
    UNITED STATES of America, Appellee, v. Daniel BONVENTRE, Annette Bongiorno, Joann Crupi, aka "Jodi," Jerome O'Hara, and George Perez, Defendants-Appellants.
    
    Nos. 14-4714-cr(L), 14-4715-cr(Con), 14-4716-cr(Con), 14-4719-cr(Con), 15-50-cr(Con).
    United States Court of Appeals, Second Circuit.
    April 20, 2016.
    
      Andrew J. Frisch (Jeremy B. Sporn, Amanda L. Bassen, on the brief), Law Offices of Andrew J. Frisch, New York, NY, for Daniel Bonventre.
    Roland G. Riopelle, Sercarz & Riopelle, LLP, New York, NY, for Annette Bongior-no.
    Eric R, Breslin (Melissa S. Geller, on the brief), Duane Morris LLP, Newark, NJ, for Joann Crupi.
    Gordon Mehler (Sarah Lum, Rebecca Stack Campbell, on the brief), Mehler Law PLLC, New York, NY, for Jerome O’Hara.
    Larry H. Krantz (Kimberly A. Yuhas, on the brief), Krantz & Berman LLP, New York, NY, for George Perez.
    Aimee Hector, Andrea Griswold, Assistant United States Attorneys (David Abra-mowicz, Matthew Laroche, Karl Metzner, Assistant United States Attorneys, on the brief), for Preet Bharara, United States Attorney for the Southern District of New York, New York, NY.
    PRESENT: JOHN M. WALKER, JR., REENA RAGGI and CHRISTOPHER F. DRONEY, Circuit Judges.
    
      
       The Clerk of Court is directed to amend the caption as set forth above.
    
   SUMMARY ORDER

Defendants, all former employees of Bernard L. Madoff Investment Securities (“BLMIS” or the “Firm”), stand convicted after trial of multiple counts of conspiratorial and substantive securities fraud, bank fraud, and records ■ falsification; making false SEC and IRS filings; obstructing enforcement of tax laws; and tax evasion for their participation in a massive scheme to defraud thousands of investors of tens of billions of dollars. On appeal, defendants challenge various trial court rulings, the sufficiency of the evidence, the government’s trial conduct, and the judgments of forfeiture. We assume the parties’ familiarity with the facts and record of prior proceedings, which we reference only as necessary to explain our decision to affirm,

1. Bill of Particulars

Bonventre argues that, as to Counts Nine through Fourteen of the Eighth Superseding Indictment, charging falsification of investment adviser and broker-dealer records, see 15 U.S.C. §§ 78q(a), 78ff, 80b-4, 80b-17; 17 C.F.R. §§ 240.17a-3, 275.204-2, he was entitled to particulars as to the records alleged to be false, why they were false, and how Bon-ventre knew of their falsity. See Fed. R.Crim.P. 7(f). The challenge fails because such “evidentiary detail is not the function of the bill of particulars.” United States v. Torres, 901 F.2d 205, 234 (2d Cir.1990) (internal quotation marks omitted). Particulars are necessary only where indictment charges are “so general that they do not advise the defendant of the specific acts of which he is accused.” United States v. Chen, 378 F.3d 151, 163 (2d Cir.2004) (internal quotation marks omitted). That is not this case.

As to the 1992 receivership of investor fund Avellino & Bienes, Count Eleven charged Bonventre with knowingly causing the Firm’s general ledger falsely to reflect payment to the receiver from Firm assets instead of proceeds from loans collateral-ized by its clients’ securities. Counts Ten and Thirteen alleged that Bonventre not only knowingly created documents falsely showing that BLMIS had executed trades with European counterparties to frustrate SEC reviews, but also that Bonventre caused those documents to reflect the same trades with American counterparties, thereby frustrating reviews by European accountants during the same period. Regarding the Firm’s 2005-06 liquidity crisis, Counts Nine and Twelve charged Bonven-tre with knowingly causing the Firm’s general ledger falsely to reflect that four specific wire transfers were used to purchase assets, when, in fact, they were used to satisfy clients’ requests for withdrawals. Finally, Count Fourteen alleged that Bon-ventre knowingly underreported $299 million of BLMIS liabilities in a FOCUS report filed with the SEC on May 22, 2006.

These pleadings present none of the concerns identified in United States v. Davidoff 845 F.2d 1151, 1154 (2d Cir.1988) (noting indictment alleged extortion aimed at one company while trial evidence showed extortion aimed at different companies), and United States v. Bortnovsky, 820 F.2d 572, 574-75 (2d Cir.1987) (noting indictment alleged merely that defendants submitted false claims for burglary and fire loss, without specifying dates of staged burglaries or which of “some 4,000 documents” were fraudulent), on which Bon-ventre relies.

Nor did the volume of discovery warrant particulars. To the contrary, the district court adequately addressed that concern by ordering early identification of prosecution exhibits and the defendants to whom they pertained. See United States v. Rigas, 490 F.3d 208, 237 (2d Cir.2007) (recognizing that bill of particulars enables trial preparation and prevents surprise); United States v. Chen, 378 F.3d at 163 (explaining'that particulars are unnecessary where government has made sufficient disclosures of evidence and witnesses by other means).

Bonventre also was not prejudiced by the government’s failure to particularize whether he was charged with knowingly participating in Bernard MadofPs Ponzi scheme — as opposed to securities fraud generally — because such knowledge was not a required element of the charged crimes.

Accordingly, the denial of particulars manifests no abuse of discretion. See United States v. Chen, 378 F.3d at 163 (stating standard of review).

