
    UNITED STATES of America, Appellee, v. Jesse C. LITVAK, Defendant-Appellant.
    No. 14-2902-CR.
    United States Court of Appeals, Second Circuit.
    Argued: May 13, 2015.
    Decided: Dec. 8, 2015.
    
      Kannon K. Shanmugam, (Dane H. But-swinkas, Allison B. Jones, Masha G. Hans-ford, on the brief), Williams & Connolly LLP, Washington, DC, for Jesse C. Lit-vak.
    Jonathan N. Francis (Heather Cherry, Sandra S. Glover, on the brief), Assistant United States Attorneys, for Deirdre M. Daly, United States Attorney for the District of Connecticut, New Haven, CT.
    Before: STRAUB, PARKER and CARNEY, Circuit Judges.
   STRAUB, Circuit Judge:

After trial in the District of Connecticut (Janet C. Hall, Chief Judge), a jury convicted Defendant-Appellant Jesse C. Lit-vak of various charges of securities fraud, fraud against the United States, and making false statements. On appeal, Litvak challenges these convictions on several grounds.

First, Litvak contends that, for the purposes of the fraud against the United States and making false statements counts, the evidence adduced at trial provided an insufficient basis for a rational jury to conclude that his misstatements were material to the Department of the Treasury, the pertinent government entity. We agree, and accordingly reverse the District Court’s judgment of conviction as to those charges.

Second, Litvak argues that his misstatements were, as a matter of law, immaterial to a reasonable investor, which would require reversal of the securities fraud counts as well. However, because a rational jury could conclude that Litvak’s misstatements were material, the materiality inquiry — a mixed question of fact and law- — -was properly reserved for the jury’s determination.

Third, Litvak claims that, in respect of the scienter element of the securities fraud counts, the evidence was insufficient to support the verdict and that the District Court failed adequately to instruct the jury. Because Litvak is incorrect that “contemplated harm” is a requisite component of the scienter element of securities fraud, we reject this challenge.

Fourth, Litvak asserts a number of evi-dentiary errors at trial. We agree that the exclusion of certain proffered expert testimony exceeded the District Court’s allowable discretion, and that such error was not harmless. Accordingly, we vacate the District Court’s judgment of conviction as to the securities fraud charges and remand for a new trial. Because the other evidentiary rulings that Litvak challenges on appeal are likely to be at issue on remand, we also address those claims and conclude that the District Court exceeded its allowable discretion in certain of those rulings as well.

BACKGROUND

The charges in this case arise from Lit-vak’s conduct as a securities broker and trader at Jefferies & Company (“Jeffer-ies”), a global securities broker-dealer and investment banking firm.

In January 2013, the government filed an indictment charging Litvak with eleven counts of securities fraud, see 15 U.S.C. §§ 78j(b), 78ff (Counts 1-11), one count of fraud against the United States, see 18 U.S.C. § 1031 (Count 12), and four counts of making false statements, see 18 U.S.C. § 1001 (Counts 13-16). The indictment alleged that Litvak made three kinds of fraudulent misrepresentations to several of Jefferies’s counterparties, some of which were Public-Private Investment Funds (“PPIFs”), in order to covertly reap excess profit for Jefferies in the course of transacting residential mortgage-backed securities (“RMBS”). First, the indictment alleged that Litvak fraudulently misrepresented to purchasing counterparties the costs to Jefferies of acquiring certain RMBS. Second, the indictment alleged that Litvak fraudulently misrepresented to selling counterparties the price at which Jefferies had negotiated to resell certain RMBS. Third, the indictment alleged that Litvak fraudulently misrepresented to purchasing counterparties that Jefferies was functioning as an intermediary between the purchasing counterparty and an unnamed third-party seller, where in fact Jefferies owned the RMBS and no third-party seller was extant.

In February and March 2014, a fourteen-day trial by jury was held on the charges described above, except for Count Seven (a securities fraud charge), which was dismissed on the government’s motion the day before trial commenced. “Viewing the evidence, as we must, in the light most favorable to the government,” United, States v. McGinn, 787 F.3d 116, 120 (2d Cir.2015), we find that the jury could have reasonably concluded the following from the evidence adduced at trial.

As a bond trader at Jefferies during the relevant time period, Litvak bought and sold RMBS on Jefferies’s behalf, sometimes as a middleman (holding the RMBS only briefly when facilitating a transaction between two other parties) and sometimes holding the RMBS for a longer period of time in Jefferies’s “inventory.” Joint App’x at 376. Between 2009 and 2011, Litvak made three types of misrepresentations to representatives of the counterparties with whom he transacted on Jefferies’s behalf in order to increase Jefferies’s profit margin on the transactions in which he engaged. First, he misrepresented to purchasing counterparties Jefferies’s acquisition costs of certain RMBS. For example, in the course of the transaction at issue in Counts One, Twelve and Thirteen, Litvak falsely represented to Michael Canter, a representative of the AllianceBernstein Legacy Securities Fund (“AllianceBern-stein Fund”), a PPIF, that Jefferies had purchased certain RMBS at a price of $58.00 (based on $100.00 face value), when in fact Litvak knew that Jefferies had purchased those securities at $57.50. Jef-feries subsequently sold the securities to the AllianceBernstein Fund at a price of $58.00. Canter testified that this difference would have “mattered” and been “important” to him. Id. at 381. If Jefferies and the AllianceBernstein Fund had instead transacted at a price of $57.50, the Fund would have paid approximately $60,000 less for the securities (the total cost was approximately $12 million).

Second, Litvak misrepresented to selling counterparties the price at which Jefferies had negotiated to resell certain RMBS. In the course of the transaction at issue in Count Eight, for example, Litvak falsely stated to a representative of York Capital Management (“York”), a hedge fund that owned certain RMBS, that Litvak had arranged for Jefferies to resell those securities to a third party at a price of $61.25 (based on $100.00 face value). Litvak and York’s representative, Kathleen Corso, agreed that Jefferies would purchase the securities from York at a price of $61.00, in order to allow Jefferies to reap a $0.25 profit when resold to the third party at $61.25. However, Litvak had actually arranged for Jefferies to resell the securities to the third party at a price of $62,375. Indeed, York sold the securities to Jeffer-ies at a price of $61.00 and Jefferies then resold the securities to the third party at a price of $62,375 (for a profit of $1,375). Corso testified that this difference would have been “important” to her. Id. at 576. If Jefferies and York had instead transacted at a price of $62.125, providing Jefferies with a profit of $0.25, as Litvak had represented to Corso, Jefferies would have paid York approximately $228,500 more for the securities (the total cost was approximately $20 million).

Third,' Litvak misrepresented to purchasing counterparties that Jefferies was functioning as an intermediary between the purchasing counterparty and an unnamed third-party seller, where in fact Jefferies owned the RMBS and no third-party seller existed. In the course of the transaction at issue in Count Eleven, for example, Litvak falsely represented to a representative of Magnetar Capital (“Magnetar”), a hedge fund, that Litvak was actively negotiating with a seller of certain RMBS (i.e., acting as a middleman) when, in fact, Litvak knew that Jefferies held the securities in its inventory. Lit-vak’s negotiations with Vladimir Lemin, Magnetar’s representative, began with Le-min’s offer to purchase the securities at a price of $50.50. Litvak then described to Lemin a fictional back-and-forth between himself and an unnamed, non-existent third-party seller, which concluded with Litvak’s false representation to Lemin that he had contemporaneously purchased the securities on Jefferies’s behalf at a price of $53.00. Lemin then agreed for Magnetar to purchase from Jefferies the securities at a price of $53.25, in order to allow Jefferies to reap a $0.25 profit (or “commission”) when resold. Id. at 543. However, the securities purchased from Jefferies by Magnetar were actually held in Jefferies’s inventory and had been acquired by Jef-feries several days prior at a price of $51.25. Lemin testified that this distinction reflected “a very different situation” from that which he understood at the time of the transaction. Id. at 544. If Jeffer-ies and Magnetar had instead transacted at a price of $53.00, the agreed-upon transaction price of $53.25 less the understood $0.25 “commission” for Jefferies, Magnetar would have paid Jefferies approximately $14,000 less for the securities (the total cost was approximately $5.5 million).

At the conclusion of the trial, the jury convicted Litvak of securities fraud (Counts 1-6, 8-11), fraud against the United States (Count 12), and making false statements (Counts 13-16). Litvak moved for judgment of acquittal or, in the alternative, a new trial on several grounds, including those raised on appeal. The District Court denied Litvak’s motion in a published opinion, see United States v. Litvak, 30 F.Supp.3d 143 (D.Conn.2014), and sentenced him to 24 months’ imprisonment, three years’ supervised release, and a $1.75 million fine.

This timely appeal followed. A prior panel of this Court granted Litvak’s motion for release pending appeal because he “raised a substantial question of law or fact likely to result in reversal.” Order, United States v. Litvak, No. 14-2902-cr (2d Cir. Oct. 3, 2014), ECF No. 41 (alteration and internal quotation marks omitted).

DISCUSSION

Litvak challenges his convictions on several grounds, four of which we reach in this opinion. First, Litvak contends that, for purposes of the fraud against the United States and making false statements counts, the evidence adduced at trial provided an insufficient basis for a rational jury to conclude that his misstatements were material to the Department of the Treasury, the pertinent government entity. We agree, and accordingly reverse the District Court’s judgment of conviction as to those charges.

Second, Litvak urges us to hold that his misstatements were, as a matter of law, immaterial to a reasonable investor, which would require reversal of the securities fraud counts as well. However, because a rational jury could conclude that Litvak’s misstatements were material, the materiality inquiry — a mixed question of fact and law — was properly reserved for the jury’s determination.

Third, Litvak claims that, in respect of the scienter element of the securities fraud counts, the evidence was insufficient to support the verdict and the District Court failed adequately to instruct the jury. Because Litvak is incorrect that “contemplated harm” is a requisite component of the scienter element of securities fraud, we reject this challenge.

Fourth, Litvak asserts a number of evi-dentiary errors at trial. We agree that the exclusion of certain proffered expert testimony exceeded the District Court’s allowable discretion, and that such error was not harmless. Accordingly, we vacate the District Court’s judgment of conviction as to the securities fraud charges and remand for a new trial on those charges. Because the other evidentiary rulings that Litvak challenges on appeal are likely to be at issue on remand, we also address those claims and conclude that the District Court exceeded its allowable discretion in certain of those rulings as well.

