” based on the trial’s opening statements and “saw everything through that lense [sic].” The government asked the court to dismiss the juror. Instead, the court reminded the jury “that the lawyers’ statements and arguments are not evidence. If what a lawyer said is different from the evidence as you remember it, the evidence is what counts.” The next day, the jury found Smith and Nowak guilty on all substantive counts but acquitted them of the conspiracy charges. Each moved for acquittal or a new trial, but the court denied those motions .

The government tried Jordan separately and, following Smith and Nowak's trial, dropped the conspiracy counts against him. Jordan, for his part, openly admitt ed that he spoofed. Instead, his defense was that he spoofed without the criminal intent necessary to support a conviction for wire fraud affecting a financial institution.

Page 9FBI A gent Jonathan Luca testified for the government. Agent Luca had investigated Jordan and interviewed him in 2018. During the interview, Jordan admitted that as a trader he had placed “small iceberg orders on one side of the market and larger noniceberg orders on the other side of the market in which he intended to cancel” and acknowledged that this pattern was consistent with spoofing. He explained that he spoofed 'to mislead the market, to outperform the algorithms, and to make—and get the best possib le fi ll s for his boss.” The government characterized this interview as a confession. However, Jordan also told Agent Luca that he “did not think what he was doing was wrong.” Jordan sought to admit this statement under a hearsay exception commonly known as the rule of completeness, Fed. R. Evid. 106, but the court denied his motion.

To demonstrate Jordan’s state of mind, the government introduced statements he made during a 2010 deposition before the Commodity Futures Trading Commission. In stark contrast to his interview with Agent Luca, Jordan swore during the deposition that he never placed an order that he didn’t intend to execute, and “would only cancel something if [he] changed [his] mind or if it was put in error.” He further stated that he never engaged in trading 'for the purpose of influencing the price” of the commodity exchange.

The director and global head of CME’s rules and regulatory outreach group, Erin Middleton, also testified . Middleton said that CME rules require every order to be bona fide — meaning they must “represent a true intent to buy or sell a particular price or quantity'-to maintain the integrity of their markets. She acknowledged, however, that the word spoofing does not appear in the text of CME Rule 432 and that Page 10such language would have clarified that the rule prohibited spoofing . Representatives from JPMorgan and Credit Suisse similarly testified that spoofing would have violated the policies in place when Jordan worked at their banks, even though they did not explicitly mention spoofing either. Jordan sought to challenge these statements with post-2010 compliance policies and CME documents that, unlike the policies in place when he was an employee, expressly identifi ed spoofing as a prohibited trading policy. The district court excluded these exhibits under Federal Rule of Evidence 403, though, finding that they posed a risk of confusing the jury and erroneously injecting a mistake of law defense into the case.

The court also rejected Jordan’s request for a jury instruction on good faith. Specifically, he sought an instruction that if he acted in good faith, “then he lacked the intent to defraud required to prove the offense of wire fraud.' The court found this instruction unnecessary because Jordan could always argue that he lacked an intent to defraud and the instruction posed a similar risk of misleading the jurors into thinking that mistake of law was a viable defense.

The court did, however, instruct the jury on the mental state necessary to show an intent to defraud. The jury was instructed that Jordan must have acted knowingly, which the court defined in part as being “aware of the nature of his conduct.' During deliberations, the jury requested clarification on this definition, and the court responded that 'the definition of ‘knowingly’ … does not mean that the defendant must be aware of whether his alleged conduct violated federal law.” The jury returned a guilty verdict, and the court denied Jordan’s motions for acquittal and a new trial .

Page 11Smith, Nowak, and Jordan all appeal the denial of their motions for acquittal and a new trial. They also challenge several of the district judge’s rulings at trial. We take their arguments in turn.