2. Joinder of Charges and Defendants

a. Joinder of Tax Fraud Charges

Crupi and Bonventre argue that certain tax fraud charges should have been severed as insufficiently related to the securities fraud.perpetrated at the Firm. See Fed.R.Crim.P. 14(a). Under Fed. R.Crim.P. 8, which governs joinder of offenses and defendants in criminal trials, tax counts can properly be joined with non-tax counts where the revenue at issue “arose directly” from the latter crimes, or when one scheme “stemmed” from the other, such that proof of one is “indispensable for a full understanding of the other,” United States v. Turoff, 853 F.2d 1037, 1043-44 (2d Cir.1988). Applying these standards de novo, we identify no joinder error compelling, severance. See United States v. Rittweger, 524 F.3d 171, 177 (2d Cir.2008).

According to the indictment, Crupi’s-misuse of a corporate credit card was one of the means by which Madoff financially rewarded her participation in the securities fraud. Moreover, insofar as the Firm’s legitimate operations did not generate sufficient revenue to meet its expenses by 2002, Crupi’s use of a BLMIS card to pay personal charges from 2004-08 resulted in her receipt of unreported income representing “funds derived from non-tax violations.” United States v. Turoff, 853 F.2d at 1043. United States v. Halper, on which Crupi relies, is distinguishable because the government there conceded that sums charged in an income-tax evasion indictment were not the same as those at issue in a Medicaid fraud. See 590 F.2d 422, 429 (2d Cir.1978).

Insofar as Bonventre argues that “neither the evidence accessible to the district court before trial, nor the proof at trial itself, established that the two categories of crimes [he committed] were somehow interdependent,” Bonventre Br. 100, the argument fails because the propriety of joinder turns on what is alleged in the indictment, not on evidence later adduced. See United States v. Rittweger, 524 F.3d at 178 & n. 3. The indictment here alleged that, in carrying out tax offenses, Bonven-tre utilized the same methods — backdated trades and fictitious records to generate “profits” and “losses” in investment accounts — that were central to the Firm’s securities fraud. Joinder was, therefore, proper because Bonventre’s tax fraud “hinged on” the same activities taken to advance the, securities fraud. United States v. Turoff, 853 F.2d at 1044; cf. United States v. Litwok, 678 F.3d 208, 217 (2d Cir.2012) (identifying “no evidentiary overlap” between alleged tax violation and fraudulent insurance claim); United States v. Shellef, 507 F.3d 82, 99 (2d Cir.2007) (noting that alleged tax violations predated alleged wire fraud conspiracy).

Nor has Bonventre carried the “heavy burden” of showing that the failure to sever the tax counts caused prejudice so severe as to result in “a miscarriage of justice.” United States v. Rittweger, 524 F.3d at 179. Bonventre’s argument — that his knowing involvement in the securities counts was rendered more plausible by unrelated conduct alleged in the tax counts — is undermined by indictment allegations that he engaged in identical fraudulent conduct to commit both crimes. Accordingly, the district court did not abuse its “virtually unreviewable” discretion by denying severance, id. (internal quotation marks omitted), particularly in light of its repeated limiting instructions, see J.A. 10850, 11930.

b. Pre-Trial Motion To Sever O’Hara and Perez

O’Hara and Perez argue that the failure to grant them severance precluded a reliable jury determination of guilt because they were “mid-level technical workers with narrow roles,” and other defendants had worked at BLMIS for “much longer periods,” exercised management roles, had direct client contact, used corporate charge cards, and received “significantly higher” compensation. O’Hara Br. 92-93. Yet “differing levels of culpability and proof are inevitable in any multi-de-fendant trial and, standing alone, are insufficient grounds for separate trials.” United States v. Spinelli, 352 F.3d 48, 55 (2d Cir.2003) (alteration and internal quotation marks omitted). In any event, the indictment alleged — and trial record established — that O’Hara and Perez, who were each employed by the Firm for approximately two decades, were integral members of the securities fraud conspiracy insofar as they created multiple computer programs falsely documenting nonexistent transactions, thereby deceiving regulators and auditors and enabling Madoff to perpetuate the fraud without discovery. See also id. at 55 (deeming joint trials particularly appropriate where defendants are charged with participation in same criminal conspiracy). O’Hara’s claim that separate trials would have avoided prejudicial spillover fails because he and Perez collaborated with co-conspirators Crupi, Bonven-tre, Enrica Cotellessa-Pitz, and Frank DiPascali, requiring much the same evidence whether their trials were severed or not. See id. at 55-56. Under these circumstances, and in light of the federal preference for joint trials of co-conspirators and the district court’s careful limiting instructions, see, e.g., United States v. O’Connor, 650 F.3d 839, 858 (2d Cir.2011), we identify no abuse of discretion in the denial of pretrial severance.

c. O’Hara’s Mid-Trial Severance Motion

O’Hara asserts that a mid-trial severance motion should have been granted because of the admission of a modified version of Perez’s inculpatory statement. We review challenged evidentiary rulings for abuse of discretion, see United States v. Kaplan, 490 F.3d 110, 120 (2d Cir.2007), which we do not identify here.

Not only did Perez’s modified statement not reference O’Hara, but the district court also instructed the jury that the statement was admitted only against Perez. See J.A. 1060. O’Hara’s assertion that these factors should not be determinative is at odds with the very case on which he relies. See United States v. Gomez, 617 F.3d 88, 92 (2d Cir.2010) (observing that main import of challenged hearsay was its impermissible inculpatory identification of defendant).

Accordingly, O’Hara’s argument for mid-trial severance also fails on the merits.

.3. Brady/Giglio Claim

Perez argues that the government violated Brady v. Maryland, 373 U.S. 83, 83 S.Ct. 1194, 10 L.Ed.2d 215 (1963), and Giglio v. United States, 405 U.S. 150, 92 S.Ct. 763, 31 L.Ed.2d 104 (1972), by failing to disclose a summary of its interview with retired FBI Agent Keith Kelly, in which Kelly described a prior statement by Matthew Cohen. To prevail on this claim, Perez must demonstrate the undisclosed statement’s materiality. See Kyles v. Whitley, 514 U.S. 419, 434, 115 S.Ct. 1555, 131 L.Ed.2d 490 (1995) (stating that withheld evidence is “material” if there is “reasonable probability’ that disclosure would have'resulted in different outcome (internal quotation marks omitted)); see also Wearry v. Cain, — U.S.-, 136 S.Ct. 1002, 1006, 194 L.Ed.2d 78 (2016). On de novo review, see United States v. Mahaffy, 693 F.3d 113, 127 (2d Cir.2012) (according trial judge’s factual conclusions as to effect of nondisclosure great weight, but determining materiality de novo), we conclude that Perez fails to carry his burden.