I. Fraud Against the United States and Making False Statements

Litvak contends that, in respect of the fraud against the United States and making false statements counts, the evidence adduced at trial was insufficient to establish the materiality of his misstatements to the Department of the Treasury — the relevant government entity. Because we conclude that the evidence was insufficient to permit a rational jury to find that Litvak’s misstatements were material to the Treasury, we reverse his convictions on those charges (Counts 12-16).

A. Standard of Review

“As a general matter, a defendant challenging the sufficiency of the evidence bears a heavy burden, as the standard of review is exceedingly deferential.” United States v. Brock, 789 F.3d 60, 63 (2d Cir.2015) (internal quotation marks omitted). “Specifically, we must view the evidence in the light most favorable to the Government, crediting every inference that .could have been drawn in the Government’s favor, and deferring to the jury’s assessment of witness credibility and its assessment of the weight of the evidence.” Id. (internal quotation marks omitted). “Although sufficiency review is de novo, we will uphold the judgments of conviction if any rational trier of fact could have found the essential elements of the crime beyond a reasonable doubt.” Id. (internal quotation marks omitted).

B. Materiality for Purposes of 18 U.S.C. §§ 1001, 1031

Litvak was convicted under 18 U.S.C. § 1001 for making false statements (Counts 13-16) and 18 U.S.C. § '1031 for fraud against the United States (Count 12). Section 1001 proscribes one from, inter alia, “knowingly and willfully ... makfing] any materially false, fictitious, or fraudulent statement or representation” “in any matter within the jurisdiction of the executive, legislative, or judicial branch of the Government of the United States.” 18 U.S.C. § 1001(a)(2); see also United States v. Shanks, 608 F.2d 73, 75 (2d Cir.1979) (per curiam) (explaining that Section 1001 was “designed to protect the authorized functions of governmental departments and agencies from the perversion which might result from ... deceptive practices” (internal quotation marks omitted)), cert. denied, 444 U.S. 1048, 100 S.Ct. 740, 62 L.Ed.2d 736 (1980). Section 1031 prohibits one from, inter alia, “knowingly execut[ing] ... any scheme or artifice with the intent ... to obtain money or property by means of false or fraudulent pretenses, representations, or promises, ... including through the Troubled Asset Relief Program, an economic stimulus, recovery or rescue plan provided by the Government, or the Government’s purchase of any troubled asset as defined in the Emergency Economic Stabilization Act of 2008----” 18 U.S.C. § 1031(a)(2).

“[I]n order to secure a conviction under [18 U.S.C.] § 1001(a)(2), the Government must prove that a defendant (1) knowingly and willfully, (2) made a materially false, fictitious, or fraudulent statement, (3) in relation to a matter within the jurisdiction of a department or agency of the United States, (4) with knowledge that it was false or fictitious or fraudulent.” United States v. Coplan, 703 F.3d 46, 78 (2d Cir.2012), cert. denied, — U.S. -, 134 S.Ct. 71, 187 L.Ed.2d 29 (2013). For purposes of the second element, which is at issue here, “a statement is material if it has a natural tendency to influence, or be capable of influencing, the decision of the decisionmaking body to which it was addressed. ...” Id. at 79 (emphasis added).

We have not previously addressed the contours of materiality for purposes of 18 U.S.C. § 1031. Because the parties agree that materiality is an element of Section 1031, and that such requirement is coextensive with Section 1001’s materiality element, we assume as much and therefore have no occasion to address the issue here. The parties also agree that the “decisionmaking body” in this case is the Department of the Treasury.

C. The Government’s Evidence

The government relies primarily upon the testimony of David Miller, formerly chief investment officer for the Treasury’s Office of Financial Stability, in its attempt to identify sufficient evidence from which a rational jury could have concluded that Litvak’s misstatements were material to the Treasury.

As relevant to this case, Miller’s role at the Treasury “was to oversee the investment program[] that [was] created as a result of the financial crisis,” Joint App’x at 309, which formed and invested in the PPIFs. PPIFs were “partnership^]” between the Treasury and private investors established to purchase “troubled assets,” including certain RMBS that had “rapidly deteriorated] in value during the financial crisis.” Id. at 310; see also supra notes 2-3, 8.

Miller explained that the Treasury was responsible for overseeing the PPIFs. The Treasury selected the PPIF asset managers and prescribed rules governing “how they would invest the capital.” Joint App’x at 312. To enable the Treasury to perform its oversight duties, the PPIFs were required to provide the Treasury “access” to detailed “trade level data” upon request. • Id. at 314. Such data might be used to explore “concerns about the internal conflicts of interest that [the Treasury] wanted to be able to check upon,” such as assuring that firms with “multiple funds that invested in these type of securities” erected “certain separations and walls.” Id. In addition, Miller testified that the Treasury received “formal monthly report[s]” of each PPIF’s “top 10 positions” and “market color,” and that it participated in periodic “update calls” with PPIF managers. Id. at 315-16.

Miller also explained, however, that because the Treasury did not have the “expertise” to purchase and manage the assets at issue, the “investment decisions were managed by the fund managers” it had selected — “expertf ]”. asset managers that “were well established in the field.” Id. at 310, 312. The fund managers were given “complete discretion over which eligible assets to buy and sell.” Id. at 323.

The government also elicited testimony regarding Miller’s prior duty to report fraud. While employed by the Treasury, if Miller received reports of fraud from PPIF managers, he would “refer that information” to the special inspector general that- had been established to “provide essentially independent audit and oversight ... to prevent fraud, waste and abuse of the [PPIFs].” Id. at 313, 316.

D. The Evidence Was Insufficient To Establish Capability to Influence a Decision of the Treasury

Even viewing the evidence in the light most favorable to the government, there was insufficient evidence for a rational jury to conclude that Litvak’s misstatements were reasonably capable of influencing a decision of the Treasury. Despite adducing evidence that Litvak’s misstatements may have negatively impacted the Treasury’s investments, that this impact would have been reflected in aggregate monthly reports submitted by PPIF managers to the Treasury, and that the misstatements were the impetus for an investigation by the Treasury that eventually led to Litvak’s prosecution, the government submitted no evidence that Litvak’s misstatements were capable of influencing a decision of the Treasury. To the contrary, on cross-examination, Miller’s testimony was unequivocal that the PPIFs were deliberately structured in a manner that “[kept] the Treasury away from making buy and sell decisions.” Id. at 319. To that end, Miller explained, the Treasury cast itself as a limited partner in the PPIFs, and retained “no authority to tell the investment managers” which RMBS to purchase or at what price to transact. Id. at 320.

In defending Litvak’s convictions for' fraud against the United States and making false statements, the government advances three grounds for affirmance, each of which we find unpersuasive. First, the government suggests that a jury could reasonably conclude that Litvak’s misstatements stymied certain PPIFs from transacting RMBS “at the best possible prices,” thereby impeding the Treasury’s ability to reap optimal returns on their investments in those funds. Gov’t Br. at 43 (quoting Joint App’x at 316). Nevertheless, even if a rational jury could accept the underlying assertion — that Litvak’s misstatements ultimately, though indirectly, frustrated the Treasury’s achievement of its investment goals — it may not then infer solely therefrom that those misstatements were capable of influencing a decision of the Treasury. Such speculation is not permitted; rather, for a jury to so conclude, the government must have adduced evidence of an actual decision of the Treasury that was reasonably capable of being influenced by 'Litvak’s misstatements. See United States v. Gaudin, 515 U.S. 506, 512, 115 S.Ct. 2310, 132 L.Ed.2d 444 (1995) (“Deciding whether a statement is material requires the determination of ... [the] question[ ] ... what decision was the agency trying to make?” (internal quotation marks omitted)). To form the basis of a jury’s conclusion, evidence of such a decision cannot be purely theoretical and evidence of such a capability to influence must exceed mere metaphysical possibility.

Second, the government suggests that we may affirm because “the information the PPIFs reported to [the] Treasury was affected by Litvak’s conduct.” Gov’t Br. at 45-46. Viewing the evidence in the light most favorable to the government, we accept that Litvak’s misstatements resulted in the PPIFs with which he transacted buying or selling RMBS at slightly lower or higher prices than they would have absent the misstatements. It may follow that the government’s underlying contention — that information reported to the Treasury was “affected” by' Litvak’s misstatements — is accurate insofar as the monthly reports submitted by the PPIFs to the Treasury reflected marginally higher or lower aggregate balances in light of the prices at which RMBS were bought or sold in the transactions at issue. See id. at 46. However, even if the PPIFs’ monthly reports- to the Treasury (accurately) reflected slightly higher or lower balances than would have been reported but for Litvak’s misstatements, such evidence is insufficient to permit a rational jury to find materiality. Indeed, the government has failed to identify any evidence tending to show that these minor variations in the reports’ aggregate balances had the capability to influence a decision of the Treasury.

Third, the government suggests that “[t]he fact that [the] Treasury actually referred the matter to [the special inspector general] for investigation demonstrates that [the] Treasury regarded Litvak’s conduct as significant.” Id. at 45 (internal citation omitted). But, of course, every prosecution for making a false statement undoubtedly involves “decisions” by the government to refer for investigation, investigate, and prosecute the defendant for making the false statement at issue. These “decisions” are necessarily “influenced” by the false statement, but the materiality element would be rendered meaningless if it were sufficient for the government merely to establish the capability of the false statement to influence an agency staffer’s, investigator’s, or prosecutor’s “decision” to refer for investigation, investigate, or prosecute the defendant for the very statement at issue. Therefore, neither the fact that the Treasury decided to refer Litvak’s statements for investigation, nor that the government subsequently decided to conduct an investigation and prosecute Litvak for those statements, has any bearing on the materiality of those statements as required by the statute in the instant context.