All three defendants argue that their fraud convictions cannot stand because spoofing does not involve a misrepresentation about an essential element of the bargain for futures contracts. We review this threshold legal challenge de novo. United States v. Rivers , 108 F.4th 973, 978 (7th Cir. 2024) ( de novo review applies to “legal questions wrapped up in challenges to the sufficiency of the evidence'). Their argument fails for several reasons.

Both wire and commodities fraud require as an element “a scheme or artifice to defraud.” 18 U.S.C. §§ 1343 & 1348(1). The Supreme Court has interpreted this element to prohibit only deceptive schemes where “money or property was an object ” of the fraud. Ciminelli v. United States , 598 U.S. 306, 312 (2023) (quotation omitted). Building on this, some circuits previously drew 'a fine line between schemes that do no more than cause their victims to enter into transactions they would otherwise avoid” and “schemes that depend for their completion on a misrepresentation of an essential element of the bargain.” United States v. Shellef , 507 F.3d 82, 108 (2d Cir. 2007). In these circuits, only the latter constitute d a scheme to defraud that violated the fraud statutes. Id. ; United States v. Takhalov , 827 F.3d 1307, 13 13–14 (11th Cir. 2016); United States v. Guertin , 67 F.4th 445, 451 –52 (D.C. Cir. 2023); United States v. Bruchhausen , 977 F.2d 464, 467 -69 (9th Cir. 1992). A scheme to Page 12defraud, they reasoned, requires a lie about the 'nature of the bargain itself,” such as one concerning 'price' or 'characteristics of the good,” Takhalov , 827 F.3d at 1313 –14, or some “explicit promise[]” that had been made, Unit ed States v. Schwartz , 924 F.2d 410, 420 (2d Cir. 1991).

The defendants ask us to apply the essential element of the bargain requirement here. Because spoofing misrepresents market supply and demand, rather than the price or another characteristic of the futures contract itself, they contend that the other parties to the transaction 'received exactly what they paid for.” Takhalov , 827 F.3d at 1314 (quotation omitted) . They liken spoofing to misrepresentations about 'negotiating positions” in arm’s length transactions, which are not fraud. United States v. Weimert , 819 F.3d 351, 357 (7th Cir. 2016). Under this theory, spoofing simply does not amount to a scheme to defraud within the scope of the fraud statutes, even if the parties would not have otherwise executed the transaction.

Our task is made easy by the Supreme Court’s decision in Kousisis v. United States , 145 S. Ct. 1382 (2025), which came down after oral argument in this case. There, the defendant had secured contracts with the Pennsylvania Department of Transportation to paint two projects in Philadelphia. Id. at 1388–89. He represented that he would acquire painting supplies from 'a prequalified disadvantaged business ,” but in fact used the prequalified disadvantaged business as a mere pass-through entity to funnel payments. Id. at 1389. The Court affirmed the defendant’s wire fraud convictions and directly abrogated the line of cases that the defendants in this case invoke. Id. at 1390–92, 1398; see also United States v. Runner , 143 F.4th 146, 154– 55 (2d Cir. 2025) (recognizing abrogation). The wire fraud statute, the Court explained , 'is agnostic about Page 13economic loss.” Kousisis , 145 S. Ct. at 1392. Rather, a fraud conviction can stand if the defendant did no more than “use[] a material misstatement to trick a victim into a contract that requires handing over her money or property.” Id. at 1388, 1391.

Because Kousisis forecloses the defendants' essential element of the bargain argument, we easily conclude based on wellestablished precedent that spoofing constitutes a scheme to defraud within the meaning of the wire and commodities fraud statutes. United States v. Pacilio , 85 F.4th 450, 460 (7th Cir. 2023); United States v. Chanu , 40 F.4th 528, 541 (7th Cir. 2022); United States v. Coscia , 866 F.3d 782, 797 (7th Cir. 2017) .

