
    UNITED STATES, Appellee, v. Alberto VILAR and Gary Alan Tanaka, Defendants-Appellants.
    Docket Nos. 10-521-cr(L), 10-580-cr(CON), 10-4639-cr(CON).
    United States Court of Appeals, Second Circuit.
    Argued: Aug. 21, 2012.
    Decided: Aug. 30, 2013.
    
      Vivian Shevitz, Jane Simkin Smith (Susan C. Wolfe, Joanna Eftichyiou, on the brief), Brooklyn, NY, for Alberto Vilar.
    Alan Dershowitz (Victoria B. Eiger, Nathan Z. Dershowitz, Dershowitz, Eiger & Adelson, P.C., New York, NY, on the brief), Cambridge, MA, for Gary Alan Ta-naka.
    Benjamin A. Naftalis, Justin Anderson (Sarah E. Paul, Katherine Polk Failla, on the brief), Assistant United States Attorneys, for Preet Bharara, United States Attorney for the Southern District of New York, New York, NY, for the United States.
    Before: NEWMAN, CABRANES, and STRAUB, Circuit Judges.
   JOSÉ A. CABRANES, Circuit Judge.

Alberto Vilar and Gary Alan Tanaka appeal their judgments of conviction, entered on February 8, 2010, and February 10, 2010, respectively, in the United States District Court for the Southern District of New York (Richard J. Sullivan, Judge.) In simple terms, a jury found that Vilar and Tanaka lied to clients about the nature and quality of certain investments. This appeal raises a number of substantial issues, including a question left open after the Supreme Court’s decision in Morrison v. National Australia Bank Ltd., 561 U.S. 247, 130 S.Ct. 2869, 177 L.Ed.2d 535 (2010): whether criminal liability under Section 10(b) of the Securities Exchange Act of 1934 (“Section 10(b)”) extends to conduct in connection with an extraterritorial purchase or sale of securities.

We conclude as follows. First, Section 10(b) and its implementing regulation, Rule 10b-5, do not apply to extraterritorial conduct, regardless of whether liability is sought criminally or civilly. Accordingly, a defendant may be convicted of securities fraud under Section 10(b) and Rule 10b-5 only if he has engaged in fraud in connection with (1) a security listed on a U.S. exchange, or (2) a security purchased or sold in the United States. Although the District Court did not require proof of domestic securities transactions in this case, this error was not “plain” since it did not affect the outcome of the proceedings, and therefore did not affect Vilar and Ta-naka’s substantial rights.

Second, when proceeding criminally or civilly under Section 10(b) or Rule 10b-5, the government need not prove that the victims of a fraudulent scheme actually relied on the alleged material misrepresentations or omissions. Because reliance is not an element of a Section 10(b) offense, the District Court did not err by not instructing the jury on the issue of reliance.

Third, although the mail fraud charge in the indictment specified that the mailing itself was false or fraudulent, the District Court’s instruction permitting the jury to convict the defendants based on a mailing that itself contained no false or fraudulent statement did not “constructively amend” the indictment.

Fourth, on remand, the District Court must decide what acts constitute the offense conduct for the purposes of calculating the appropriate loss amount at sentencing, and re-determine the amount of money subject to forfeiture. Further, the District Court must, in accordance with the Mandatory Victim Restitution Act, limit its restitution order to victims of the scheme who purchased securities domestically.

Fifth, with the exception of Vilar’s ineffective assistance of counsel claim, which we do not reach, Vilar and Tanaka’s remaining claims are without merit. '

BACKGROUND

It is fair to say that, from the mid-1980s until their arrest in 2005, Vilar and Tanaka were prominent investment managers and advisers. Prior to the technology market crash of 2000-2001, they were responsible for managing approximately $9 billion in investments for their clients.

Vilar and Tanaka managed their clients’ assets through a number of different funds and entities. In 1986, they founded and became the sole shareholders of Amerindo Investment Advisors Inc. (“Amerindo U.S.”), an investment adviser registered with the Securities and Exchange Commission (“SEC”). Amerindo U.S. was a California corporation with principal offices in San Francisco and New York City. Vilar and Tanaka also founded and were the sole shareholders of (1) Amerindo Investment Advisors, Inc. (“Amerindo Panama”), a corporation organized under the laws of the Republic of Panama that managed an off-shore investment fund offered to U.S. investors, and (2) Amerindo Investment Advisors (UK) Ltd. (“Amerindo U.K.”), a United Kingdom corporation, which managed portfolios of U.S. emerging growth stocks for U.K.-based clients.

From at least July 1986 until May 2005, Vilar and Tanaka offered clients the opportunity to invest in “Guaranteed Fixed Rate Deposit Accounts” (“GFRDAs”). The GFRDA program was made available only to a select group of individual clients, who were generally close friends or family members of Vilar or Tanaka. Vilar and Tanaka promised investors in the GFRDA program that they would receive a high, fixed rate of interest over a set term, and that the overwhelming majority of the GFRDA funds would be invested in high-quality, short-term deposits, including U.S. Treasury bills. The balance of the capital in the GFRDAs—generally no more than twenty-five percent—was to be invested in publicly traded emerging growth stocks.