Our decision in United States v. Rigas, 490 F.3d 208 (2d Cir.2007), supports our conclusion in this case. In Rigas, we evaluated the sufficiency of the evidence in the context of a criminal prosecution for bank fraud, which implicates the same materiality standard applicable here. See supra note 9. We explained that “ ‘relevance’ and ‘materiality’ are not synonymous.” 490 F.3d at 234. Like the limitations placed on the Treasury’s discretion here, see Joint App’x at 321 (“Q. ... [T]he general partner [i.e., the institutional manager of the fund] and the investment managers had all the authority? [Miller]. Correct.”), in Ri-gas, the banks’ discretion was also “limited,” 490 F.3d at 235. In that case, we found certain misstatements material where there was evidence that the banks would have decided to charge a different interest rate had the statements been accurate. See id. at 235-36. However, we found other misstatements, like those here, immaterial even where the government adduced evidence that the banks had received the misstatements and that its staffs had reviewed them, but there was no evidence that the statements were capable of influencing one of the banks’ decisions. See id. at 236. We therefore held that although “[defendants’ misrepresentations certainly concerned a variable that mattered to the banks,” the government must offer sufficient evidence that the misstatements were “capable of influencing a decision that the bank was able to make.” Id. at 234-35.

Here, the government has established that Litvak’s misstatements may have been relevant to the Treasury, and even contrary to its interest in maximizing the PPIFs’ returns. But the evidence also shows that the Treasury’s discretion in the matters at issue was greatly constrained by its status as a limited partner in the PPIFs. See supra note 12 (Miller’s testimony that the Treasury retained “no authority to tell the investment managers” which RMBS to purchase or the prices at which to transact (quoting Joint App’x at 320)). Similarly to Rigas, the exacting circumscription of the Treasury’s role as a decisionmaker highlights the difficulty the government faced in adducing evidence sufficient to identify a decision capable of being influenced.

Therefore, because the government adduced insufficient evidence for a rational jury to conclude that Litvak’s misstatements were reasonably capable of influencing a decision of the Treasury, we reverse the District Court’s judgment of conviction as to the fraud against the United States and making false statements charges (Counts 12-16).

II. Securities Fraud

Litvak raises three primary arguments in respect of the securities fraud counts. First, Litvak contends that the District Court erred in concluding that the evidence was sufficient to support a rational jury’s conclusion that the misrepresentations on which his securities fraud convictions were premised are material. Second, Litvak claims that, in respect of the scien-ter element of these counts, the evidence was insufficient to support the verdict, and the District Court failed adequately to instruct the jury. Third, Litvak challenges the District Court’s exclusion of nearly all of the expert testimony he proffered at trial. We reject the first and second arguments, but agree with Litvak that the District Court exceeded its allowable discretion in excluding certain portions of his experts’ proffered testimony, and that the exclusion of at least one portion was not harmless. Accordingly, we vacate the District Court’s judgment of conviction as to the securities fraud counts (Counts 1-6, 8-11) and remand for a new trial.

A. Materiality or Immateriality as a Matter of Law

Litvak argues that the misrepresentations he made to counterparties during negotiations for the sale of bonds are immaterial as a matter of law because they did not relate to the bonds’ value (as opposed to their price). Although the District Court did not squarely address this argument, it held that the trial evidence sufficiently supported a finding of materiality. See Litvak, 30 F.Supp.3d at 149-50. We reject Litvak’s argument because, on the trial record before us, a rational jury could have concluded that Litvak’s misrepresentations were material.

1.Standard of Review

As explained above, see Part I.A, “a defendant challenging the sufficiency of the evidence bears a heavy burden, as the standard of review is exceedingly deferential.” Brock, 789 F.3d at 63 (internal quotation marks omitted).

2.Governing Law

Determination of materiality under the securities laws is a mixed question of law and fact that the Supreme Court has identified as especially “well suited for jury determination.” United States v. Bilzerian, 926 F.2d 1285, 1298 (2d Cir.) (citing TSC Indus., Inc. v. Northway, Inc., 426 U.S. 438, 450, 96 S.Ct. 2126, 48 L.Ed.2d 757 (1976)), cert. denied, 502 U.S. 813, 112 S.Ct. 63, 116 L.Ed.2d 39 (1991). A misrepresentation is material under Section 10(b) of the Securities Exchange Act and Rule 10b-5 where there is “a substantial likelihood that a reasonable investor would find the ... misrepresentation important in making an investment decision.” United States v. Vilar, 729 F.3d 62, 89 (2d Cir.2013), cert. denied, — U.S. -, 134 S.Ct. 2684, 189 L.Ed.2d 230 (2014). Where the misstatements are “so obviously unimportant to a reasonable investor that reasonable minds could not differ on the question of their importance,” we may find the misstatements immaterial as a matter of law. Wilson v. Merrill Lynch & Co., Inc., 671 F.3d 120, 131 (2d Cir.2011) (internal quotation marks omitted).

3.Materiality Was Properly Reserved for the Jury’s Determination

We conclude that, on the trial record before us, a rational jury could have found that Litvak’s misrepresentations were material. The trial record includes testimony from several representatives of Litvak’s counterparties that his misrepresentations were “important” to them in the course of the transactions on which the securities fraud charges were predicated, see, e.g., supra notes 5-7, and that they or their employers were injured by those misrepresentations, see, e.g., supra notes 5-6. This testimony precludes a finding that no reasonable mind could find Litvak’s statements material. See Wilson, 671 F.3d at 131.

In trying to persuade us otherwise, Litvak relies principally upon Feinman v. Dean Witter Reynolds, Inc., 84 F.3d 539 (2d Cir.1996), in which purchasers of securities brought suit against stock brokers with whom they dealt. The purchasers alleged that the brokers charged transaction fees that far exceeded the cost to the firms of the items or services for which the purchasers were ostensibly charged, as described on the trade confirmations (e.g., “handling, postage and insurance if any,” “handling,” “service,” or “processing”). 84 F.3d at 540. The purchasers asserted that these fees were hidden, fixed commissions disguised to circumvent rules prohibiting fixed rates and to prevent customers from negotiating fees. Id.

In affirming the district court’s grant of summary judgment for defendants, we held that “no reasonable investor would have considered it important, in deciding whether or not to buy or sell stock, that a transaction fee of a few dollars might exceed the broker’s actual handling charges.” Id. at 541; see also Id. (“[Rjeasonable minds could not find that an individual ... would be affected ... by knowledge that the broker was pocketing a dollar or two of the fee charged for the transaction.”). We noted that “[e]ach of the defendants’ confirmation slips itemized the amount of the fee; the appellants were never charged more than the amounts reported on these slips.” Id. Thus, “[i]f brokerage firms are slightly inflating the cost of their transaction fees, the- remedy is competition among the firms in the labeling and pricing of their services, not resort to the securities fraud provisions.” Id.

Feinman is readily distinguishable from the case presented. First, the brokers in Feinman did not mislead their customers as to what portion of the total transaction cost was going toward purchasing securities versus the cost of the broker’s involvement. There, the brokers were truthful in stating that a certain portion of the total transaction cost — a specific amount for each broker, up to $4.85 per trade — was charged on behalf of the broker, and that the rest of the transaction’s total cost was used to purchase securities. See id. at 540. “[T]he fees were correctly stated, and the market was not otherwise alleged to have been distorted as a result.” Lit-vak, 30 F.Supp.3d at 150 n. 1 (citing Fein-man, 84 F.3d at 541-42). Unlike the stock transactions in Feinman, “the transaction costs for [Litvak’s] bid list and order trades — as agreed-upon markups or commissions ... — were embedded in the price, and the evidence showed that price was a heavily negotiated term and that the markups Litvak represented himself to be taking were false.” Id. Therefore, unlike in Feinman, Litvak was untruthful about the portion of each transaction’s total cost that would be used to purchase securities and the portion that would be retained by Jef-feries, and in each transaction at issue he falsely understated the latter portion.

Second, the amounts “pocketfed]” by Litvak on behalf of Jefferies in the transactions at issue were substantially larger than “a dollar or two” per transaction, Feinman, 84 F.3d at 541; the difference between the profit his counterparties were led to believe Jefferies yielded and the amount that it actually yielded averaged more than $100,000 per transaction in the twelve transactions at issue (ranging from $276.38 to $602,396.91). See Joint App’x at 1034.

Third, the remedy for the behavior described in Feimnan — '“competition among the firms in the labeling and pricing of their services,” 84 F.3d at 541 — is not applicable to Litvak’s behavior. Those he dealt with were unaware that he was taking a larger cut on behalf of Jefferies than he had represented to them. Without knowledge of Litvak’s actions, the financial consequences of negotiations colored by false representations were virtually undis-coverable in the opaque RMBS market. See Litvak, 30 F.Supp.3d at 149 (“As Lit-vak stresses, and as is undisputed by the government, unlike the stock market, the RMBS market is not transparent....”). Until Litvak’s misrepresentations were brought to light by his colleague’s inadvertent email to a counterparty’s representative, his counterparties were not aware of the unusually high cost of doing business with Litvak and Jefferies, and were not able to properly compare his services with Jefferies’s competitors.

Setting aside Feinman, acceptance of Litvak’s argument is also inconsistent with the “longstanding principle enunciated by the Supreme Court that § 10(b) should be construed not technically and restrictively, but flexibly to effectuate its remedial purposes, and to protect against fraudulent practices, which constantly vary.” Parkcentral Global Hub Ltd. v. Porsche Auto. Holdings SE, 763 F.3d 198, 221 (2d Cir.2014) (per curiam) (internal citations and quotation marks omitted). Finding Section 10(b) inapplicable here, as a matter of law, would require an imper-missibly technical and restrictive construction. There is no dispute that Litvak misrepresented facts related to the securities transactions at issue, and that several of his counterparties’ representatives testified at trial that they considered the misrepresentations meaningful in the course of those transactions and that they or their employers were harmed by Litvak’s misleading course of conduct. In addition, the public interest is implicated by the involvement of the Treasury as a major investor, in several of Litvak’s counterparties in the transactions at issue. Thps, enforcement of Section 10(b) here is consistent with the Supreme Court’s instruction to apply the statute flexibly, see id., and with the statute’s purpose of “remedying] deceptive and manipulative conduct with the potential to harm the public interest or the interests of investors,” id. at 209 (internal quotation marks omitted).

For these reasons, we do not find Lit-vak’s misrepresentations immaterial as a matter of law, and we therefore conclude that the District Court appropriately left this issue, a mixed question of law and fact, see Bilzerian, 926 F.2d at 1298, for the jury to determine.