Perez argues that Kelly’s statement is both exculpatory and impeaching because Cohen does not therein state that Perez accepted compensation notwithstanding his discomfort in doing so. Perez contends that the absence of this detail suggests that he was comfortable writing the programs at issue, which is consistent with the defense theory that he was duped by Madoff and DiPascali and, therefore, lacked criminal intent. This possibility, which is hardly the only interpretation of the undisclosed statement, is not enough “ ‘to put the whole case in such a different light as to undermine confidence in the verdict.’ ” Id. (quoting Youngblood v. West Virginia, 547 U.S. 867, 870, 126 S.Ct. 2188, 165 L.Ed.2d 269 (2006)). This is particularly so given other more significant impeachment of Cohen’s credibility, such as FBI Agent Paul Takla’s testimony that Cohen himself had earlier relayed a version of events- somewhat different from that testified to at trial. Cf. United States v. Spinelli, 551 F.3d 159, 165 (2d Cir.2008) (“[I]f the information withheld is merely cumulative of equally impeaching evidence introduced at trial, so that it would not have materially increased the jury’s likelihood of discrediting the witness, it is not material.”).

More importantly, Cohen’s trial testimony was corroborated by other evidence of Perez’s guilty knowledge, notably, the September 13, 2006 handwritten letter that Perez himself produced to the government, in which he acknowledged telling DiPascali of “my unwillingness to work on projects which I am uncomfortable with.” J.A. 12288; see id. at 10830. DiPascali, a cooperating witness, also testified that, in 2006, Perez — along with O’Hara — confronted Madoff and expressed their discomfort working on computer programming for the investment advisory (“IA”) business, but ultimately accepted compensation for continuing to do certain aspects of this work. See id, at 5519-28.

Under these circumstances, we identify no error in the denial of Rule 33 relief on Brady/Giglio grounds.

4. Sufficiency of the Evidence

O’Hara, Perez, Bongiorno, and Crupi each challenge the sufficiency of the evidence supporting certain of their convictions. Although we review such claims de novo, defendants bear “a very heavy burden,” United States v. Abur-Jihaad, 630 F.3d 102, 135 (2d Cir.2010) (internal quotation marks omitted), because the standard of review is “exceedingly deferential,” United States v. Brock, 789 F.3d 60, 63 (2d Cir.2015) (internal quotation marks omitted). We must affirm if, viewing the evidence in the light most favorable to the government, “any rational trier of fact could have found the essential elements of the crime beyond a reasonable doubt.” Jackson v. Virginia, 443 U.S. 307, 319, 99 S.Ct. 2781, 61 L.Ed.2d 560 (1979) (emphasis in original); accord United States v. Binday, 804 F.3d 558, 572 (2d Cir.2015).

a. ' Securities Fraud Convictions of O’Hara and Perez

O’Hara, joined by Perez, argues that, notwithstanding their extensive and undisputed involvement in the work of the fraudulent IA business, evidence of their criminal intent was in equipoise and, thus, legally insufficient to sustain any of their convictions. See O’Hara Br. 53-54 (citing, inter alia, United States v. Glenn, 312 F.3d 58, 70 (2d Cir.2002)). The argument fails because trial evidence was not in equipoise but tilted decidedly in favor of a finding of culpable mens rea.

O’Hara and Perez (1) designed computer programs that created books-and records filled with randomly generated numbers in order to deceive regulators and clients; (2) became so uncomfortable with their work that, by 2006, they feared for their jobs, families, and lives, see J.A. 12286, 12288; see also id. at 10830; (3) unsuccessfully urged Madoff to shut down the IA business, see id, at 5519-23; (4) accepted additional compensation and continued programming for the IA business, even after expressing their discomfort, see id. at 5527-29; (5) deleted from the server “special programs” they had created to produce fictitious material for SEC and KPMG audits, see id. at 5528-29, 8209-10; and (6) implicitly advised a colleague to close his IA account, see id. at 7374-76. This was sufficient to allow a reasonable juror to infer both defendants’ awareness of the fraud and their intent that it succeed. See, e.g., United States v. Singh, 390 F.3d 168, 188 (2d Cir.2004) (recognizing that proof of fraudulent intent is often circumstantial rather than direct); United States v. Panza, 750 F.2d 1141, 1150 (2d Cir.1984) (holding that -jury reasonably could infer from number of “red flags” to which defendant was exposed that he knew he was participating in fraudulent scheme, even though he may not have known all details).

To the extent O’Hara invites this court to re-weigh evidence, draw inferences in his favor, or re-assess credibility, see O’Hara Br. 57-58, the jury verdict precludes such undertakings. See United States v. Binday, 804 F.3d at 572.

b. Tax Evasion Convictions of Crupi and Bongiorno

Crupi and Bongiorno challenge the sufficiency of their tax evasion convictions, see 26 U.S.C. § 7201, insofar as they were found liable for a “substantial tax debt.” United States v. Coplan, 703 F.3d 46, 66 (2d Cir.2012). Their challenges fail.