Despite Vilar and Tanaka’s description of the GFRDA program, they invested all of the funds in technology and biotechnology stocks, presumably in the hopes of meeting or even exceeding the high “guaranteed” rates of return. The downside of this scheme, of course, was that the GFRDAs were volatile and not safe investments at all. And so, when the so-called dot-com bubble “burst” in the fall of 2000, the value of the investments held by the GFRDAs dropped precipitously. Accordingly, Vilar and Tanaka could not pay the promised rates of return and, as a consequence, several GFRDA investors lost millions of dollars.

In June 2002, as the GFRDA scheme was falling apart, Vilar and Tanaka approached a long-standing client, Lily Cates, with the opportunity to invest in a type of venture known as a Small Business Investment Company (“SBIC”). Vilar told Cates that he and Tanaka had been approved for an SBIC license, which would allow the SBIC to obtain matching funds from the federal government’s Small Business Administration (“SBA”) for the SBIC’s investments. In fact, Vilar and Tanaka had never received an SBIC license and, indeed, had been denied such a license multiple times.

On June 20, 2002, Cates invested $5 million in the SBIC formed by Amerindo, and her funds were deposited into an Am-erindo bank account at Bear, Stearns & Co., in the name of a Panamanian corporation called “Amerindo Management Inc.” (“AMI”). Vilar and Tanaka quickly drew on these funds in order to meet various personal and corporate obligations. Notably, Vilar and Tanaka made the following transactions: (1) on June 25, 2002, Tanaka transferred $1 million to a personal bank account held by Vilar, and Vilar immediately used that money for a variety of personal expenses, including a substantial donation to his alma mater; and (2) on July 9, 2002, Vilar and Tanaka wired approximately $2.85 million of Cates’s money from the AMI account to an account in Luxembourg, as part of a settlement agreement with a former GFRDA investor. Over the next two years—during which Vilar repeatedly assured Cates that her funds were safely in escrow—Vilar and Tanaka continued to use Cates’s SBIC investment account for their own needs. For example, in 2003, Tanaka forged Cates’s signature to authorize a $250,000 transfer from her SBIC account to one of Vilar’s personal accounts. More than $50,000 of that transfer was used by Vilar to make a personal mortgage payment.

In early 2005, Cates requested that Vi-lar return her money and close her account. Vilar responded that she would have to make her request of Amerindo Panama—an organization with which she had never previously interacted. With her suspicions raised, Cates reported Vilar and Tanaka to the SEC. Vilar made several false statements in response to the SEC’s inquiries, hoping to obscure the SBIC scheme.

On August 15, 2006, the Department of Justice indicted Vilar and Tanaka, charging them in twelve counts with: (1) conspiracy to commit securities fraud, investment adviser fraud, mail fraud, wire fraud, and money laundering, in violation of 18 U.S.C. § 371 (Count One); (2) securities fraud, in violation of 15 U.S.C. §§ 78j(b), 78ff and 17 C.F.R. § 240.10b-5 (Counts Two and Three); (3) investment adviser fraud, in violation of 15 U.S.C. §§ 80b-6 and 80b-7 (Count Four); (4) mail fraud, in violation of 18 U.S.C. § 1341 (Count Five); (5) wire fraud, in violation of 18 U.S.C. § 1343 (Counts Six and Seven); (6) money laundering, in violation of 18 U.S.C. § 1957 (Counts Eight through Eleven); and (7) the making of false statements to the SEC, in violation of 18 U.S.C. § 1001(a) (Count Twelve).

Trial began before Judge Sullivan and a jury on September 22, 2008. On November 19, 2008, after a nine-week trial, the jury convicted Vilar on all twelve counts and convicted Tanaka on Counts One (conspiracy), Three (securities fraud relating to the GFRDA scheme), and Four (investment adviser fraud). Tanaka was acquitted on the other nine counts. On February 8, 2010, the District Court sentenced Vilar principally to a term of 108 months’ imprisonment. Two days later, Tanaka was sentenced to a term of sixty months’ imprisonment. On April 5, 2010, the District Court ordered both defendants to pay almost $35 million in restitution, including a 9% compounding interest rate, and to forfeit more than $54 million.

Vilar and Tanaka now appeal.

DISCUSSION

Vilar and Tanaka raise what can only be described as a host of challenges to their convictions and sentences. For ease of comprehension, we address, first, Vilar and Tanaka’s claim that the conduct underlying their convictions for securities fraud was “extraterritorial,” and therefore not criminal under Section 10(b) or Rule 10b-5; second, their challenges to the indictment; third, their various challenges to the admission of evidence introduced by the government at trial; fourth, their challenges to the District Court’s jury instructions; fifth, their challenges to the sufficiency of the evidence supporting their convictions; sixth, their challenges to their sentences; and, finally, seventh, their claims of ineffective assistance of counsel.