B. Scienter

Litvak contends that the scienter element of Section 10(b) requires proof of “contemplated harm” (or “intent to harm”), that the District Court erred in failing to so instruct the jury, and that the evidence adduced at trial was insufficient to permit a rational jury to find that Litvak had such intent. In ruling on Litvak’s post-trial motions, the District Court reaffirmed its view that “intent to harm” is not an element of securities fraud. See Litvak, 30 F.Supp.3d at 150-51. We agree.

“Liability for securities fraud [] requires proof that the defendant acted with scienter, which is defined as ‘a mental state embracing intent to deceive, manipulate or defraud.’ ” United States v. Newman, 773 F.3d 438, 447 (2d Cir.2014) (quoting Ernst & Ernst v. Hochfelder, 425 U.S. 185, 193 n. 12, 96 S.Ct. 1375, 47 L.Ed.2d 668 (1976)), cert. denied, — U.S. -, 136 S.Ct. 242, 193 L.Ed.2d 133 (2015). Litvak urges us to read “intent to deceive, manipulate or defraud,” Hochfelder, 425 U.S. at 193 n. 12, 96 S.Ct. 1375, in the same manner in which we have interpreted “intent to defraud” in the mail and wire fraud contexts (i.e., as requiring proof of “contemplated harm”), see, e.g., United States v. Novak, 443 F.3d 150, 156 (2d Cir.2006) (explaining that, in the context of mail and wire fraud, “[o]nly a showing of intended harm will satisfy the element of fraudulent intent” (internal quotation marks omitted)). Litvak’s view, however, is contrary to our precedent.

In United States v. Vilar, 729 F.3d 62 (2d Cir.2013), the defendant similarly argued that the evidence was insufficient to support his conviction for securities fraud because the government failed to prove that he “intended to steal” from the victim. 729 F.3d at 92. We rejected that argument, holding that it “misse[d] the mark because the government was under no obligation to prove that [the defendant] wanted to steal [the victim’s] money, only that he intended to defraud her in connection with his sale of the [securities].” Id. at 98. Vilar’s holding is consistent with our earlier observation that “the Government’s burden with respect to criminal intent on [ ] Securities Exchange Act counts [is] less than under [] mail fraud counts,” United States v. Dixon, 536 F.2d 1388, 1398 (2d Cir.1976), and forecloses Litvak’s argument here.

In sum, because “intent to harm” is not a component of the scienter element of securities fraud under Section 10(b), the District Court did not err in refusing to provide such an instruction to the jury and we need not inquire into whether the evidence was sufficient for the jury to conclude that such intent was proven.

C. Evidentiary Rulings

Litvak argues that the District Court erred in excluding certain portions of his experts’ proposed testimony. We largely agree. We principally conclude that the District Court exceeded its allowable discretion in excluding Ram Willner’s testimony concerning the selection and valuation process undertaken by investment managers, and his expert opinion that a sell-side bond trader’s statements, such as Litvak’s, would be widely considered within the industry as “biased” and “often misleading,” and that excluding such testimony was not harmless. On this basis alone, we vacate Litvak’s convictions for securities fraud and remand for a new trial.

In order to assist the District Court and the parties on remand, we also address Litvak’s other claims of evidentiary error, and find some of his claims meritorious and others without merit.

1. Standard of Review

“We review a district court’s evidentiary rulings under a deferential abuse of discretion standard, and we will disturb an evidentiary ruling only where the decision to admit or exclude evidence was manifestly erroneous.” McGinn, 787 F.3d at 127 (internal quotation marks omitted). “Moreover, even if a ruling was manifestly erroneous, we will still affirm if the error was harmless.” Id. (internal quotation marks omitted).

2. Evidentiary Standard

“Evidence is relevant if: (a) it has any tendency to make a fact more or less probable than it would be without the evidence; and (b) the fact is of consequence in determining the action.” Fed.R.Evid. 401. “To be relevant, evidence need not be sufficient by itself to prove a fact in issue, much less to prove it beyond a reasonable doubt.” United States v. Abu-Jihaad, 630 F.3d 102, 132 (2d Cir.2010), cert. denied, — U.S. -, 131 S.Ct. 3062, 180 L.Ed.2d 892 (2011); see also United States v. Certified Envtl. Servs., Inc., 753 F.3d 72, 90 (2d Cir.2014) (“[T]he definition of relevance under Fed.R.Evid. 401 is very broad.”); United States v. White, 692 F.3d 235, 246 (2d Cir.2012) (explaining that Rule 401 prescribes a “very low standard” (internal quotation marks omitted)). “[U]n-less an exception applies, all ‘relevant evidence is admissible.’ ” White, 692 F.3d at 246 (alteration omitted) (quoting Fed.R.Evid. 402).

3. Exclusion of Expert Testimony

Litvak proffered two experts to testify at trial: Ram Willner, a business school professor and former portfolio manager, and Marc Menchel, a regulatory and compliance attorney. The District Court excluded all of Willner’s proposed testimony and most of Menchel’s proposed testimony. Litvak argues that the District Court erred in excluding certain portions of Will-ner’s and Menchel’s testimony. Because we agree that the District Court exceeded its allowable discretion and conclude that at least one error was not harmless, we vacate Litvak’s convictions on the securities fraud charges and remand for a new trial.

a. Ram Willner

The first expert witness Litvak proffered was Ram Willner. According to Litvak’s expert disclosure to the government, Willner holds advanced degrees in business administration with a focus on finance, served as a professor at leading business schools, and gained “extensive experience in portfolio management in the fixed income asset class, including extensive experience in the analysis and purchase of Residential Mortgage Backed Securities” during his employment by, at various times, Bank of America, Morgan Stanley, PIMCO, and a hedge fund. Joint App’x at 207. The government has not suggested Willner’s lack of qualification as a ground to affirm, and its motion to exclude Willner’s testimony before the District Court included only a perfunctory request, in the “[a]lternative[,]” for a hearing pursuant to Daubert v. Merrell Dow Pharmaceuticals, Inc., 509 U.S. 579, 113 S.Ct. 2786, 125 L.Ed.2d 469 (1993). Gov’t Mot. to Preclude Def.’s Experts at 9, United States v. Litvak, No. 3:13-cr-19 (D.Conn. Jan. 17, 2014), ECF No. 160. On the government’s motion, the District Court excluded the entirety of Willner’s testimony. On appeal, Litvak contends that the District Court exceeded its allowable discretion in excluding key portions of Willner’s testimony. We largely agree.

i. 'Exclusion of Willner’s “Materiality” Testimony Exceeded the District Court’s Allowable Discretion

Litvak contends that the District Court erred in barring Willner from testifying “about the process investment managers use to evaluate a security, and the irrelevance of the broker-dealer’s acquisition price to that process, [which] was directly probative of whether Mr. Litvak’s misstatements would have been material to a reasonable investor.” Litvak Br. at 43-44.

Before the District Court, Litvak proposed that Willner opine, in pertinent part, as follows:

[T]hat where a manager follows rigorous valuation procedures, as was the case here, consideration of, or reliance on, statements by sell-side salesmen or traders concerning the value of a RMBS or the price at which the broker-dealer acquired it or could acquire it, are not relevant to that fund’s determination with respect to how much to pay for a bond. In Mr. Willner’s opinion, such statements from sell-side sales representatives or traders are generally biased, often misleading, and unworthy of consideration in trading decisions. Accordingly, such statements from sell-side sales representatives or traders are not material to a professional investment manager’s decision-making.

Joint App’x at 208 (emphasis added). Lit-vak also offered Willner to testify in respect of “the process of selecting and valuing RMBS for inclusion in an investment portfolio, including analytical tools and methods available to an investment manager, and the development of an investment thesis for a particular RMBS.” Id. at 207-OS. The District Court excluded the entirety of Willner’s proffered testimony.

The government defends the District Court’s ruling on the ground that “[t]he materiality of Litvak’s lies was for the jury to decide.” Gov’t Br. at 60 (citing Bilzeri-an, 926 F.2d at 1295 (“[Testimony encompassing an ultimate legal conclusion based upon the facts of the case is not admissible, and may not be made so simply because it is presented in terms of industry practice.”)). But that is true in respect of only the italicized portion of the excerpted proposed opinion testimony, and in any event, the District Court did not exclude Willner’s testimony on “ultimate issue” grounds. Rather, the District Court appears to have excluded all of Willner’s proffered testimony on relevance grounds (relying on Rule 401, Rule 403, or possibly both), without ruling specifically on this part of Willner’s proposed testimony. See Tr. at 35 (“JUDGE STRAUB: ... As I understand it, [Willner’s] testimony was excluded on the basis of relevance.... MR. FRANCIS: Correct.”).

We conclude that the District Court exceeded its allowable discretion in excluding Willner’s testimony in respect of the process by which investment managers value RMBS and the likely impact on the final purchase price of a broker’s statements made to a counterparty during the course of negotiating a RMBS transaction. These portions of Willner’s testimony would have been highly probative of materiality, the central issue in the case. This is particularly true because of the meaningful distinction between the complex securities at issue in this case and the common equities and bonds traded in “traditional,” efficient markets {e.g., shares of corporate entities traded on the New York Stock Exchange). The pricing of RMBS is “more complicated” because it “tend[s] to be more subjective, [is] available mainly or only from dealers, and [is] often based on models as opposed to prices from prior transactions.” Thomas P. Lemke, Gerald T. Lins & Marie E. Picard, Mortgage-Backed Securities § 5:14 (Westlaw 2015); see also id. § 5:12 (explaining that “complicated nature” of RMBS “makes placing value on them more subjective”).

Consistent with this understanding, Willner’s proffered testimony could have educated the jury (which was likely only familiar, if at all, with securities traded on public exchanges) about the highly-specialized field of RMBS trading. Because RMBS lack an efficient, transparent secondary market through which value can be determined objectively, traders set the value of the security, and hence the price each is willing to accept as a seller or buyer, by engaging in “rigorous valuation procedures” involving the use of certain “analytical tools and methods.” Joint App’x at 208. Thus, firms trading RMBS rely upon sophisticated computer-pricing models, often developed by professionals with applied-mathematics backgrounds, to determine the subjective “value” of the securities. Certain testimony at trial supported a conclusion that this process, and a determination of the amount an investment manager is willing to pay for a security, nearly always takes place prior to the manager approaching a dealer such as Jefferies, here represented by Litvak, to negotiate the price of that security.