The government adduced evidence that, between 2003 and 2008, Crupi used a BLMIS credit card to pay over $288,000 in personal .expenses, which — for tax years 2004, 2007, and 2008 — resulted in more than $134,000 in unreported income and a $38,000 tax deficiency. Crupi argues that the American Express statements were insufficient to prove that the charges were, in fact, personal. But assuming, as we must, that the jury credited DiPascali’s testimony that it was not Crupi’s job to entertain clients, the personal nature of her charges could reasonably be inferred from: (1) the amount, vendor, and purchase location (often near Crupi’s home, as opposed to the Firm’s Manhattan office) of the non-travel expenses; and (2) the names of Crupi’s family members on many of the travel expenses. Nor, as Crupi insists without supporting authority, was the government required to prove a negative, i.e., that Crupi had not reimbursed BLMIS for her personal expenses. See United States v. Downing, 297 F.3d 52, 56-57 (2d Cir.2002) (refusing to overturn jury verdict merely because exculpatory account is “plausible,” because “the government need not disprove every possible hypothesis of innocence” (alteration and internal quotation marks omitted)).

Bongiorno’s challenge is equally meritless. The government presented the jury with evidence that she failed to report as taxable income $813,727 withdrawn, between 1994 and 2008, from the Firm’s “Special 1” and “Special 2” accounts via the Chase '703 account, resulting in a $239,334 tax deficiency. Bongiorno’s contention that the withdrawals were nontaxable capital and not taxable income fails because the jury, in convicting her of securities fraud, necessarily concluded that Bongiorno knew these accounts held no capital. Rather, every withdrawal was taxable income because it was effectively a theft of client funds from the Chase account. No different conclusion is warranted by the fact that the district court, for purposes of Guidelines calculation, assumed that Bongiorno had been convicted on a “conscious avoidance” theory. That theory “permits a finding of knowledge even where there is no evidence that the defendant possessed actual knowledge.” United States v. Svoboda, 347 F.3d 471, 477-78 (2d Cir.2003) (internal quotation marks omitted).

c. Crwpi’s Bank Fraud Conviction

Crupi argues that she could not have intended to commit bank fraud, or conspired to do so, see 18 U.S.C. §§ 1344, 1349, because she lacked access to full information about the value of David Ku-gel’s accounts and merely relied on Kugel’s own analysis. The argument fails because, even if Crupi lacked such access, the trial evidence showed that she independently fabricated information that she reported to lenders on the Kugel family’s behalf. Specifically, Crupi (1) reported account values that did not conform even to Kugel’s requested amounts; and, on one occasion, (2) provided Kugel with an entirely fictitious account statement. Moreover, to the extent Crupi relied on Kugel’s representations notwithstanding the verification documents’ warnings of “severe penalties” for any fraud or misrepresentation, J.A. 12295, 12301, 12302, the jury was entitled to consider this as consistent with fraudulent intent. Similarly, the jury could reasonably infer Crupi’s intent to defraud banks from her misrepresentation that Kugel’s account values had been verified independently by a depository, when she knew the information was supplied by Kugel, the mortgage applicant.

As for the materiality of her misrepresentations, Crupi provides no support for the counterintuitive proposition that a depository’s overstatement of a loan applicant’s assets by a multiple of 15 to facilitate a mortgage application is immaterial to the financial institution. In any event, the government adduced sufficient evidence for a reasonable jury to infer that Crupi’s misrepresentations had “a natural tendency to influence, or [were] capable of influencing,” the banks’ decisions. Neder v. United States, 527 U.S. 1, 16, 119 S.Ct. 1827, 144 L.Ed.2d 35 (1999). This included evidence of Crupi’s communications with mortgage company employees seeking verification and Kugel’s testimony about conversations with Crupi explaining that he “needed [the] letter” to obtain mortgages. J.A. 2330. United States v. Rigas, 490 F.3d 208 (2d Cir.2007), on which Crupi relies, is not to the contrary. In that “rather unusual bank fraud case,” id. at 234, we concluded that misstatements of a bank’s leverage ratios were not material because they were incapable of affecting the victim depository’s decision, which was limited by the terms of a specific loan agreement, see id. at 235 (noting that bank could only determine amount of interest to be charged, an objective decision cabined by ranges set in Co-Borrowing Agreements). By contrast, the evidence here demonstrated that Crupi’s misrepresentations were “reasonably likely to influence” the lenders’ subjective decisions regarding whether to extend a loan.

Accordingly, defendants’ sufficiency challenges fail on the merits.

5. Conscious Avoidance Instruction

Bonventre and Bongiorno challenge their securities fraud convictions, see 18 U.S.C. § 2,15 U.S.C. §§ 78j(b), 78ff; 17 C.F.R. § 240.10b-5, arguing that trial evidence did not provide a sufficient factual basis for a “conscious avoidance” instruction. A sufficient basis exists when the evidence “would permit a rational juror to conclude beyond a reasonable doubt that the defendant was aware of a high probability of the fact in dispute and consciously avoided confirming that fact.” United States v. Cuti, 720 F.3d 453, 463 (2d Cm. 2013) (internal quotation marks omitted); see also id. (reviewing this question de novo).

Bonventre argues that no such conclusion was possible here because the “red flags” identified by the government are suspicious only in hindsight. The argument is defeated by Bonventre’s own statement to AlixPartners employee Meghan Schmidt, who testified that Bonven-tre told her in December 2008 that he closed his IA account in 2006 because he had awoken “with a sick feeling in his stomach” and “had always questioned the consistent high returns that he earned on that account.” J.A. 1244. Nor are we persuaded by Bonventre’s insistence that his lack of actual knowledge resulted not from any “deliberate steps,” Bonventre Reply 8 (emphasis in original), but, rather, from DiPascali’s and Madoffs lies about the legitimacy of their work. “[A] defendant’s ‘purposeful contrivance’ to avoid knowledge may not manifest in an affirmative act because ‘the very nature of conscious avoidance makes it unlikely that the record will contain directly incriminating statements.’” United States v. Whitman, 555 Fed.Appx. 98, 105-06 (2d Cir.2014) (quoting United States v. Svoboda, 347 F.3d at 480, and United States v. Kozeny, 667 F.3d 122, 134 (2d Cir.2011)).