I. “Extraterritoriality”

Vilar and Tanaka contend that their respective convictions for securities fraud must be reversed because their conduct was extraterritorial, meaning that it “occurred] in the territory of [a] sovereign [other than the United States],” Kiobel v. Royal Dutch Petroleum Co., — U.S. -, 133 S.Ct. 1659, 1669, 185 L.Ed.2d 671 (2013), and therefore was not proscribed by Section 10(b) or Rule 10b-5. They rely on the Supreme Court’s holding in Morrison, which was decided after Vilar and Tanaka were convicted, and which limited Section 10(b) and Rule 10b-5 to prohibiting fraud committed in connection with “transactions in securities listed on domestic exchanges, and domestic transactions in other securities.” Morrison, 130 S.Ct. at 2884. Observing that Momson was a civil lawsuit, the government responds that Morrison’s geographic limit on the reach of Section 10(b) and Rule 10b-5 applies only in the civil context and therefore is no bar to Vilar and Tanaka’s criminal convictions. In the alternative, the government argues that Vilar and Tanaka’s illegal conduct was “territorial” within the meaning of Morrison, inasmuch as at least some of the transactions were “domestic transactions in other securities.” Id. Although we conclude that Morrison does apply to criminal cases brought pursuant to Section 10(b) and Rule 10b-5, we agree that the record in this case confirms that Vilar and Tanaka did perpetrate fraud in connection with domestic securities transactions, and we therefore affirm their convictions.

A. Standard of Review

It is an axiom of appellate review that “[a] federal court of appeals normally will not correct a legal error made in criminal trial court proceedings unless the defendant first brought the error to the trial court’s attention.” Henderson v. United States, - U.S. -, 133 S.Ct. 1121, 1124, 185 L.Ed.2d 85 (2013). Accordingly, where, as here, defendants present us with a claim that they did not give the district court an opportunity to consider, we limit our review to curing “plain error.” United States v. James, 712 F.3d 79, 96 (2d Cir.2013). This standard is met when “(1) there is an error; (2) the error is clear or obvious, rather than subject to reasonable dispute; (3) the error affected the appellant’s substantial rights, which in the ordinary case means it affected the outcome of the district court proceedings; and (4) the error seriously affects the fairness, integrity or public reputation of judicial proceedings.” United States v. Marcus, 560 U.S. 258, 130 S.Ct. 2159, 2164, 176 L.Ed.2d 1012 (2010) (internal quotation marks and brackets omitted).

Plain error review applies equally where the defendant did not object before the trial court because he failed to recognize an error, and where the defendant did not object because the trial court’s decision was correct at the time but assertedly became erroneous due to a supervening legal decision. See Johnson v. United States, 520 U.S. 461, 466-67, 117 S.Ct. 1544, 137 L.Ed.2d 718 (1997). In all cases, we look not to the law at the time of the trial court’s decision to assess whether the error was plain, but rather, to the law as it exists at the time of review. See Henderson, 133 S.Ct. at 1129-30. In other words, a decision of the trial court that was perfectly proper when issued may nonetheless be considered “plainly erroneous” on appeal due to a supervening change in the law.

B. Analysis

1. “Clear or Obvious Error”

The question presented here requires us to consider yet another issue created by the Supreme Court’s far-reaching holding in Morrison. Section 10(b) and Rule 10b-5 together proscribe the use of fraudulent schemes “in connection with the purchase or. sale of any security registered on a national securities exchange or any security not so registered....” 15 U.S.C. § 78j (b). Prior to the Supreme Court’s decision in Morrison, “[i]n determining whether § 10(b) and Rule 10b-5 could apply extraterritorially, this Court had ... applied the so-called conduct and effects test, which focused on: (1) whether the wrongful conduct occurred in the United States, and (2) whether the wrongful conduct had a substantial effect in the United States or upon United States citizens.” Absolute Activist Value Master Fund Ltd. v. Ficeto, 677 F.3d 60, 65 (2d Cir.2012) (internal quotation marks omitted). Morrison did away with this test. Relying on the “longstanding principle of American law that legislation of Congress, unless a contrary intent appears, is meant to apply only within the territorial jurisdiction of the United States,” Morrison, 130 S.Ct at 2877 (internal quotation marks omitted), the Supreme Court rejected any extraterritorial application of Section 10(b) and 10b-5, and instructed that “Section 10(b) reaches the use of a manipulative or deceptive device or contrivance only in connection with the purchase or sale of a security listed on an American stock exchange, and the purchase or sale of any other security in the United States.” Id. at 2888.