It bears noting that the defendants’ argument would fail even without Kousisis . Unlike the transactions in Kousisis or Weimert , where the defendants directly lied to the purported victims , the deception from spoofing is filtered through third parties and the market as a whole. Spoofing advances an implied misrepresentation that the fraud statutes prohibit — “namely the public perception of the intent to trade and the private intent to cancel.” Pacilio , 85 F.4th at 460. In this way, spoofing is more akin to theories of securities fraud and fraud-on-the-market, which predicate liability on misrepresentations that undermine the integrity of the marketplace. See United States v. Gilbertson , 970 F.3d 9 39 , 947 (8th Cir. 2020) (in the context of securities fraud, the “gravamen of manipulation is deception of investors into believing that prices at which they purchase and sell securities are determined by the natural interplay of supply and demand, not rigged by manipulators”) (qu otation omitted) .

The defendants also claim the fraud statutes are unconstitutionally vague as applied to their conduct. We have already Page 14rejected this argument, Pacilio , 85 F.4th at 460–61, and decline to revisit that conclusion. Once again, we confirm that spoofing violates the federal wire and commodities fraud statutes, 18 U.S.C. §§ 1343 & 1348(1).

Smith and Nowak argue that even if spoofing amounts to wire and commodities fraud (it does), the evidence cannot sustain their convictions because they did not engage in the practice. They claim that spoofing requires an unconditional intent to cancel a bid or offer before execution, whereas the evidence at trial established, at best, a conditional intent to cancel the orders if the order on the other side was filled . Smith and Nowak concede, as they must, that each of their convictions is predicated on the same spoofing conduct, meaning the convictions all stand or fall with the government's ability to establish that they spoofed . Spoofing not only violates the federal fraud statutes, as discussed, but the Dodd-Frank Act provides that any person who knowingly violates its antispoofing provision, 7 U.S.C. § 6c(a)(5)(C), is guilty of attempted price manipulation under 7 U.S.C. § 13(a)(2). According to Smith and Nowak, since the government cannot prove that they placed trade orders with the requisite intent fo r a spoofing conviction, they are entitled to a judgment of acquittal across the board. Though formally we review a judgment denying acquittal de novo, 'practically speaking' our 'standard of review is that for sufficiency of the evidence.' United States v. Peterson , 823 F.3d 1113, 1120 (7th Cir. 2016) ; see also Rivers , 108 F.4th at 978 (de novo review for threshold legal questions).

The parties spend considerable time and energy debating the standard for intent and, frankly, we struggle to Page 15understand why. Smith and Nowak won this battle in the district court. The court instructed the jury that spoofing requires an unconditional purpose to cancel the entire bid or offer . The jury thus considered—and rejected—Smith and Nowak’s argument that the evidence does not show such unconditional intent. We measure intent at the moment the order was placed. Coscia , 866 F.3d at 795 (a conviction for spoofing requires proving that the defendant “knowingly entered bi ds or offers with the present intent to cancel the bid or offer prior to execution”). If a party possesses a conditional intent to trade, he necessarily lacks an intent to cancel at the time the order is placed. The word unconditional is redundant and unnecessary.

The key question in spoofing cases is whether an order is placed on the opposite side of the commodities market with the intent to cancel before execution in order to manipulate the market. Chanu , 40 F.4th at 540. Even if Smith and Nowak waited to cancel the spoof orders until the legitimate trade was executed, what counts is that the trades “were designed specifically to avoid being filled.' Coscia , 866 F.3d at 789. It makes sense that a spoofing trader would wait to cancel until his legitimate order was filled -that's the whole point of spoofing. Cf. id. (defendant's software program canceled spoof orders “in three particular circumstances: (1) based on the passage of time …; (2) the partial filli ng of the large orders; or (3) complete filling of the small orders ”) (emphasis added). The 'unconditional' semantics aside, the question is whether Smith’s and Nowak’s “purpose was not to trade on those orders, but rather to use them to shift the market up or down.” Id. at 795 & n.45.