While Bongiorno argues that her (1) lack of formal education or training in securities, (2) transparent record-keeping, and (3) failure to liquidate her investment account before the Firm’s collapse manifest her ignorance of the fraud, these arguments were properly made to the jury in arguing that the government failed to prove knowledge even through conscious avoidance. They are not grounds for disallowing the instruction. Indeed, Bongior-no’s “purported lack of knowledge defense, despite [her] deep involvement in the transactions that effectuated the fraud, all but invited the conscious avoidance charge.” United States v. Cuti, 720 F.3d at 464. Notably, Bongiorno re-wrote three years’ worth of account statements for Avellino & Bienes in connection with the SEC’s 1992 investigation, replacing a transfer from another customer account with a purported dividend from General Motors. She also played a significant role in managing and organizing backdated trading in clients’ accounts and in her own, including retroactively selling Lehman Brothers stock after that firm declared bankruptcy. In light of this “overwhelmingly suspicious” behavior, a reasonable jury could have found that her professed ignorance was a “purposeful contrivance to avoid guilty knowledge.” United States v. Kozeny, 667 F.3d at 134 (internal quotation marks omitted).

Accordingly, defendants’ challenge to the conscious avoidance instruction is mer-itless.

6. Government Misconduct

Defendants assert that prosecutorial misconduct in addressing the jury warrants a new trial. To secure such relief, they must show misconduct “so severe and significant” as to deny a “fair trial.” United States v. Coplan, 703 F.3d 46, 86 (2d Cir.2012) (internal quotation marks omitted). Such cases are “rare,” United States v. Caracappa, 614 F.3d 30, 41 (2d Cir, 2010), and arise only when improper comments so infect the trial as a whole as to result in conviction violative of due process, see United States v. Truman, 688 F.3d 129, 144 (2d Cir.2012); United States v. Ferguson, 676 F.3d 260, 283 (2d Cir. 2011) (stating that improper comments do not deny due process “unless they constitute egregious misconduct” (internal quotation marks omitted)). In evaluating whether defendants have carried this burden, we consider (1) the severity of the misconduct, (2) the measures adopted to cure it, and (3) the certainty of conviction in the absence of the misconduct. See United States v. Coplan, 703 F.3d at 86. Applying these principles here, we conclude that they have not, substantially for the reasons stated by the able trial judge. See United States v. Bonventre, No. 10CR228-LTS, 2014 WL 3673550, at *12-17 (S.D.N.Y. July 24, 2014).

a. Opening Statement

O’Hara argues that the government’s opening statement misrepresented the evidence, inappropriately referred to defendants collectively, and bolstered the credibility of cooperating witnesses. In fact, the prosecution statements anticipating evidence fell within the “broad latitude” of reasonable inferences, United States v. Salameh, 152 F.3d 88, 138 (2d Cir.1998), and collective references, as defense counsel later acknowledged, were “inevitable and ... probably appropriate” in the context of the charged conspiracy, J.A. 11041.

As to bolstering, the government concedes that a prosecutor cannot reference the bolstering aspects of witnesses’ cooperation agreements during opening argument. See United States v. Certified Envtl. Servs., Inc., 753 F.3d 72, 86 (2d Cir.2014). However, any such error here, viewed in the context of the entire trial, was not so severe as to deny due process because not only did defense openings attack the credibility of prosecution witnesses, but also district court instructions ameliorated any prejudice.

b. Rebuttal Summation

Defendants advance a litany of objections to the prosecution’s rebuttal summation. In reviewing these objections, we are mindful both of the trial court’s criticism, see, e.g., United States v. Bonventre, 2014 WL 3673550, at *16 (characterizing many remarks in rebuttal summation as “ill-conceived and unworthy of the institutional stature of the United States Attorney’s Office”), and its ultimate rejection of defendants’ due process challenge in the context of (1) the “meticulous presentation” of incriminating evidence; (2) the totality of arguments made at trial; and (3) contemporaneous curative instructions, id. Having carefully reviewed the record, we identify no abuse of discretion in this conclusion. See United States v. Banki, 685 F.3d 99, 119-20 (2d Cir.2012) (identifying standard of review).

1. Seventy of Misconduct

The prosecution’s repeated characterization of defense arguments as “ridiculous” or “absurd,” e.g., J.A. 11750, 11751, was not improper. See United States v. Rivera, 971 F.2d 876, 884 (2d Cir.1992) (rejecting challenge to prosecution’s characterization of defense arguments as “ridiculous” because “prosecutor is not precluded from vigorous advocacy, or the use of colorful adjectives, in summation”); accord United States v. Farhane, 634 F.3d 127, 168 (2d Cir.2011). The disputed characterizations were directed to particular defense arguments and supported by specific record evidence. Thus, this case is not analogous to Floyd v. Meachum, 907 F.2d 347, 353-55 (2d Cir. 1990) (faulting prosecutor for characterizing non-testifying defendant as “liar” more than 40 times, improperly referencing Fifth Amendment, and inviting jury to assess her own personal integrity and professional ethics), or to United States v. Drummond, 481 F.2d 62, 63-64 (2d Cir. 1973) (faulting prosecutor who dismissed defense arguments as “preposterous” for improperly interjecting his beliefs and his own credibility into case and misrepresenting trial testimony).

While defendants assert that the prosecution here repeatedly mischaraeter-ized the record, the district court reasonably concluded that, in most instances, the challenged arguments represented fair — if aggressive — inferences that the jury was entitled to draw from the evidence. See, e.g., United States v. Salameh, 152 F.3d at 138 (concluding that government had not misrepresented evidence by arguing for inference that, even if not grounded in direct evidence, did not exceed its “broad latitude to suggest reasonable inferences”). Defendants were entitled to — and, in fact, did — argue for opposing inferences on the basis of the same evidence. See, e.g., J.A. 11435. That defendants disagree with the strength of the government’s inferences does not establish prosecutorial misconduct. See generally United States v. Wilner, 523 F.2d 68, 74 (2d Cir.1975) (“A prosecuting attorney is not an automaton whose role on summation is limited to parroting fact already before the jury.”).