Despite the supposed bright-line nature of Morrison’s holding, there has been no shortage of questions raised in its wake. This appeal requires us to decide whether Morrison’s limit on the scope of Section 10(b) liability extends to criminal prosecutions brought under that provision. Although we have not yet addressed this specific issue, we have no problem concluding that Morrison’s holding applies equally to criminal actions brought under Section 10(b), and that this result is “clear or obvious” for the purposes of plain error review. We reach this result for two reasons: (1) the presumption against extraterritoriality applies to criminal statutes, and (2) the presumption against extraterritoriality applies to Section 10(b).

i. Criminal Statutes

First, the government is incorrect when it asserts that “the presumption against extraterritoriality for civil statutes ... simply does not apply in the criminal context.” Gov’t Br. 96. As we have observed, “[i]t is beyond doubt that, as a general proposition, Congress has the authority to ‘enforce its laws beyond the territorial boundaries of the United States.’ ” United States v. Yousef, 327 F.3d 56, 86 (2d Cir.2003) (quoting EEOC v. Arabian Am. Oil Co., 499 U.S. 244, 248, 111 S.Ct. 1227, 113 L.Ed.2d 274 (1991)). But the courts have also recognized the “eom-monsense notion that Congress generally legislates with domestic concerns in mind,” Smith v. United States, 507 U.S. 197, 204 n. 5, 113 S.Ct. 1178, 122 L.Ed.2d 548 (1993), and “the presumption that United States law governs domestically but does not rule the world,” Kiobel, 133 S.Ct. at 1664 (internal quotation marks omitted). For these reasons, “[w]hen a statute gives no clear indication of an extraterritorial application, it has none.” Morrison, 130 S.Ct. at 2878.

The government contends, relying on United States v. Bowman, 260 U.S. 94, 43 S.Ct. 39, 67 L.Ed. 149 (1922), that the presumption against extraterritoriality has no place in our reading of criminal statutes. To the contrary, no plausible interpretation of Bowman supports this broad proposition; fairly read, Bowman stands for quite the opposite. In Bowman, the Supreme Court was asked to consider criminal charges brought against sailors who, while at sea, conspired to defraud a company owned by the United States. See id. at 95-96, 43 S.Ct. 39. The Court explained:

Crimes against private individuals or their property, like assaults, murder, burglary, larceny, robbery, arson, embezzlement and frauds of all kinds, which affect the peace and good order of the community, must of course be committed within the territorial jurisdiction of the government where it may properly exercise it. If punishment of them is to be extended to include those committed outside of the strict territorial jurisdiction, it is natural for Congress to say so in the statute, and failure to do so will negative the purpose of Congress in this regard.

Id. at 98, 43 S.Ct. 39. The Court nonetheless concluded that charges could be brought in district court in that case, because “the same rule of interpretation should not be applied to criminal statutes which are, as a class, not logically dependent on their locality for the Government’s jurisdiction, but are enacted because of the right of the Government to defend itself against obstruction, or fraud ivherever perpetrated, especially if committed by its own citizens, officers, or agents.” Id. (emphasis supplied). In other words, the presumption against extraterritoriality does apply to criminal statutes, except in situations where the law at issue is aimed at protecting “the right of the government to defend itself.” Id.

Indeed, we have repeatedly observed that Bowman makes precisely this distinction. For example, in United States v. Gatlin, 216 F.3d 207 (2d Cir.2000), we observed that “[sjtatutes prohibiting crimes against the United States government may be applied extraterritorially even in the absence of ‘clear evidence’ that Congress so intended,” but that “the Bowman Court explicitly stated that the presumption against extraterritoriality does apply to ‘[cjrimes against private individuals or their property----’ ” Id. at 211 n. 5 (quoting Bowman, 260 U.S. at 98, 43 S.Ct. 39) (emphases in Gatlin); see also Yousef, 327 F.3d at 87-88. And, we have explicitly recognized that “although there is no general bar against the extraterritorial application of our criminal laws to American citizens, the Supreme Court has long recognized a presumption against such applications.” United States v. Kim, 246 F.3d 186, 188-89 (2d Cir.2001); see also Small v. United States, 544 U.S. 385, 388-89, 125 S.Ct. 1752, 161 L.Ed.2d 651 (2005) (using the presumption against extraterritoriality as guidance in the criminal context); United States v. Ayesh, 702 F.3d 162, 166 (4th Cir.2012) (“Whether Congress has exercised that authority is a matter of statutory construction and, generally, statutes enacted by Congress, including criminal statutes, apply only within the territorial jurisdiction of the United States.”).

The government nonetheless argues that we have previously interpreted Bowman as limiting the presumption against extraterritoriality to civil statutes. The government draws our attention to United States v. Siddiqui, 699 F.3d 690 (2d Cir.2012), where we stated that “[tjhe ordinary presumption that laws do not apply extraterri-torially has no application to criminal statutes,” id. at 700, and United States v. Al Kassar, 660 F.3d 108 (2d Cir.2011), where we similarly wrote that “[tjhe presumption that ordinary acts of Congress do not apply extraterritorially ... does not apply to criminal statutes,” id. at 118.