With such testimony before it, a jury could reasonably have found that misrepresentations by a dealer as to the price paid for certain RMBS would be immaterial to a counterparty that relies not on a “market” price or the price at which prior trades took place, but instead on its own sophisticated valuation methods and computer model. The full context and circumstances in which RMBS are traded were undoubtedly relevant to the jury’s determination of materiality.

Aside from Willner’s testimony in respect of the nature of the RMBS market, there are few ways in which Litvak could put forth evidence to rebut the alleged victims’ testimony that Litvak’s misstatements were important to them, or otherwise counter the government’s argument that a reasonable investor would have found Litvak’s statements material. The District Court’s “relevance” concerns were unfounded, cf. United States v. Avasso, 23 Fed.Appx. 33, 35 (2d Cir.2001) (summary order) (affirming admission of expert testimony that certain information “is a material fact in a purchaser’s decision which must be disclosed under NASD rules”), and there was minimal risk of confusion because Willner’s testimony in respect of an “ultimate question” before the jury could have been properly limited by the District Court.

If we were to conclude otherwise, Litvak would be put in an untenable position whereby he could not introduce testimony that either (1) the specific statements at issue in the case would not be important to a reasonable investor (due to “ultimate issue” concerns) or (2) the types of statements at issue are generally not important to a reasonable investor. Litvak would be left only with the “victims” of his conduct as sources of potential testimony on this issue, an odd limitation where the jury is to evaluate materiality in an objective manner. See Amgen Inc. v. Conn. Ret. Plans & Trust Funds, — U.S. -, 133 S.Ct. 1184, 1191, 185 L.Ed.2d 308 (2013) (“Materiality is judged according to an objective standard....”).

We conclude that this error was not harmless. See United States v. Vayner, 769 F.3d 125, 133 (2d Cir.2014) (“An erroneous evidentiary decision that has no constitutional dimension is reviewed for harmless error.”). “[U]nder harmless error review, we ask whether we can conclude with fair assurance that the errors did not substantially influence the jury.” United States v. Gupta, 747 F.3d 111, 133 (2d Cir.2014) (internal quotation marks omitted). Specifically, if defense evidence has been improperly excluded by the trial court, we normally consider the following factors:

(1) the importance of ... unrebutted assertions to the government’s case; (2) whether the excluded material was cumulative; (3) the presence or absence of evidence corroborating or contradicting the government’s case on the factual questions at issue; (4) the extent to which the defendant was otherwise permitted to advance the defense; and (5) the overall strength of the prosecution’s case.

Id. at 133-34 (internal quotation marks omitted).

The District Court’s exclusion of this portion of Willner’s testimony was not harmless, and the government does not suggest otherwise. Materiality was an issue central to Litvak’s case and was hotly contested at trial. The government called to testify several purported victims (portfolio managers and traders), each of whom testified that Litvak’s misstatements were important to them in the course of the trades charged in the indictment. Litvak’s primary defense was that, despite the victims’ testimony, Litvak’s statements were not material to a reasonable investor. See TSC Indus., 426 U.S. at 445, 96 S.Ct. 2126 (“The question of materialityf ] ... is an objective one, involving the significance of an omitted or misrepresented fact to a reasonable investor.” (emphasis added)).

Without Willner’s testimony on this point, Litvak was left with little opportunity to present his non-materiality defense. Though the government adduced substantial evidence of materiality, we cannot conclude with fair assurance that the jury would not have found differently if it were presented with information about the functioning of the specialized RMBS market and the valuation process employed by those who participate therein. See United States v. Blum, 62 F.3d 63, 69 (2d Cir.1995) (explaining that, where “defense went to the core of the prosecution’s case, we cannot view the exclusion of the testimony as harmless”). Therefore, we vacate the District Court’s judgment of conviction as to the securities fraud charges and remand for a new trial.

Though our conclusion that vacatur is warranted on this ground alone relieves us of an obligation to address Litvak’s additional claims of error in respect of the District Court’s evidentiary rulings as to the securities fraud claims, we proceed to address them for purposes of judicial economy, as the same issues are likely to arise on remand. See, e.g., Chavis v. Chappius, 618 F.3d 162, 171 (2d Cir.2010) (addressing an additional “matter in the interest of judicial economy, since it appears likely to arise upon remand”).

In respect of materiality, Litvak also claims that the District Court erred in excluding another portion of Willner’s proposed testimony: “that minor price variances would not have mattered to sophisticated investors[, which] also tended to show that Mr. Litvak’s statements about his acquisition price would not have been material.” Litvak Br. at 44. We have recognized that a misstatement may not be material where it resulted in a mere “slightf ] inflation]” of transaction costs, Feinman, 84 F.3d at 541, and district courts in this Circuit have held repeatedly in the analogous civil context that “the sophistication of [the investor] is relevant [both] to the adequacy of [the defendant’s] disclosure, and to the extent of the [investor’s] reliance [ ] on any alleged misrepresentations,” Quintet Corp. N.V. v. Citibank, N.A., 596 F.Supp. 797, 802 (S.D.N.Y. 1984) (internal citations omitted); see also, e.g., Steed Fin. LDC v. Nomura Sec. Int'l, Inc., No. 00-cv-8058, 2004 WL 2072536, at *6 (S.D.N.Y. Sept. 14, 2004); In re AES Corp. Sec. Litig., 849 F.Supp. 907, 910 (S.D.N.Y.1994); Davidson Pipe Co. v. Laventhol & Horwath, 120 F.R.D. 455, 460 (S.D.N.Y.1988); cf. Republic of Iraq v. ABB AG, 768 F.3d 145, 182 (2d Cir.2014) (Droney, J., concurring in part and dissenting in part) (noting that, in certain circumstances, “sophisticated buyer[s]” may “not necessarily need the protection of the Securities Act” (internal quotation marks omitted)). Because this testimony would have been relevant to the element of materiality, we conclude that the District Court exceeded its allowable discretion in excluding this portion as well. Since a non-harmless error has already been identified, and therefore vacatur found necessary, we need not determine whether this error was harmless.

ii. Exclusion of Willner’s “Fair Market Value” and “Profitability” Testimony Did Not Exceed the District Court’s Allowable Discretion

Litvak also claims that the District Court exceeded its allowable discretion in excluding testimony concerning the (1) fair market value and (2) profitability of the trades at issue. We disagree.

First, Litvak contends that the District Court erred in excluding Willner’s testimony “that the trades at issue were executed at a fair market value,” which Litvak views as “highly probative of the absence of materiality and fraudulent intent, because it would have demonstrated that a reasonable investor would have transacted at those prices regardless of Mr. Litvak’s explanation of how the price was derived.” Litvak Br. at 44. Before the District Court, Litvak proposed that Willner be permitted to testify that “prices paid for RMBS [in the trades at issue] were in the context of the market and within the range of fair value and that [they] did hot take place at inflated prices.” Joint App’x at 208.

The District Court did not exceed its allowable discretion in excluding this portion of Willner’s testimony. Whether the prices were “fair” was not an element of any of the crimes with which Litvak was charged and the potential confusion from such testimony might have outweighed any probative value. The principal issues at trial were whether a reasonable investor might have found the misstatements important and whether Litvak intended to deceive the purported victims. This testimony would not have addressed either; the District Court did not exceed its allowable discretion in concluding that whether the price the alleged victims paid was within a range of “fairness” was not relevant to determining if the misstatements themselves were important to a reasonable investor' or whether Litvak intentionally deceived the counterparties’ representatives.

Second, Litvak claims that the District Court erred in excluding Willner’s testimony “that the bonds were profitable,” which “bore on the issue of Mr. Litvak’s intent, even if it was not determinative.” Litvak Br. at 44. The District Court did not exceed its allowable discretion in finding this portion of Willner’s testimony of minimal relevance, and that any probative value would likely have been outweighed by its potential for confusion. Whether a victim later made a profit or loss on the bonds it purchased fhom Litvak has no bearing on whether Litvak’s misrepresentations were material or whether Litvak intended to deceive the purported victims. Thus, the District Court did not exceed its allowable discretion in excluding this portion of Willner’s testimony.

b. Marc Menchel

The second expert witness Litvak proffered was Marc Menchel. As established at trial, Menchel is an attorney who served in various legal and compliance positions for broker-dealers and securities-industry regulators, most significantly as general counsel of the Financial Industry Regulatory Authority (“FINRA”). The government has not suggested Menchel’s lack of qualification as a ground to affirm, and its motion to exclude Menchel’s testimony before the District Court did not suggest exclusion on that ground.

Litvak sought to elicit Menchel’s testimony on several topics at trial. On the government’s motion, the District Court excluded the entirety of Menchel’s testimony except in respect of the definition of certain terminology used during trial. On appeal, Litvak contends that the District Court exceeded its allowable discretion in precluding Menchel from testifying about “the arm’s-length nature of the relationship between a broker-dealer and counterparty [which] was relevant to prove that Mr. Litvak was not acting as an agent for the counterparties.” Id. at 45 (citing Joint App’x at 517-18). We agree.

While the issue of whether Litvak was acting as agent or principal is not an element of any offense charged, Litvak posits that this proposed testimony “bore on .both materiality and fraudulent intent.” Id. In support of this argument, Litvak highlights the testimony of one of the counter-parties’ representatives, Joel Wollman, who, despite the government’s subsequent concession that “what Mr. Litvak was doing was acting as a principal,” Tr. at 32, testified for the government as follows:

[Direct Examination:]
Q. In effect, did you understand — what did you understand, Mr. Litvak was acting as a principal or as an agent?
A. An agent.
Joint App’x at 517.
[Cross-Examination:]
Q. And [Jefferies] own[s] [the bond] as principal and they hold it in their own account, right?
A. I do not believe that they are acting as principal in their relationship to me. I feel that in the transaction they are acting as agent to me even though they have to principally acquire the bond.

Id. at 518.