To the extent some of the prosecution’s rebuttal arguments created unnecessary evidentiary ambiguity, we make some allowance for the fact that rebuttal summations are “not detached expositions .... carefully constructed before the event.” United States v. Farhane, 634 F.3d at 167 (alterations, citation, and internal quotation marks omitted). In any event, the concern was adequately addressed by the district court’s instructions that only the jury’s own recollection of the evidence controlled. .

Defendants’ claims of improper vouching fail because prosecutors are permitted vigorously to argue for their witnesses’ credibility so long as they do not interject their own credibility into the case, see United States v. Rivera, 971 F.2d at 884, or imply the existence of extraneous proof, see United States v. Bagaric, 706 F.2d 42, 61 (2d Cir.1983). As the district court reasonably concluded, neither occurred here. Defense counsel not only repeatedly characterized DiPascali’s. testimony as “lies,” but also accused prosecutors of orchestrating perjury among the cooperating witnesses. The law is clear: “the government is allowed to respond to an argument that impugns its integrity or the integrity of its case, and when the defense counsel have attacked the prosecutor’s credibility or the credibility of the government agents, the prosecutor is entitled to reply with rebutting language suitable to the occasion.” United States v. Carr, 424 F.3d 213, 227 (2d Cir.2005) (internal quotation marks omitted).

The same reasoning applies to defendants’ claim that the prosecutor imper-missibly “cast himself as an expert witness on crime and criminals.” Crupi Br. 39. Viewed in context, most of the comments were permissible appeals to jurors’ common sense in response to' defense arguments. See United States v. Huezo, 546 F.3d 174, 182 (2d Cir.2008) (“[JJurors are entitled, and routinely encouraged, to rely on their common sense and experience in drawing inferences.”); see also United States v. Anderson, 747 F.3d 51, 70 .(2d Cir.2014). To the extent the prosecution went further, the district court’s actions sustaining objections and giving curative instructions adequately safeguarded against prejudice.

The government’s use of analogies to enable jurors unfamiliar with securities trading to evaluate evidence in the context of “more accessible” crimes was not a model of advocacy. J.A. 11849. But the government is not barred from using such rhetorical devices so as to require a new trial here. See United States v. LaMorte, 950 F.2d 80, 85 (2d Cir.1991) (concluding that reference to bomb exploding on airplane, in context of prosecution for marijuana distribution, did not deny defendant fair trial).

The same conclusion obtains for prosecution references to fictional works. These remarks, made only briefly and in passing, encouraged the jury to apply its common sense in determining whether participants in criminal conspiracies were likely to lie to one another. See J.A. 11820-21. Indeed, defense counsel also referenced popular culture in appealing to jurors’ experience. In any event, the district court’s prompt and appropriate curative instruction adequately ensured against prejudice. See id. at 11821.

Finally, the prosecutor’s reference to Constance Baker Motley was, as the district court observed, “at best ambiguous and at worst unfathomable.” United States v. Bonventre, 2014 WL 3673550, at *16; see J.A. 11917. Nevertheless, the record does not admit the inference urged by defendants, that is, that the prosecution was appealing to racial bias. Rather, the government appears to have attempted to respond — somewhat opaquely — to defendants’ own curious historical analogies. While the prosecutor’s choice of subject was peculiar, and his rhetoric needlessly grandiose, it did not constitute severe misconduct. See United States v. Farhane, 634 F.3d at 167.

2. Substantial Prejudice

Defendants maintain that even if no individual prosecution argument manifested severe misconduct, the cumulative effect of the challenged remarks was so prejudicial as to deny due process. We identify no abuse of discretion in the district court’s rejection of this argument in light of (1) the trial judge’s prompt, frequent, and apt jury instructions; and (2) compelling trial evidence of each defendant’s guilt, which included (a) testimony from five cooperating witnesses who directly inculpated defendants in the securities fraud, (b) defendants’ own verbal and written statements manifesting their guilty knowledge, and (c) voluminous financial and computer records demonstrating the brazen nature of the fraud in which defendants had engaged. Accordingly, the strength of the evidence here indicates that the same result would have obtained, even without the purported government misconduct.

In sum, while it properly faulted aspects of the government’s rebuttal summation, the district court acted within its discretion in concluding that this is not one of the “rare cases” in which defendants have demonstrated that they were denied due process so as to require a new trial.

7. Forfeiture Order

O’Hara and Perez challenge the $19,707,987,337.00 forfeiture order, an amount representing the total client investment in the Firm’s IA business after January 1, 2006 — the point at which the district court found these defendants to have joined the securities fraud conspiracy. See 18 U.S.C. §§ 981(a)(1)(C), 1956(c)(7)(A), 1961(1); 28 U.S.C. § 2461(c). In evaluating this challenge, we review the district court’s legal conclusions de novo and its factual findings for clear error. See United States v. Sabhnani, 599 F.3d 215, 261 (2d Cir.2010).

O’Hara faults the district court for imposing forfeiture of gross, as opposed to “net,” proceeds under 18 U.S.C. § 981(a)(2). The argument fails because the evidence showed that the criminal conspiracy at issue did not sell or provide “lawful services ... in an illegal manner” so as to require deduction of direct costs. Id. § 981(a)(2)(B); see also In re Rothstein, Rosenfeldt, Adler, P.A., 717 F.3d 1205, 1212 (11th Cir.2013) (observing that, under § 981(a)(2)(A), “whatever money” defendant obtained through Ponzi scheme was forfeitable as “proceeds” of offense). Even if the Firm had provided lawful services, there were no direct costs to deduct because BLMIS never purchased any securities on behalf of its IA clients in exchange for their investments, and the forfeiture statute excludes “any part of the overhead expenses of the entity” from the meaning of “direct costs.” 18 U.S.C. § 981(a)(2)(B); see also id. (stating that defendant has burden of proof of direct costs). Accordingly, the district court correctly ordered forfeiture based on the gross proceeds generated by defendants’ fraudulent scheme.