However broadly worded, these statements must be understood in their context. In Al Kassar, we considered the extraterritorial application of four counts of conviction that relied on statutes with “explicit provisions applying them extraterritorially,” and one count for “conspiracy to kill U.S. officers or employees,” which we held applies extraterritorially in light of “the nature of the offense—protecting U.S. personnel from harm when acting in their official capacity.” Al Kassar, 660 F.3d at 118. Siddiqui also addressed statutes designed to protect U.S. personnel engaged in the performance of their duties from assault or interference. Siddiqui, 699 F.3d at 701. In other words, Al Kassar and Siddiqui both followed Bowman’s rule precisely—they required that the relevant statutes either contain a clear indication of Congress’s intent to provide for extraterritorial application or relate to crimes against the United States government. Inasmuch as these cases relied upon Bowman to reach this result, they surely do not require that the presumption against extraterritoriality be laid aside in all criminal cases. They are simply applications of Bowman’s holding.

Further, the government provides little reason, beyond its misplaced reliance on Bowman, for why the presumption against extraterritoriality should not apply to criminal statutes. The government argues that criminal statutes “are concerned with prohibiting individuals ... from defrauding American investors and from using the infrastructure of American commerce to defraud investors” and that applying the presumption against extraterritoriality to criminal statutes “would create a broad immunity for criminal conduct simply because the fraudulent scheme culminates in a purchase or sale abroad.” Gov’t Br. 98-99. But much the same could be said of civil fraud statutes: Applying the presumption against extraterritoriality immunizes thieves and swindlers from civil liability for defrauding Americans abroad.

More to the point, the distinction the government attempts to draw between civil and criminal laws is no response to the fundamental purposes of the presumption. The Supreme Court has emphasized that we apply this rule of statutory interpretation because we understand that “Congress generally legislates with domestic concerns in mind,” Smith, 507 U.S. at 204 n. 5, 113 S.Ct. 1178, and because the presumption “serves to protect against unintended clashes between our laws and those of other nations which could result in international discord,” Kiobel, 133 S.Ct. at 1664 (internal quotation marks omitted). We discern no reason that these concerns are less pertinent in the criminal context.

Finally, the government argues, that Section 10(b) belongs to the “class [of statutes that are] not logically dependent on their locality for the Government’s jurisdiction, but are enacted because of the right of the Government to defend itself against obstruction, or fraud wherever perpetrated, especially if committed by its own citizens, officers or agents.” Bowman, 260 U.S. at 98, 43 S.Ct. 39. We are not persuaded. Although Section 10(b) clearly forbids a variety of fraud, its purpose is to prohibit “[c]rimes against private individuals or their property,” which Bowman teaches is exactly the sort of statutory provision for which the presumption against extraterritoriality does apply. Id. In sum, the general rule is that the presumption against extraterritoriality applies to criminal statutes, and Section 10(b) is no exception.

ii. Section 10(b)

Second, even if it were the case that we do not generally apply the presumption against extraterritoriality to criminal statutes, Section 10(b) would still not apply extraterritorially in criminal cases. The reason is simple: The presumption against extraterritoriality is a method of interpreting a statute, which has the same meaning in every case. The presumption against extraterritoriality is not a rule to be applied to the specific facts of each case. See Morrison, 130 S.Ct. at 2877. A statute either applies extraterritorially or it does not, and once it is determined that a statute does not apply extra-territorially, the only question we must answer in the individual case is whether the relevant conduct occurred in the territory of a foreign sovereign.

The Supreme Court has already interpreted Section 10(b), and it has done so in unmistakable terms: “Section 10(b) reaches the use of a manipulative or deceptive device or contrivance only in connection with the purchase or sale of a security listed on an American stock exchange, and the purchase or sale of any other security in the United States.” Id. at 2888. To permit the government to punish extraterritorial conduct when bringing criminal charges under Section 10(b) “would establish ... the dangerous principle that judges can give the same statutory text different meanings in different cases.” Clark v. Martinez, 543 U.S. 371, 386, 125 S.Ct. 716, 160 L.Ed.2d 734 (2005).

The government nonetheless insists that Section 10(b) is interpreted differently in the criminal and civil contexts because different elements are required to prevail in each. More specifically, the government observes that only private plaintiffs must prove reliance, economic loss, and loss causation, whereas only the government (in criminal cases) must prove that the fraud was committed willfully. Critically, however, none of these differences relate to the conduct proscribed by Section 10(b).

Reliance, economic loss, and loss causation relate to who (other than the government) may bring suit and not to the conduct prohibited by Section 10(b). The Supreme Court has made this distinction clear, explaining that

[i]n our cases addressing § 10(b) and Rule 10b-5, we have confronted two main issues. First, we have determined the scope of conduct prohibited by § 10(b). Second, in cases where the defendant has committed a violation of § 10(b), we have decided questions about the elements of the 10b-5 private liability scheme: for example, whether there is a right to contribution, what the statute of limitations is, whether there is a reliance requirement, and whether there is an in pan delicto defense.
The latter issue, determining the elements of the 10b-5 private liability scheme, has posed difficulty because Congress did not create a private § 10(b) cause of action and had no occasion to provide guidance about the elements of a private liability scheme.