In light of this and other testimony elicited at trial, Litvak is correct that Menchel’s testimony regarding the agent/principal distinction would have been relevant to materiality. In determining whether a reasonable investor would have found Litvak’s misstatements important in the course of a transaction, a jury might construe such statements as having great import to a reasonable investor if coming from the investor’s agent. Cf. Knudsen v. Torrington Co., 254 F.2d 283, 286 (2d Cir.1958) (“[T]he agency relationship is normally grounded on the trust and confidence the principal places in his agent....”). If, on the other hand, Litvak was acting on his own behalf (i.e., as a principal), and not as the purported victims’ agent, a jury may well construe that relationship as providing a distance between Litvak and a reasonable investor, which may tend to show that his statements could not have been reasonably viewed as important in the course of a transaction. Cf. In re Mid-Island Hosp., Inc., 276 F.3d 123, 130 (2d Cir.) (“[W]hen parties deal at arms length in a commercial transaction, no relation of confidence or trust sufficient to find the existence of a fiduciary relationship will arise absent extraordinary circumstances.” (internal quotation marks omitted)), cert. denied, 537 U.S. 882, 123 S.Ct. 104, 154 L.Ed.2d 140 (2002).

Menchel was similarly prepared to testify in respect of the significance of the agent/principal distinction in the RMBS context. Litvak offered Menchel to testify that “[t]he term ‘commission’ applies when a broker-dealer is acting in the capacity of agent and are virtually unheard of in the fixed-income market (which includes RMBS).” Joint App’x at 219. Menchel also would have testified, for example, that “all trades with a broker-dealer acting as principal are ‘all-in’ because when an agreement is reached, the deal is always memorialized as one price to the customer for a quantity of a bond. There are no other separate fees or charges for the transaction.” Id. Thus, Menchel was prepared to testify that, contrary to the government’s characterization in summation that Jefferies’s profits on the trades at issue were “commission[s],” id. at 870, Jef-feries’s role was that of a principal (not an agent or broker) earning a profit as would any other buyer or seller.

Without the aid of Menchel’s testimony, the jury might easily have misconstrued the nature of the transactions at issue, believing (mistakenly, according to Men-chel) that Jefferies’s profits were commissions paid for Litvak’s facilitation of the transactions, rather than ordinary profits earned in a standard buyer-seller context. The nature of Litvak’s relationship with the alleged victims formed the context in which the jury had to consider whether the portfolio managers and traders who testified reflected the views of a reasonable investor; this portion of Menchel’s proposed testimony would have supported Lit-vak’s materiality defense and could have rebutted Wollman’s above-quoted testimony..

Therefore, the District Court exceeded its allowable discretion in excluding this portion of Menchel’s testimony. Because we have already determined that the securities fraud convictions must be vacated on the basis of a different evidentiary error, see supra Part II.C.3.a.i, we address this claim of error solely to assist the District Court on remand, see, e.g., Chavis, 618 F.3d at 171, and we need not determine whether this error was harmless.

4. Exclusion of “Good Faith” Evidence

Litvak challenges the District Court’s exclusion of “testimony and documents about the widespread use of similar negotiation tactics at Jefferies” which “would have shown that others at Jefferies engaged in the same conduct and that it was approved by supervisors and by Jefferies’ compliance department.” Litvak Br. at 46. The “good faith” evidence Litvak proffered at trial may be separated into two categories: (1) evidence of Litvak’s supervisors’ knowledge or approval of Lit-vak’s “price misrepresentation^]” and “inventory misrepresentation^]” and (2) evidence of Jefferies managers’, including Litvak’s supervisors, knowledge or approval of other ■employees’ similar conduct. Joint App’x at 643. The District Court permitted the first category of evidence, allowing Litvak to adduce evidence that his supervisors “approved” or “encouraged” him to misrepresent price, cost, or a seller’s identity because such evidence “terid[s] to prove the absence of intent” and could provide a basis for the jury to make “a reasonable inference ... that they should find no intent to defraud given the nature of what happened at Jefferies.” Id. at 644-45.

The second category of evidence was the subject of a lengthy colloquy between Litvak’s counsel and the District Court. After the District Court called the relevance of this evidence into question, Litvak’s counsel responded as follows:

This is an ongoing alleged scheme ... with the same supervisors in place for the entire time with repeated examples of the two types of alleged misrepresentations we have been talking about here. So, your Honor, I think that evidence that supervisors approve this conduct and participate in the conduct on a repeated basis is a fair basis upon which to infer that when Mr. Litvak did the very same thing, that the supervisors saw and approved of as standard operating procedure, that Mr. Litvak lacked the intent to defraud. That’s a fair inference from that evidence. It is a circumstantial basis to infer that Mr. Litvak had a belief, as we have contended, that he was not committing fraud....

Id. at 644; see also id. (Litvak’s counsel explaining that “the supervisors understood what Mr. Litvak had done not to be fraudulent because it was approved [and] because [they] were sales tactics that were widely employed.... That’s the environment in which Mr. Litvak is operating. It all goes back to state of mind.”). The District Court rejected this argument and prohibited Litvak from adducing evidence of “other people at Jefferies engaging in the same type of conduct” or “any supervisor approving others engaging in the conduct” because such evidence is “irrelevant when it does not involve [Litvak].” Id. at 645 (emphasis added); see also id. at 643 (District Court explaining that “I don’t think it matters what the culture, at Jeffer-ies is.”).

Unfortunately, the precise basis for the District Court’s oral ruling excluding the second category — lack of relevance under Federal Rule of Evidence 401, probative value substantially outweighed by other considerations under Federal Rule of Evidence 403, or both — is not clear from the record. In our view, the soundest reading. of the District Court’s ruling is that it rested solely on relevance grounds. Therefore, our inquiry is whether the District Court exceeded its allowable discretion in concluding that the excluded evidence would not have “any tendency to make a fact [of consequence in determining the action] more or less probable than it would be without the evidence.... ” Fed. R.Evid. 401.

On appeal, Litvak argues that the excluded evidence “would have been relevant to demonstrate [his] lack of fraudulent intent and good faith, because it would have tended to show that [he] was unaware that his actions were unlawful.” Litvak Br. at 46. In relevant part, the District Court instructed the jury that the government must prove as to each securities fraud count “that Mr. Litvák participated in the scheme to defraud knowingly, willfully, and with intent to 'defraud.” Joint App’x at 978 (emphasis added). The District Court instructed the jury in respect of the “intent to defraud” prong as follows:

[I]f you find that Mr. Litvak acted in good faith, or held an honest belief that his actions (as charged in a given count) were proper and not in furtherance of any unlawful activity, you cannot convict him of that count. Mr. Litvak, however, has no burden to prove a defense of good faith. The burden is on the government to prove beyond a reasonable doubt Mr. Litvak’s fraudulent intent. Under the anti-fraud statutes, false representations or statements or omissions of material facts do not amount to a fraud unless done with fraudulent intent. However misleading or deceptive a plan may be, it is not fraudulent if it was devised or carried out in good faith.

Id. at 979; see also id. at 978 (District Court instructing the jury that, in order to establish the “willfully” prong of the second element, “[t]he government must prove ... that [Litvak] was aware of the generally unlawful nature of his acts”).

Litvak sought to introduce evidence that, during the relevant time period, supervisors at-Jefferies — including his supervisors — regularly approved of conduct identical to that with which Litvak was charged. The District Court characterized the proffered evidence as improperly “suggest[ing] that everybody did it and therefore it isn’t illegal.” Id. at 645. But Lit-vak’s counsel did not proffer the evidence for that purpose and such an argument in summation could have been properly proscribed by the District Court. As Litvak’s counsel stated at trial, this evidence would provide “a fair basis upon which to infer that when Mr. Litvak did the very same thing, ... the supervisors saw and approved of [it] as standard operating procedure.” Id. at 644. Such an inference would support Litvak’s attempt to introduce a reasonable doubt as to his intent to defraud, ie., that he held an honest belief that his conduct was not improper or unlawful, a belief the jury may have found more plausible in light of his supervisors’ approval of his colleagues’ substantially similar behavior. While the District Court was correct that this evidence is less probative of Litvak’s intent as the evidence regarding transactions in which he was directly involved (the first category), the District Court exceeded its allowable discretion in concluding that this testimony was not relevant under the low threshold set forth by Federal Rule of Evidence 401, see White, 692 F.3d at 246, in determining whether Litvak “held an honest belief that his actions ... were proper and not in furtherance of any unlawful activity,” Joint App’x at 979; see United States v. Brandt, 196 F.2d 653, 657 (2d Cir.1952) (“since [good faith] may be only inferentially proven, no events or actions which bear even remotely on its probability should be withdrawn from the jury unless the tangential and confusing elements interjected by such evidence clearly outweigh” its relevance (internal citation omitted)); see also United States v. Collorafi, 876 F.2d 303, 305 (2d Cir.1989) (same).

Because we have already determined that vacatur is warranted due to the District Court’s erroneous exclusion of certain portions of Litvak’s proffered expert testimony, see swpra Part II.C.3.a.i, we address this claim of error solely to assist the District Court on remand, see, e.g., Chavis, 618 F.3d at 171, and we need not separately address whether this error was harmless.

CONCLUSION

We REVERSE the District Court’s judgment of conviction as to the fraud against the United States and making false statements charges (Counts 12-16), VACATE the District Court’s judgment of conviction as to the securities fraud charges (Counts 1-6, 8-11), and REMAND for a new trial on the securities fraud charges. 
      
      . “The three principal capacities in which firms act in [the securities] business are as broker, dealer, and investment adviser. The 1934 [Securities Exchange] Act defines a ‘broker’ as a 'person engaged in the business of effecting transactions in securities for the account of others,’ while a 'dealer' is a 'person engaged in the business of buying and selling securities for such person’s own account.' An 'investment adviser' is defined in [Section] 202(a)(ll) of the Investment Advisers Act of 1940 as a 'person who, for compensation, engages in the business of advising others ... as to the advisability of investing in, purchasing or selling securities,’ but broker-dealers who render such advice as part of their brokerage activities are exempt from the definition.” 5 Thomas Lee Hazen, Treatise on the Law of Securities Regulation § 14.1 [3][B] (Westlaw 2015) (footnotes omitted).
     
      
      . A PPIF is "a financial vehicle that is — (1) established by the Federal Government to purchase pools of loans, securities, or assets from a financial institution ...; and (2) funded by a combination of cash or equity from private investors and funds provided by the Secretary of the Treasury or funds appropriated under the Emergency Economic Stabilization Act of 2008.” 12 U.S.C. § 5231a(e); see also generally Jason H.P. Kravitt, Robert F. Hugi & Jeffrey P. Taft, Securitization of Financial Assets § 21.04 (Westlaw 2015).
     