O’Hara also faults the district court for failing to exclude “massive” deposits from what he contends was a separate check-kiting scheme that was the basis for a deferred prosecution agreement (“DPA”) between the government and JPMorgan Chase (“JPMorgan”) in a related action. O’Hara Br. 100. The argument fails because the district court limited O’Hara’s forfeiture order to client investments in the IA business after January 1, 2006, and, as O’Hara has acknowledged,the purported check-kiting scheme ceased operating in 2003. See also DPA, Ex. C ¶27, United States v. JPMorgan Chase Bank, N.A., No. 14 Cr. 007(PKC). In any event, the DPA states only that the- transactions in question “appeared to be a ‘check-kiting’ scheme” to the bank. Id. ¶25. The government adduced evidence, however, that these deposits facilitated the charged securities fraud, as they were reflected in Crupi’s records of the Firm’s IA account activity, recordkeeping in which O’Hara was also involved. See Appellee Br. 235.

O’Hara argues that the challenged forfeiture also violates the Eighth Amendment’s proscription of excessive fines. See United States v. George, 779 F.3d 113, 122 (2d Cir.2015) (stating that criminal forfeiture is unconstitutionally excessive if it is “grossly disproportional” to gravity of defendant’s offense (internal quotation marks omitted)). To assess gross disproportion-ality, we consider all relevant factors, including (1) the essence of defendant’s crime and its relation to other criminal activity, (2) whether defendant fits into the class of persons for whom the statute of conviction was principally designed, (3) the maximum sentence and fíne that could have been imposed, and (4) the nature of harm caused by defendant’s conduct. See id.; see also United States v. Viloski, 814 F.3d 104, 110-11 (2d Cir.2016) (holding that four-factor test is not exhaustive). We conclude that the ordered forfeiture, while monumental, was not “grossly disproportional” to the gravity of the crimes of conviction.

. While O’Hara contends that he was “several steps removed from the heart of the fraud,” O’Hara Br. 102, the district court did not clearly err in finding to the contrary because O’Hara’s “special programming” work was “the essential backbone of the infrastructure through which the IA fraud was perpetrated,” J.A. 13350, and O’Hara himself altered general ledger and securities records and knowingly and deliberately prepared falsified documents for SEC and client audits, see id. at 13351. As for O’Hara’s claim that the securities fraud statute does not target “computer programmers or other technical workers whose specialized services [are] needed to carry out the core fraud,” O’Hara Br. 102, the district court reasonably concluded that O’Hara was no mere “technical worker,” but a vital member of the conspiracy. Moreover, insofar as the statute focuses on knowing misrepresentation of material facts to defraud investors, see, e.g., United States v. Nouri, 711 F.3d 129, 141-42 & n. 3 (2d Cir.2013), O’Hara’s special-programming work falls squarely within its reach because the only purpose of that programming was to effect misrepresentations efficiently. Indeed, without the programming, the fraudulent scheme could not have been sustained.

Because O’Hara faced a maximum prison sentence of 100 years — effectively a life sentence — the challenged forfeiture cannot be deemed disproportional notwithstanding the statutory maximum fine of $10 million. See United States v. Varrone, 554 F.3d 327, 333 n. 4 (2d Cir.2009) (stating that forfeiture in excess of maximum fine “is not necessarily constitutionally excessive”; ultimate question is.how forfeiture amount compares to “gravity of the defendant’s offense” (internal quotation marks omitted)). Where, as here, forfeiture ordered is in an amount equivalent to the undisputed, actual proceeds of the fraud (from the point O’Hara understood the criminal nature of his actions), we cannot conclude that the order was grossly disproportional to the gravity of his offense.

As to the fourth factor, the nature of the harm caused by defendants’ conduct, as the district court observed, was “financial devastation of unprecedented magnitude” resulting in confidence in securities institutions and regulatory agencies being eroded and thousands of “innocent lives [being] irreversibly upended.” J.A. 13204, 13352. This assessment was not erroneous, much. less clearly so. Further, although the district court recognized that O’Hara’s participation in the fraud was “more limited” and “less enthusiastic” than that of certain confederates, id. at 13351, it found his role essential to a scheme that even defense counsel described as “the greatest fraud in American history,” id. at 11388. For that reason, O’Hara’s comparison to the $1.7 billion forfeiture judgment paid by JPMor-gan under its DPA is inapt. JPMorgan agreed to pay that amount in exchange for a deferral of prosecution in connection with its failure to detect the fraud. By contrast, O’Hara was convicted at trial of actively perpetrating the fraud by creating the deceitful records that effectively concealed it from detection for so long.

Accordingly, we reject O’Hara’s Eighth Amendment challenge.

8. Conclusion

We have considered defendants’ remaining arguments and conclude that they are without merit. Accordingly, the district court’s judgments are AFFIRMED. 
      
      . Although the parties appear to agree that Rule 8(b) — and not Rule 8(a) — governs join-der of offenses in multi-defendant trials, we have yet to resolve the matter. See United States v. Shellef, 507 F.3d 82, 97 n. 12 (2d Cir.2007). Nor must we do so here, insofar as joinder was proper under either standard.
     
      
      . The statement originally indicated that Perez told Matthew Cohen that Madoff "had asked the programmers to create certain computer programs that made them uncomfortable, and had paid them $100,000” for doing so. J.A. 12732 (emphasis added). At trial, it was modified so that Cohen testified as follows:
      I asked Mr. Perez what led to him opening and then subsequently closing this account. He told me that Mr. Madoff had asked him to make some changes to one of the AS/400 programs in order to modify statements that had already been printed and sent to a customer. He told me that he was uncomfortable doing this and that he had told Mr. Madoff that, and Mr. Madoff had said, I’ll give you some money, just do it, and he did.
      