Cent. Bank of Denver, N.A. v. First Interstate Bank of Denver, N.A., 511 U.S. 164, 172-73, 114 S.Ct. 1439, 128 L.Ed.2d 119 (1994) (internal brackets and citations omitted). Accordingly, “when it comes to ‘the scope of the conduct prohibited by Rule 10b-5 and § 10(b), the text of the statute controls our decision’ ” and “[i]t is only with respect to the additional ‘elements of the 10b-5 private liability scheme’ that we ‘have had to infer how the 1934 Congress would have addressed the issues had the [civil] 10b-5 action been included as an express provision in the 1934 Act.’ ” Morrison, 130 S.Ct. at 2881 n. 5 (quoting Cent. Bank of Denver, 511 U.S. at 173, 114 S.Ct. 1439) (brackets omitted).

As for the element of willfulness in criminal cases, it comes directly from Section 32 of the Securities Exchange Act of 1934, which permits criminal liability to attach to a violation of Section 10(b), only when the violation is willful. 15 U.S.C. § 78ff(a). But like the elements relevant only to private plaintiffs, the requirement of proving willfulness has nothing to do with the text or interpretation of Section 10(b). In other words, Section 32 provides no basis for expanding the conduct for which a defendant may be held criminally liable under Section 10(b).

Nor, for that matter, can Rule 10b-5 provide for the extraterritorial reach that its underlying statute lacks. Although the Supreme Court has approved the delegation of authority to the SEC to create rules with criminal penalties, see United States v. O’Hagan, 521 U.S. 642, 650-51, 117 S.Ct. 2199, 138 L.Ed.2d 724 (1997), “criminal liability under SEC regulations for insider trading may not extend beyond the conduct that Congress intended to encompass in § 10(b) of the 1934 Act,” United States v. Gansman, 657 F.3d 85, 90 n. 5 (2d Cir.2011).

2. “Substantial Rights”

Having concluded that it would be clear or obvious error to apply Section 10(b) and Rule 10b-5 to extraterritorial criminal conduct in light of Morrison, we now turn, in our analysis of the asserted “plain error,” to whether “the error affected the appellant’s substantial rights, which in the ordinary case means it affected the outcome of the district court proceedings.” Marcus, 130 S.Ct. at 2164 (internal quotation marks omitted).

Under Morrison, a defendant may be convicted of securities fraud under Section 10(b) and Rule 10b-5 if he has engaged in fraud with respect to either (1) a security listed on an American exchange, or (2) a security purchased or sold in the United States. Morrison, 130 S.Ct. at 2888. There is no claim that any of the securities sold in this ease were listed on an American exchange. We ask, therefore, whether the jury would have found, beyond a reasonable doubt, that Vilar and Tanaka engaged in fraud in connection with a domestic purchase or sale of securities, in violation of Section 10(b) and Rule 10b-5. Cf. Needham, 604 F.3d at 679-80 (explaining that a defendant has not demonstrated plain error where, absent the asserted error, the government still would have proved its case beyond a reasonable doubt.).

On this issue, we are guided by our test, recently enunciated in the aftermath of Morrison, for determining whether a security not listed on an American exchange was purchased or sold in the United States: “[A] securities transaction is domestic when the parties incur irrevocable liability to carry out the transaction within the United States or when title is passed within the United States.” Absolute Activist, 677 F.3d at 69. More specifically, a domestic transaction has occurred when “the purchaser [has] incurred irrevocable liability within the United States to take and pay for a security, or ... the seller [has] incurred irrevocable liability within the United States to deliver a security.” Id. at 68 (emphasis supplied).

As to the GFRDA fraud (Counts One and Three), the government contends that one set of victims, the Mayer family, entered into and renewed their agreement in Puerto Rico, and another victim, Graciela Lecube-Chavez, did so in New York. See Gov’t Br. 101. As to the SBIC scheme (Count Two), the government points to evidence that Lily Cates “executed the documents necessary to invest in the SBIC in her own New York apartment and handed those documents to a New York messenger.” Gov’t Sur-Reply 12. In light of these domestic transactions, we are persuaded that, based on the record evidence, a jury would have found that Vilar and Tanaka engaged in fraud in connection with a domestic purchase or sale of securities pursuant to Section 10(b) and Rule 10b-5.