Page 16More importantly, all that matters is whether a rational trier of fact could have come to that conclusion. Peterson , 823 F.3d at 1120 (“We consider the evidence in the light most favorable to the government and affirm the conviction if any rational trier of fact could find the defendant guilty beyond a reasonable doubt.'). This hurdle is “nearly insurmountable .” United States v. Sorensen , 134 F.4th 493, 498 (7th Cir. 2025) (quotation omitted) . In particular, Smith and Nowak’s focus on intent makes our “job relatively easy,” for “once a jury has weighed the evidence and found guilt beyond a reasonable doubt, a challenge to the sufficiency of the evidence proving intent is exceedingly difficult to win.' Pacilio , 85 F.4th at 463 (cleaned up).

After reviewing the evidence, we are confident that a jury could have found Smith and Nowak placed spoof orders with the requisite intent to cancel. The government presented substantial data evidence depicting the scheme, and the jury heard extensive testimony from cooperating witnesses, fi nancial experts, and investigators supporting an inference of guilt. This evidence was bolstered by contemporaneous chat messages showing that Smith and Nowak placed (and then canceled) orders on the opposite side of the market from the legitimate orders that they intended to execute. Smith and Nowak argue that this evidence is all circumstantial, as the government identified no direct evidence of their state of mind. Even so, 'direct evidence of intent is often unattainable, and specific intent to defraud may be established by circumstantial evidence and by inferences drawn from examining the scheme itself.” Id. at 464 (quotation omitted). Undeterred, Smith and Nowak counter that the circumstantial evidence cannot support their convictions because it is equally consistent with their innocence. But Smith and Nowak were free Page 17to argue to the jury that there were legitimate explanations for their trading patterns and to cross-examine the witnesses on their conclusions and credibility —indeed, that was the heart of their entire defense at trial. As we have often observed, “the fact that there existed other possible explanations … that were fully consistent with innocence did not require a jury to believe them.” United States v. Maxwell , 143 F.4th 844, 858 (7th Cir. 2025) (quotation omitted). We find more than sufficient evidence to justify the jury’s conclusions.

Briefly, Smith and Nowak also challenge the antispoofing statute , 7 U.S.C. § 6c(a)(5)(C), as void for vagueness. As with fraud, our precedent squarely forecloses this argument. Coscia , 866 F.3d at 793 –95. The spoofing statute is not unconstitutionally vague, and ample evidence supported Smith's and Nowak’s convictions under it.

In short, Smith and Nowak's sufficiency of the evidence challenge fails as to all convictions. There was more than sufficient evidence that Smith and Nowak engaged in spoofing in violation of 7 U.S.C. § 6c(a)(5)(C). And because spoofing constitutes a scheme to defraud under the wire and commodities fraud statutes, 18 U.S.C. §§ 1343 & 1348(1), and amounts to attempted price manipulation, 7 U.S.C. § 13(a)(2), there was sufficient evidence that they committed those crimes as well . Because the jury's verdict is supported by substantial evidence on all charges, they are not entitled to a new trial on these grounds either. Peterson , 823 F.3d at 1122; United States v. Conley , 875 F .3d 391, 399–400 (7th Cir. 2017) ( when motions for acquittal and for a new trial are based on the same claim that the government failed to prove the elements of the offenses beyond a reasonable doubt, we will affirm both if sufficient evidence supports the guilty verdict).

Page 18Smith and Nowak next turn their attention to the district court's decision to admit much of the evidence discussed above . They claim the court’s rulings were erroneous and ask for a judgment of acquittal or a new trial in the alternative. We review the district court’s evidentiary rulings for an abuse of discretion. Pacilio , 85 F.4th at 464. We will only reverse if we are 'left with the definite and firm conviction that a mistake has been committed.' Id. (quotation omitted). Smith and Nowak assert that the district court abused its discretion by admitting: (1) lay opinion testimony from the three cooperating witnesses, (2) Wika's lay opinion testimony, and (3) Wika’s investigative report.