      
      .RMBS are "a type of asset-backed security — that is, a security whose value is derived from a specified pool of underlying assets. Typically, an entity (such as a bank) will buy up a large number of mortgages from other banks, assemble those mortgages into pools, securitize the pools (i.e., split them into shares that can be sold off), and then sell them, usually as bonds, to banks or other investors.” City of Pontiac Policemen’s & Firemen’s Ret. Sys. v. UBS AG, 752 F.3d 173, 177 n. 7 (2d Cir.2014) (internal quotation marks omitted).
     
      
      . "The face, or maturity, value of the bond is its denomination.'' Jay Alix, Ted Stenger & Lawrence R. Ahern, III, Financial Handbook for Bankruptcy Professionals § 10.11 (2d ed. Westlaw 2015). "Bond prices are referred to in terms of 100’s. For instance, a bond with a face (par) value of $1,000 may be offered at a price of 103.5, which means that the bond has a market value of $1,035.” Id.
      
     
      
      . Canter testified as follows:
      Q. Would it have mattered to you at the time if you had known that Mr. Litvak actually paid 57-and-a-half?
      A. Yes.
      Q. Why?
      A. Because we use that information of him buying at 58 to set the price that we would buy it at. If we could have bought it cheaper, that would have been better for my investors.
      Q. Would it have been important for you to know at the time that Mr. Litvak was taking 16 ticks [thirty-seconds of a point], or half a point, instead of zero [as profit for Jeffer-ies]?
      A. Yes.
      Q. Can you explain why?
      A. Well, certainly, if I knew that he was being untruthful about it, then it would have affected us doing future business with him. But if just in terms of the numbers, if we could have gotten it — if we could have bought the bond at a lower price, that would have been more profitable for my clients.
      Joint App’x at 381.
     
      
      . Corso testified as follows:
      Q. ... Would it have been important for you to know that, in fact, your bonds were sold that day not at [$61.25] but at [$62.375]?
      A. Yes.
      Q. Could you explain to the jury why that would be important for you to know?
      A. Because that means that I didn't get the best execution and that he sold them for a lot higher than what he had told me.
      Q. If you had had that information at the time, what would you have done?
      A. At the time, I would have either tried to rip up the trade or try to get compensation for the difference or it would have affected our relationship with Jefferies.
      Joint App'x at 576-77.
     
      
      . Lemin testified as follows:
      Q. And if you had known at the time of this trade that in truth Jefferies owned the bond in its inventory and these negotiations that Mr. Litvak claims happened, didn't happen, would you have paid a commission?
      A. Then the term commission wouldn't have applied. It would have been a very different situation.
      Q. And, sir, do you pay commission on inventory trades, Mr. Lemin?
      A. We do not.
      Joint App'x'at 544.
     
      
      . As defined in the Emergency Economic Stabilization Act of 2008, troubled assets include "residential or commercial mortgages and any securities, obligations, or other instruments that are based on or related to such mortgages, that in each case was originated or issued on or before March 14, 2008, the purchase of which the Secretary [of the Treasury] determines promotes financial market stability." 12 U.S.C. § 5202(9)(A).
     
      
      . See Brief for Defendant-Appellant Jesse C. Litvak ("Litvak Br.”) at 51 ("Although this Court has not addressed Section 1031 directly, it has held that materially identical language in the bank-fraud statute requires that a misstatement 'be capable of influencing a decision that the bank was able to make.' [iUnited States v. Rigas, 490 F.3d 208, 235 (2d Cir.2007), cert. denied, 552 U.S. 1242, 128 S.Ct. 1471, 170 L.Ed.2d 296 (2008).] The bank-fraud statute served as the model for Section 1031, which, as is relevant here, simply substituted 'the United States' for 'a financial institution.' See H.R.Rep. No. 100-610, at 5 (1988).”); Brief for Appellee United States of America ("Gov't Br.”) at 42 ("This Court has not addressed materiality under 18 U.S.C. § 1031, but the parties agree that because that statute is based on the mail, wire and bank fraud statutes, materiality under § 1031 should follow the well-established definition of materiality from those fraud crimes.”).
     
      
      . The Office of Financial Stability was created "to implement the Troubled Asset Relief Program (TARP) to help stabilize the U.S. financial system and promote economic recovery, following the 2008 financial crisis.” About OFS, U.S. Dep’t of Treasury, http:// www. treasury. gov/initiatives/financial-stability/Pages/about-ofs.aspx (last visited Dec. 7, 2015); see also 12 U.S.C. § 5211(a)(3)(A); Judicial Watch, Inc. v. U.S. Dep’t of Treasury, 796 F.Supp.2d 13, 19 (D.D.C.2011).
     
      
      . Alan Vlajinac, a representative of Wellington Management Company, a Jefferies coun-terparty, who dealt with Litvak, testified that "[c]olor is anything that has to do with any information going on in the marketplace.” Joint App'x at 474.
     
      
      . Miller testified on cross-examination as follows:
      Q. The Treasury had no authority to tell the investment managers which bonds to buy, correct?
      A. Correct.
      Q. The Treasury had no authority to tell the general partner [i.e., the institutional manager of the fund] of each of these funds how much to pay for a bond, correct?
      A. Correct.
      Q. All of that decision-making under this program, as [the] Treasury designed it, was sent over to the investment managers, correct?
      A. By design. Once [the PPIF contracts] were signed, they had the authority to — to invest.
      Joint App’x at 320.
     
      
      . On appeal, the government conceded that the Treasury has never made a decision in respect of the transactions at issue in Litvak’s prosecution. See Transcript of Oral Argument ("Tr.”) at 42 ("JUDGE STRAUB: So you concede [that the] Treasury never made a decision in respect of the individual purchases. MR. FRANCIS: Yes.”).
     
      
      . On appeal, the government conceded that there is no "indication [in the record] that [the] Treasury made a decision after receiving data in respect of a PPIF which was a victim of Litvak’s misrepresentation^].” Tr. at 42.
     
      
      . Even assuming, arguendo, that the government's evidence established that the Treasury regarded Litvak’s conduct as "significant,” such a metric of materiality is inapposite in the fraud against the United States and making false statements contexts. While materiality in the securities fraud context may be found where the information is "considered significant by reasonable investors,” United States v. Contorinis, 692 F.3d 136, 144 (2d Cir.2012) (emphasis added), in the government fraud and false statements contexts, we apply a different standard, see Coplan, 703 F.3d at 79 (explaining that for purposes of 18 U.S.C. § 1001(a)(2), “a statement is material if it has a natural tendency to influence, or be capable of influencing, the decision of the decisionmaking body to which it was addressed”).
     
      
      . This section (Part II) addresses, inter alia, Litvak’s argument that his misrepresentations were immaterial as a matter of law and his claims of error in the District Court's eviden-tiary rulings at trial. Though he challenges all of the counts on which he was convicted on these grounds, because we reverse Litvak’s convictions for fraud against the United States and making false statements on other grounds, see supra Part I.D, we analyze these arguments in the context of only the securities fraud charges (Counts 1-6, 8-11).
     
      
      . The government's contention that Litvak failed to raise this particular argument below is unfounded because Litvak, in his Rule 29(c) motion, did argue that the evidence at trial of materiality was insufficient as a matter of law. Even if we accept the government's narrow view of Litvak’s argument below, Lit-vak is not limited to the “precise arguments” he made before the District Court, see Yee v. City of Escondido, 503 U.S. 519, 534, 112 S.Ct. 1522, 118 L.Ed.2d 153 (1992), and may submit "additional support ... for a proposition presented below,” Eastman Kodak Co. v. STWB, Inc., 452 F.3d 215, 221 (2d Cir.2006).
     
      
      . On November 10, 2011, Canter received an email from a colleague of Litvak’s at Jef-feries which inadvertently attached a spreadsheet containing trade information to which Canter would not typically be privy. Though Canter xmderstood that the spreadsheet was not "meant for [his] eyes,” Joint App’x at 369, he reviewed the data it contained and learned that Jefferies had reaped larger profits on a RMBS trade than Litvak had represented. Canter subsequently reported his concerns to the Treasury.
     
      
      . Litvak also relies upon Barnett v. Kirshner, 527 F.2d 781 (2d Cir.1975), in which we held that the identity of the true purchaser of securities was immaterial as - a matter of law where "the sole reason for concealing [the true purchaser’s] identity was [the seller’s] dislike for him.” 527 F.2d at 785. Here, Litvak is not faulted with merely misrepresenting the identity of a purchaser. Rather, Litvak falsely stated that third-party purchasers and sellers were involved in transactions where there were no third parties involved, see, e.g., supra note 7 and accompanying text, and he misled Jefferies’s counterparties, for whom he was serving as a middleman, as to their respective positions in order to reap larger profits for Jefferies.
     
      
      .Though we side with the government on this issue, we do not adopt its apparent reliance upon the Supreme Court’s statement that " 'neither the SEC nor this Court has ever held that there must be a misrepresentation about the value of a particular security in order to run afoul of the [Securities Exchange] Act.' ” SEC v. Zandford, 535 U.S. 813, 820, 122 S.Ct. 1899, 153 L.Ed.2d 1 (2002); see Gov’t Br. at 29, 32 n. 4. Zandford addressed the “in connection with” language of Section 10(b), see 535 U.S. at 819-21, 122 S.Ct. 1899, not the standard for materiality, and is properly read as deciding whether a misrepresentation has to be tied to the "value of a particular security," id. at 820, 122 S.Ct. 1899 (emphasis added), as opposed to the overall management of an investor's securities account. It appears that neither this Court nor our sister circuits have applied this language in the context of the materiality element, and we decline to do so here.
     
      
      . The District Court noted, without deciding, that "[t]he trial evidence may also be sufficient to support a finding of intent to cause financial loss.” Litvak, 30 F.Supp.3d at 151 n. 3.
     
      
      . In an attempt to compensate for the dearth of support for his position, Litvak misleadingly quotes Hochfelder as holding that " 'intent to ... defraud’ ” is required for securities fraud liability. Reply Brief for Defendant-Appellant Jesse C. Litvak at 12 (ellipsis in original) (quoting Hochfelder, 425 U.S. at 193 n. 12, 96 S.Ct. 1375). But the ellipsis omits critical language; Hochfelder held that securities fraud requires proof of “intent to deceive, manipulate or defraud.” 425 U.S. at 193 n. 12, 96 S.Ct. 1375 (emphases added).
     