In particular, the record contains correspondence between Vilar and the Mayer family, indicating that they met in Puerto Rico, where the Mayers lived, to discuss the GFRDA program and that the Mayers committed to the investment while in Puerto Rico. See Gov’t Supp. App’x 876-79; see also Trial Tr. 849 (explaining that all of the Mayers’ meetings with Vilar to discuss the GFRDA investment occurred in Puerto Rico). Indeed, the Mayers’ GFRDA application lists their address as Santurce, Puerto Rico, and Vilar and Ta-naka sent a letter confirming the Mayers’ investment to that address. See Tanaka App’x 534-37. The evidence similarly shows that Lisa Mayer was in Puerto Rico when she re-invested her family’s money in the GFRDA program, once the original investment had expired. See Gov’t Supp. App’x at 753-54.

Much the same can be said of the evidence demonstrating that Lecube-Chavez irrevocably committed herself to her GFRDA investment while in New York. A series of letters sent by Vilar to Lecube-Chavez demonstrate that Lecube-Chavez was in New York when she received and signed the commitment forms for her GFRDA and sent the money required for opening her account. See Tanaka App’x 465-69, 520-24; Gov’t App’x 772; see also Trial Tr. 306-09 (testimony confirming that Lecube-Chavez sent a check to Amer-indo after receiving these letters).

In sum, with respect to the purchases of GFRDAs by the Mayers and Lecube-Cha-vez, the record contains facts “concerning the formation of the contracts” and “the exchange of money,” which are precisely the sort that we indicated may suffice to prove that irrevocable liability was incurred in the United States. See Absolute Activist, 677 F.3d at 70.

Despite this evidence of domestic securities transactions with the Mayers and Le-cube-Chavez, our analysis of whether the change in law created by Morrison would have affected the outcome of this case as to Counts One and Three is complicated by the fact that the jury rendered a general verdict covering all victims of the GFRDA scheme. In other words, it is possible that, in responding to a carefully drawn special verdict form, the jury would have found Vilar and Tanaka guilty only of defrauding victims outside of the United States, and not of defrauding the Mayers or Lecube-Chavez. Nonetheless, upon a review of the record, we have no doubt that the jury would have found Vilar and Tanaka guilty of violating Section 10(b) and Rule 10b-5 with respect to the Mayers and Lecube-Chavez specifically. The record contains evidence in the form of offering materials and prospectuses, as well as testimony by Lisa Mayer and Lecube-Chavez confirming beyond a reasonable doubt that Vilar and Tanaka, willfully, and with the intent to defraud, made material misrepresentations as to the nature of the GFRDA program in connection with their purchases of GFRDAs. See, e.g., Tanaka App’x 447-48 (offering circular); Gov’t Supp. App’x 878 (letter from Vilar to Dr. Herbert Mayer); Trial Tr. 301-04 (testimony of Graciela Lecube-Chavez); id. at 831-38 (testimony of Lisa Mayer). We therefore conclude that, notwithstanding the fact that the jury returned general verdicts as to Counts One and Three, the error made manifest by Morrison’s change in law would not have altered the outcome of the jury’s determinations as to Counts One or Three, and therefore did not affect Vilar and Tanaka’s substantial rights. Cf. Hedgpeth v. Pulido, 555 U.S. 57, 61, 129 S.Ct. 530, 172 L.Ed.2d 388 (2008) (harmless error analysis applied where a jury returned a general verdict after being instructed on alternative theories of guilt, one of which was erroneous).

Count Two presents no such difficulties inasmuch as the jury convicted Vilar of defrauding Cates, and the record makes clear that Cates made her investment in the SBIC scheme while in the United States. Cates testified that she met with Vilar at his apartment in New York in June 2002 to discuss the investment opportunity, and shortly thereafter signed the commitment papers. See Trial Tr. 2098-104. We do not doubt that, on this record, the jury would have found that Cates incurred irrevocable liability to purchase her SBIC investment while in the United States.

In sum, there was no plain error in Vilar and Tanaka’s convictions on Counts One, Two, or Three with respect to the territoriality of their conduct.

II. Sufficiency of the Indictment

Vilar and Tanaka challenge the indictment on two grounds. First, they claim that Count One (Conspiracy) was “duplicitous,” by which they mean that the indictment alleged one conspiracy where, in fact, there were two smaller conspiracies. Second, they claim that Count Four (Investment Adviser Fraud) was not sufficiently definite, and was later constructively amended at trial. We review de novo the denial of a motion to dismiss the indictment. United States v. Daley, 702 F.3d 96, 99-100 (2d Cir.2012). Neither claim has merit.