To begin, we confirm that Nowak may also challenge the latter two rulings. Although the report and some of Wika’s testimony pertained specifically to Smith, Wika also testified about spoofing and CME policies more broadly. Particularly in light of the joint conspiracy charge, even though this evidence focused on Smith, the jury could consider it against Nowak as relevant and in accordance with any limiting instructions. See United States v. Lopez , 6 F.3d 1281, 1286 (7th Cir. 1993) (in joint trials, juries will “sort through the evidence” and “follow instructions from the court” about separate consideration of evidence). Nowak joined Smith's objections to Wika's testimony and report and, importantly, did not receive or request a limiting instruction that the jury could only consider them against Smith.

Turning to the merits, none of these decisions was an abuse of discretion. Federal Rule of Evidence 701 permits lay witnesses to testify as to “their opinions and inferences, even about ultimate issues in the case.” United States v. Locke , 643Page 19 F. 3d 235, 239 (7th Cir. 2011). They may even testify about another person’s mental state, so long as the testimony is helpful to the jury under Rule 701 and appropriate under Rule 403’s balancing test. Id. at 239–40. Though lay witnesses may not offer legal conclusions or opine on the application of statutory elements, United States v. Noel , 581 F.3d 490, 496 (7th Cir. 2009), they can use words “in a colloquial sense” that “employ[] the vernacular of their financial professions,' even if those words mirror legal standards, Locke , 643 F.3d at 241–42 (approving of lay witnesses’ use of the words fraud and misrepresentation).

The lay testimony was proper under this standard. Smith and Nowak take issue with the witnesses’ use of the word spoofing to describe their trading activity, argue that they improperly characterized spoofing as fraud and price manipulation, and claim that the witnesses inappropriately opined on Smith’s and Nowak’s intent based on technical knowledge . But the witnesses’ use of the word spoofing was consistent with the colloquial vernacular of the trading industry, id. at 242 , and any testimony about Smith 's and Nowak's mental states was properly framed as an opinion drawn from the trading data in light of the witnesses' own experience, see United States v. Winbush , 580 F. 3d 503, 512 (7th Cir. 2009). As for the claim that the testimony improperly equated spoofing with fraud and price manipulation, the witnesses were simply explaining why they spoofed, what they had pled guilty to, or (in Wika's case) why the CME prohibits spoofing. That Smith and Nowak declined a jury instruction that the witnesses were serving in a dual role only solidifies our conclusion that no abuse of discretion occurred.

Page 20Smith and Nowak also argue that Wika should have testified as an expert, rather than a lay witness. Investigators such as Wika can testify about their role in an investigation and provide their impressions of the case without crossing into expert territory. United States v. Rollins , 544 F.3d 820, 832– 33 (7th Cir. 2008). This is permissible even if an investigator’s “specialized knowledge informed his mental state.” United States v. Oriedo , 498 F.3d 593, 602 (7th Cir. 2007). While informed by his background experience, Wika’s testimony was limited to his investigation and what it revealed to him. Even if it arguably 'approaches the line dividing lay opinion testimony from expert opinion testimony,” this testimony remained admissible, and the district court did not abuse its discretion in allowing it. Rollins , 544 F.3d at 833. At the very worst, the government’s other evidence of Smith’s and Nowak’s guilt was so extensive that even if Wika’s testimony “had crossed the line” it would have been harmless error. Id. Nor was it erroneous to admit Wika’s investigative report: investigative reports may come in as public records under Federal Rule of Evidence 803(6) if the authoring officer or investigator testifies at trial, as Wika did. United States v. King , 613 F.2d 670, 672 – 73 (7th Cir. 1980); United States v. Blackburn , 992 F.2d 666, 672 (7th Cir. 1993) (“So long as the maker of the report is available for cross-examination, … admitting the reports themselves does not contravene Rule 803(8).”).