        Id. at 1089 (emphasis added).
     
      
      . O’Hara's assertion that the government "used Cohen's testimony to argue that there was a direct bearing on [his] guilt,” O’Hara Reply 36-37 (citing J.A. 11760-61, 11772, 11827-28), is betrayed by the record O’Hara cites, which reflects the prosecutor’s discussion of the letter O’Hara wrote to his brother. See id. at 12286.
     
      
      . Insofar as O’Hara asserts a Confrontation Clause challenge to Perez's modified statement, we decline to consider an argument advanced only in a footnote or reply brief. See O’Hara Br. 89 n. 7; O’Hara Reply 29-34; see, e.g., United States v. Svoboda, 347 F.3d 471, 480 (2d Cir.2003) (regarding footnote); United States v. Yousef, 327 F.3d 56, 115 (2d Cir.2003) (regarding reply brief). In any event, the challenge is meritless because Perez’s statement was modified, consistent with Bruton and its progeny, to remove any reference to another programmer. Cf. United States v. Jass, 569 F.3d 47, 60 (2d Cir.2009) ("[T]he Supreme Court’s Confrontation Clause concern has been with juries learning that a declarant defendant specifically identified a co-defendant as an accomplice in the charged crime.”). It is therefore irrelevant that other trial evidence implicated O’Hara in Perez’s conduct. See id. at 61. Further, while O’Hara asserts that the jurors could not-follow the district court’s limiting instruction, his failure to demonstrate an "overwhelming probability of their inability to do so” defeats his challenge. Id. at 60 (emphasis in original) (internal quotation marks omitted).
     
      
      . Kelly's statement indicated, in relevant part, that "COHEN told KELLY about a conversation COHÉN had with GEORGE PEREZ, in which PEREZ indicated to COHEN that PEREZ had received compensation, whether in the form of cash or a deposit to PEREZ’s investment advisory account, in exchange for writing certain computer programs.” Suppl. App. 145. Meanwhile, Cohen testified:
      I asked Mr. Perez what led to him opening and then subsequently closing this account. He told me that Mr. Madoff had asked him to make some changes to one of the AS/400' programs in order to modify statements that had already been printed and sent to a customer. He told me that he was uncomfortable doing this and that he had told Mr. Madoff that, and Mr. Madoff had said, I’ll give you some money, just do it, and he did.
      J.A. 1089.
     
      
      . According to Takla’s notes, in April 2011 Cohen told the FBI that Perez had reported Madoff asking for changes to the system, which Perez declined to make “because he felt uncomfortable,” whereupon Madoff responded that “if Perez was not comfortable with making changes, then Perez should not do it.” J.A. 10745.
     
      
      . The jury also heard evidence that, after the Firm’s collapse, (1) O’Hara told a colleague to delay responding to investigators’ requests, and seemed upset to learn that the colleague had discussed with investigators a program that had helped perpetrate the fraud, see id. at 8706-07; and (2) Perez told Matthew Cohen, an attorney responsible for the BLMIS Trustee’s discovery and data preservation efforts, that Madoff had paid Perez to continue programming for the IA business after Perez told Madoff that he was uncomfortable doing so, see id. at 1089.
     
      
      . These included approximately $40,000 on wine purchases in New Jersey and $5,000 on pet care.
     
      
      . Bongiorno does not assert a sufficiency challenge to those convictions.
     
      
      . For example, on one occasion Crupi swore that the value of Kugel's IA account was nearly $6 million, when Firm "records” indicated it was approximately $300,000 to $400,000. See J.A. 2332.
     
      
      . Neither defendant takes issue with the substance of the instruction. Thus, insofar as Bonventre contends that the jury could have convicted him on the basis of negligence or recklessness, there is no reason to suspect that the jury ignored the district court’s explicit instruction to the contrary. See J.A. 10934.
     
      
      . None of the Assistant United States Attorneys representing the government on this appeal are the prosecutors whose remarks are at issue.
     
      
      . Indeed, O’Hara did not object on these grounds below,
     
      
      . The government's claim that O’Hara’s counsel characterized a 2006 letter as an ”act[] of courage” misstated the record, J.A. 11828; the act of courage referenced was O’Hara’s confrontation with his supervisors. See id. at 11232. In the same breath, however, O’Hara’s counsel asserted that deleting "special programs” in 2006 "was even more courageous,” id., and the government was entitled to challenge that characterization. Insofar as the government’s rebuttál — which followed several days of defense arguments— misidentified the precise conduct to which counsel had referred, this error was hardly severe given the district court’s immediate correction.
     
      
      . Forfeiture judgments of varying amounts were imposed jointly and severally against all defendants on the basis of convictions on Counts One through Three (securities and accounting fraud), and Counts Six through Eleven (falsifying records of broker-dealer and investment adviser).
     
      
      . To the extent O’Hara challenges the forfeiture of gross proceeds because neither he nor Perez had any contact with BLMIS clients, or because his participation was limited to writing computer programs, he misunderstands the district court’s preponderance finding. See United States v. Contorinis, 692 F.3d 136, 147 (2d Cir.2012) (holding that court may order defendant to forfeit proceeds received by others who participated jointly in crime "provided the actions generating those proceeds were reasonably foreseeable to the defendant"). We identify no clear error in the district court’s determination that clients’ investments were reasonably foreseeable to O'Hara.
     
      
      . Consequently, we need not address the government’s argument that the Excessive Fines Clause does not apply to forfeiture of the gross proceeds of crimes. Cf. United States v. Viloski, 814 F.3d at 109 n. 7 (casting doubt on this argument).
     
      
      . None of the defendants requested that the amount of forfeiture be submitted to the jury, see J.A. 12129, and, therefore, the district court was limited to a $10 million fine. See United States v. Pfaff, 619 F.3d 172, 175 (2d Cir.2010). In any event, defendants do not dispute the forfeiture calculation as a factual matter.
     