      
      . Accord United States v. Bennett, No. 00-1330-cr, slip op. at 4 (2d Cir. May 31, 2001) (summary order) ("Nor is there error on the securities fraud charge, because intent to harm is not an element of securities fraud at all.” (citing United States v. Chiarella, 588 F.2d 1358, 1371 (2d Cir.1978), rev’d on other grounds, 445 U.S. 222, 100 S.Ct. 1108, 63 L.Ed.2d 348 (1980))); United States v. Lince-cum, 225 F.3d 647, 2000 WL 1015927, at *1 (2d Cir.2000) (summary order) (criminal securities fraud charges do not require proof "that the defendant intended to cause harm to the victim of the fraud” (citing United States v. Dixon, 536 F.2d 1388, 1396 (2d Cir.1976))).
     
      
      . Litvak’s reliance upon United States v. De-Santis, 134 F.3d 760 (6th Cir.1998), is not persuasive. Even assuming, arguendo, that DeSantis is correctly decided, it does not hold that “contemplated harm” or "intent to harm” is a requisite component of securities fraud’s scienter element. Rather, it holds that securities fraud requires proof that the misrepresentation was made for "the purpose of inducing the victim of the fraud to part with property or undertake some action that he would not otherwise do absent the misrepresentation or omission.” Id. at 764. Under the Sixth Circuit’s formulation, moreover, "the belief, even if bona fide, that no investor will suffer a loss ... is not a defense,” id.; from this we must conclude that the intent to cause harm is not an element of the crime in the Sixth Circuit. If it were, a defendant’s bona fide belief that he will not cause such harm would necessarily constitute a defense.
     
      
      . After the District Court ruled from the bench on the government's motion to exclude Willner's testimony, Litvak’s counsel sought clarification as to whether there was "anything left of what [the defense] proposed” in respect of Willner’s testimony. Joint App'x at 254. Confusingly, .the District Court then proceeded to question Willner’s qualifications and the basis for his opinion:
      THE COURT: What's the basis of ... [Will-ner's proposed testimony that statements such as Litvak’s would not be] relevant to the fund’s determination with respect to how much to pay are obvious [sic ] misleading and unworthy of — how can he give that opinion? I can give an opinion that most lawyers lie, most shade the truth when asked about what they have done in discovery or not done in discovery. I can give that opinion? How can he give that opinion? What's the method either scientific, analytic, based on the peer review, based on the peer experience, what is his method?
      MR. SMITH: Based upon his experience as well as education.
      THE COURT: He doesn’t care. That means that’s an opinion and that proves that the market doesn't care?
      
        MR. SMITH: What he could say [is that] he worked at many buy-side shops. It is widely understood this is how you approach it.
      THE COURT: So anybody who works at a buy-side shop is an expert? So what makes him an expert?
      MR. SMITH: I think we have laid it out in his CV, Judge.
      THE COURT: He worked at those place[s], [] that’s what makes him an expert?
      MR. SMITH: He has a Ph.[D.], your Honor. Finance and quantitative methods that [are] related to what his opinions are. The principal witness from Alliance Bernstein has a Ph.[D.] in finance that will be brought to bear.
      THE COURT: He’s testifying about whether somebody told him the light was red when it was green. He’s not testifying about his ■ Ph.[D],
      Joint App’x at 254-55.
      In light of the District Court’s comments, we note that, for these purposes, “expert testimony does not [have to] rest on traditional scientific methods.’’ Davis v. Carroll, 937 F.Supp.2d 390, 412 (S.D.N.Y.2013). “Experts of all kinds tie observations to conclusions through the use of what Judge Learned Hand called 'general truths derived from ... specialized experience.' ” Kumho Tire Co. v. Carmichael, 526 U.S. 137, 148-49, 119 S.Ct. 1167, 143 L.Ed.2d 238 (1999) (quoting Learned Hand, Historical and Practical Considerations Regarding Expert Testimony, 15 Harv. L.Rev. 40, 54 (1901)). Thus, district courts must be mindful that “the Daubert factors do not all necessarily apply even in every instance in which reliability of scientific testimony is challenged, and in many cases, the reliability inquiry may instead focus upon personal knowledge and experience 'of the expert.” ' Davis, 937 F.Supp.2d at 412 (internal quotation marks omitted). Indeed, courts regularly permit testimony similar to that which Litvak proposed Willner provide. See, e.g., United States v. Romano, 794 F.3d 317, 333 (2d Cir.2015) (finding no abuse of discretion in admission of expert testimony regarding coin valuation even though “it is possible that [the expert’s] methods are not entirely replicable because they are based in part on his personal experience as a coin dealer”); In re Blech Sec. Litig., No. 94 Civ. 7696, 2003 WL 1610775, at *21 (S.D.N.Y. Mar. 26, 2003) (admitting securities industry expert’s testimony "as to what ordinary broker activity entails and as to the customs and practices of the industry”); SEC v. U.S. Envtl., Inc., No. 94 Civ. 6608, 2002 WL 31323832, at *3 (S.D.N.Y. Oct. 16, 2002) (admitting expert’s testimony that “certain trading patterns would raise red flags’ ” based on expert’s "knowledge of typical trading activity and the types of trading patterns that an experienced trader would recognize as irregular, and as such, are supported by his 30 years of experience in the securities industry"); see also Sawant v. Ramsey, 88 Fed.R.Evid. Serv. 862, 2012 WL 2046812, at *2 (D.Conn.2012) (excluding securities expert’s testimony "on the 'materiality' of the purported misrepresentations and omissions at issue ... as a legal conclusion," but noting that “in the context of a much more complicated segment of the stock market, expert testimony may be admissible as helpful to suggest 'the inference which should be drawn from applying the specialized knowledge to the facts’ ” (internal citations omitted)).
     
      
      . In its brief on appeal, the government 'contends that Litvak forfeited his argument that the District Court's exclusion of the expert evidence was erroneous because, in addition to excluding the evidence on relevance grounds pursuant to Federal Rule of Evidence 401, the District Court also excluded it based on Federal Rules of Evidence 403 and 702, which Litvak did not challenge on appeal. At oral argument, however, the government conceded that the District Court did not exclude Willner’s testimony on Rule 702 grounds. See Tr. at 35 ("JUDGE STRAUB: ... As I understand it, [Whiner’s] testimony was excluded on the basis of relevance. You did question his reliability as an expert. The judge never ruled on that. MR. FRANCIS: Correct.”). In light of this concession and the fact that the District Court was unclear in stating the bases for its ruling, we decline to construe Litvak’s arguments in a prejudicially narrow manner.
     
      
      . Pricing proxies are available for subprime RMBS, but even the sponsor of "one of the more popular” of those indices has counseled against "overplaying] their importance in valuing th[e] asset class,” Jerome S. Fons, Shedding Light on Subprime RMBS, 15 J. Structured Fin. 81, 81 (2009), and research shows that the pricing is often over- or understated, e.g., id. at 90 (finding "material discrepancies in the security valuations implied from traded prices (or close approximations thereof) on [one widely-utilized] index”); cf. Oren Bar-Gill & Elizabeth Warren, Making Credit Safer, 157 U. Pa. L.Rev. 1, 54 n. 154 (2008) (describing "the complexity and multidimensionality of subprime mortgage loans”).
     
      
      . Cf. Craig Eastland, Understanding the Financial Crisis, or How We Got in the Mess We're In, 09-6 Compensation & Benefits for L. Off. 1 (2009) (noting that “[investment banks ... employ[ ] financial engineers (or quants) to apply mathematical tools to MBS offerings”).
     
      
      . See generally Andrew Davidson & Alexander Levin, Mortgage Valuation Models: Embedded Options, Risk, and Uncertainty 121— 336 (2014).
     
      
      . In his case-in-chief, Litvak was permitted one other opportunity to introduce similar evidence, but that testimony addressed only ' that trader-witness’s personal practice (as opposed to industry-wide practice) and was elicited from a non-expert. See Joint App’x at 831-32 (Alvin Sarabanchong, a trader with whom Litvak transacted, testifying that he does not generally "rely on information provided by a broker to ultimately decide on the price level at which to buy a bond” and does not consider "how much a dealer is paying for a bond” in negotiating "the dollar price”).
     
      
      . "FINRA is a self-regulatory organization" that “creátes and enforces rules that govern the securities industry,” including "all aspects of securities trading.” NASDAQ OMX Grp., Inc. v. UBS Sec., LLC, 770 F.3d 1010, 1048 (2d Cir.2014) (Straub, J., dissenting).
     
      
      . The impact of this distinction appears to be understood by the government, which in summation compared Litvak to a real-estate agent who told his client that a bid was accepted at an amount higher than it was actually accepted, and pocketed the difference. The government invoked the same analogy at oral argument, see Tr. at 25-26, but subsequently conceded that Litvak was acting exclusively as a principal, and not as an agent, in the transactions at issue in this case, see id. at 33-34.
     
      
      . Though Menchel's excluded testimony relating to the agent/principal distinction would have focused on the transactions at issue in Counts One, Two and Five, and Wollman's testimony related solely to the transactions at issue in Counts Nine and Ten, Menchel’s testi- , mony on this point could have been rationally applied by the jury to each of the transactions at issue due to their similarities in structure.
     
      
      . In any event, the government does not contend that the exclusion of this testimony was harmless.
     
      
      . The District Court explained the basis for its ruling as follows:
      [I]f it is something Mr. [Litvak] didn't know, then it can’t go to a state of mind. If he’s not on the documents, then there’s no evidence he knew. Unless there’s a witness who will say he told it to Mr. Litvak or Mr. Litvak said I knew about all of these, we were sitting in a room, et cetera, et cetera. But without that, I don't see how it is at all relevant under 401 and that's before I even get to a 403 issue of introducing evidence to the jury that effectively, its only purpose, it seems to me, is to suggest that everybody did it and therefore it isn’t illegal, or we should feel sympathy for Mr. Litvak because he’s the only one of all [the] other people who did it who is being prosecuted. I don’t believe either of those arguments is an appropriate argument. Therefore I don't believe the evidence is appropriate.
      Joint App'x at 645.
     