For their final challenge, Smith and Nowak argue that the district court’s supplemental instructions to the jury were erroneous and impermissibly coercive. We review the district court’s decision to provide supplemental jury instructions, including its decision to read (or reread) a Silvern instruction, Page 21for abuse of discretion. United States v. Cardena , 842 F.3d 959, 974 (7th Cir. 2016) ( Silvern instruction); United States v. Sims , 329 F.3d 937, 942 (7th Cir. 2003) (supplemental instructions generally).

It was appropriate for the district court to reread the Silvern instruction. Silvern instructions are 'perfectly contentneutral and carr[y] no plausible potential for coercing the jury.” United States v. Beverly , 913 F.2d 337, 352 (7th Cir. 1990) (quotation omitted) . Rather, the district court followed our clear, established procedure and provided the model instruction to a deadlocked jury. United States v. Collins , 223 F.3d 502, 508– 09 (7th Cir. 2000).

It was similarly within the court’s discretion to remind the jury that lawyers' statements are arguments, not evidence. The court pulled the language from a pattern instruction and, despite Smith and Nowak's arguments to the contrary, crafted it carefully to avoid singling out the problematic juror. The court also refused to ask the jury whether it remained deadlocked , precisely to avoid any intrusion on their deliberations. Under the circumstances, the court proceeded thoughtfully and exercised its discretion wisely. Nowak and Smith may not like the verdict the jury reached after receiving these instructions, but that does not mean they were issued in error.

Recall that Jordan was convicted of only wire fraud under 18 U.S.C. § 1343. Jordan challenges various aspects of his separate trial. Before turning to them, we first dispense with his own sufficiency of the evidence claim. Jordan joined Smith and Nowak's argument that spoofing cannot sustain a fraud Page 22conviction because it lacks a misrepresentation about an essential element of the bargain. Because Jordan concedes that he spoofed, his argument hinges entirely on that theory. Since we rejected that argument in Section II.A , Jordan's sufficiency of the evidence challenge is a nonstarter.

Jordan's primary remaining argument concerns the district court’s decision to exclude his statement to Agent Luca that he “did not think what he was doing was wrong.” Jordan sought to admit that statement under Federal Rule of Evidence 106, often referred to as the rule of completeness. Rule 106 provides that “[i]f a party introduces all or part of a statement, an adverse party may require the introduction, at that time, of any other part—or any other statement—that in fairness ought to be considered at the same time.” They “may do so over a hearsay objection.” Fed. R. Evid. 106.

Rule 106 requires a complete statement ' to be read or heard when it is necessary to (1) explain the admitted portion, (2) place the admitted portion in context, (3) avoid misleading the trier of fact, or (4) insure a fair and impartial understanding.” United States v. Lewis , 641 F.3d 773, 785 (7th Cir. 2011) (quotation omitted). In United States v. Haddad , 10 F.3d 1252 (7th Cir. 1993), for instance, the court admitted the defendant’s statement, “Yes, I kn e w of the marijuana” but excluded the remainder that said, “but I had no knowledge of the gun.” Id. at 1259. The gun was located right next to the marijuana, so the admitted statement suggested that the defendant knew about the gun as well. Id. We concluded that Rule 106 required the admission of the exculpatory statement, in part to avoid any misleading inference. Id. 'The completeness doctrine does not, however, require introduction of portions of a Page 23statement that are neither explanatory of nor relevant to the admitted passages.' Lewis , 641 F.3d at 785 ( quoting United States v. Marin , 669 F.2d 73, 84 (2d Cir. 1982) ).

The district court was correct that Rule 106 did not compel it to admit Jordan’s statement. Jordan’s claim that he did not think he was doing anything wrong does not change the factual nature of the statement that he placed bids with the intent to cancel for the purpose of misleading the market. Nor does it correct or clarify any misleading impression about the admitted statement: mistake of law is not a defense to wire fraud, and it is irrelevant whether Jordan knew that spoofing was illegal or, as he put it, wrong. United States v. Blagojevich , 794 F.3d 729, 739 (7th Cir. 2015). Rather, the court rightly noted that Jordan was free to take the stand and testify that he did not think he was doing anything wrong. United States v. Faruki , 803 F.3d 847, 857 (7th Cir. 2015) (agreeing with the district court that “the appropriate vehicle for the introduction of such evidence would have been for [the defendant] himself to have taken the stand,” rather than Rule 106). Defendants often try to justify their actions when speaking with FBI agents and other law enforcement officials by disclaiming criminal intent . Such an exculpatory statement has nothing to do with Rule 106.

Next, Jordan claims that the district court abused its discretion by excluding certain exhibits he sought to use for impeachment. The trial concerned Jordan's trading when he worked at JPMorgan and then Credit Suisse until August 2010. Although the policies in place at the time did not explicitly mention spoofing, government witnesses testified that the practice was nonetheless prohibited by their terms. To Page 24controvert this testimony, Jordan moved to admit post-2010 compliance policies and CME documents that had been revised to expressly forbid spoofing. However, the district court excluded this evidence under Rule 403. The policies were revised to reflect the Dodd -Frank Wall Street and Consumer Protection Act, Pub . L. No. 111203, 124 Stat. 1376, which Congress passed in July 2010. Though spoofing already violated the general wire fraud statutes, the Dodd-Frank Act amended the Commodity Exchange Act to explici tly recognize spoofing as an unlawful disruptive practice amounting to price manipulation. 7 U.S.C. §§ 6c(a)(5)(C ) (defining spoofing as practice 'commonly known to the trade' of 'bidding or offering with the intent to cancel the bid or offer before execution') & 13(a)(2). Given this background, the district court thought the offered evidence posed a risk of confusin g the jury and erroneously injecting a mistake of law defense into the case and excluded it.

Jordan argues that these exhibits were highly probative and directly responsive to the witnesses’ testimony, making the district court’s decision to exclude them under Rule 403 an abuse of discretion. We disagree. Jordan conducted extensive cross-examination of the witnesses, which elicited clear testimony that the pre-2010 documents did not mention spoofing even though they could (and possibly should) have. The actual documents themselves were thus of limited additional probative value. And as the district court noted, evidence of the after-the-fact, post-Dodd-Frank policies could have led the jury to think that the wire fraud statutes were not sufficient to criminalize spoofing. The court was justified in this concern—defendants in other cases have made this same (albeit incorrect) argument. See Chanu , 40 F.4th at 534.

Page 25Because “[t]he balancing of probative value and prejudice is a highly discretionary assessment,” we give “great deference” to a district court’s decision to exclude evidence under Rule 403 and “ only disturb[] it if no reasonable person could agree with the ruling.' Pacilio , 85 F.4th at 465 (quotation omitted). Given the limited probative value of the documents and valid concerns of jury confusion, Jordan does not overcome this extremely deferential standard.

Last, Jordan says the district court erred in declining to administer a so-called good faith instruction . Specifically, Jordan sought an instruction that if he acted in good faith “then he lacked the intent to defraud required to prove the offense of wire fraud.' Though we review challenges to jury instructions de novo, 'the district court is afforded substantial discretion with respect to the precise wording of instructions so long as the final result, read as a whole, completely and correctly states the law.” Chanu , 40 F.4th at 542 (cleaned up).

We already addressed and rejected this same argument in Chanu . As the district court noted, a good faith instruction is unnecessary in wire fraud cases because a lack of good faith is a part of the charge. Id. at 543. To be sure, district courts are free to provide one if they wish. But “the rule is clear” that defendants such as Jordan cannot demonstrate that “the failure to include the good faith instruction denied [them] a fair trial.' Id. (cleaned up). Jordan admitted he spoofed, and a jury convicted him of wire fraud after a fair, properly conducted trial.

AFFIRMED