As for the “duplicity” of Count One, Vilar and Tanaka argue that the GFRDA frauds and SBIC frauds were separate conspiracies, and should have been charged as such. The District Court rejected this argument, see United States v. Vilar, No. 05 Cr. 621(RJS), 2008 WL 4298545, at *1 (S.D.N.Y. Sept. 5, 2008), and we do so as well. We have held that “[a]n indictment is impermissibly duplicitous where: 1) it combines two or more distinct crimes into one count in contravention of Fed.R.Crim.P. 8(a)’s requirement that there be a separate count for each offense, and 2) the defendant is prejudiced thereby.” United States v. Sturdivant, 244 F.3d 71, 75 (2d Cir.2001) (internal quotation marks omitted). However, “this [CJourt has long held that acts that could be charged as separate counts of an indictment may instead be charged in a single count if those acts could be characterized as part of a single continuing scheme.” United States v. Olmeda, 461 F.3d 271, 281 (2d Cir.2006) (internal quotation marks omitted). It has been established for at least seventy years that “ ‘[t]he allegation in a single count of a conspiracy to commit several crimes is not duplicitous, for [t]he conspiracy is the crime, and that is one, however diverse its objects.’ ” United States v. Williams, 705 F.2d 603, 624 (2d Cir.1983) (quoting Braverman v. United States, 317 U.S. 49, 54, 63 S.Ct. 99, 87 L.Ed. 23 (1942)).

The record leaves no doubt that the GFRDA and SBIC schemes can be characterized as part of one conspiracy to defraud investors by (1) lying about the nature of their investments and (2) continuing to mislead them into believing that their money was safe and invested in accordance with the representations they had received from Vilar and Tanaka. See, e.g., United States v. Tutino, 883 F.2d 1125, 1141 (2d Cir.1989) (“As long as the essence of the alleged crime is carrying out a single scheme to defraud, then aggregation is permissible.”).

As for the definiteness of Count Four (Investment Adviser Fraud), Vilar and Tanaka argue that the indictment was not sufficient because it did not specify that the SBIC fraud, as opposed to the GFRDA fraud, formed the basis of Count Four. Pursuant to Federal Rule of Criminal Procedure 7, “[t]he indictment or information must be a plain, concise, and definite written statement of the essential facts constituting the offense charged.... ” Fed.R.Crim.P. 7(c)(1). As we have explained, “[a]n indictment is sufficient when it charges a crime with sufficient precision to inform the defendant of the charges he must meet and with enough detail that he may plead double jeopardy in a future prosecution based on the same set of events.” United States v. Yannotti, 541 F.3d 112, 127 (2d Cir.2008) (internal quotation marks omitted). “Moreover, an indictment need do little more than to track the language of the statute charged and state the time and place (in approximate terms) of the alleged crime.” Id. (internal quotation marks omitted).

The indictment in this case sufficiently sets out the time and circumstances of the conspiracy and tracks the language of the statute charged. See Tanaka App’x 116. While it is true that the indictment does not explicitly refer to the SBIC scheme, we have little trouble concluding that it contained “sufficient precision” to inform Vilar and Tanaka of the charges to be met and to enable them to plead double jeopardy in the future. Yannotti, 541 F.3d at 127.

Vilar and Tanaka nonetheless argue that the indictment was constructively amended by the government when it narrowed Count Four to the SBIC scheme because the indictment was worded more generally and could have encompassed broader conduct. We have only recently had occasion to recall that, “[t]o prevail on a constructive amendment claim, a defendant must demonstrate that the terms of the indictment are in effect altered by the presentation of evidence and jury instructions which so modify essential elements of the offense charged that there is a substantial likelihood that the defendant may have been convicted of an offense other than that charged in the indictment.” United States v. D’Amelio, 683 F.3d 412, 416 (2d Cir.2012) (internal quotation marks omitted; emphasis in original). Although “a constructive amendment is a per se violation of the Grand Jury Clause,” we have “consistently permitted significant flexibility in proof, provided that the defendant was given notice of the core of criminality to be proven at trial.” United States v. Banki 685 F.3d 99, 118 (2d Cir.2012) (internal quotation marks and citation omitted; emphasis in Banki).

We have little doubt that Vilar and Tanaka were on notice of the “core of criminality” alleged in Count Four—namely that, between 2002 and 2005, Vilar and Tanaka defrauded Lily Cates, to whom they were investment advisers, as part of the SBIC scheme. Even if it were true that Count Four of the indictment originally contemplated both the GFRDA and SBIC schemes, rather than the latter scheme alone, “where a generally framed indictment encompasses the specific legal theory or evidence used at trial, there is no constructive amendment.” Id. (internal quotation marks and brackets omitted); see also United States v. Miller, 471 U.S. 130, 136, 105 S.Ct. 1811, 85 L.Ed.2d 99 (1985) (“As long as the crime and the elements of the offense that sustain the conviction are fully and clearly set out in the indictment, the right to a grand jury is not normally violated by the fact that the indictment alleges more crimes or other means of committing the same crime.”). Indeed, in contrast to the alleged narrowing of Count 4 here, we have specifically noted that a constructive amendment occurs “when the trial evidence or the jury charge operates to broaden the possible bases for conviction from that which appeared in the indictment.” Banki 685 F.3d at 118 (internal quotation marks omitted; emphasis supplied).

In sum, Vilar and Tanaka have established no error based on the sufficiency of the indictment.

III. Evidentiary Challenges

Vilar and Tanaka claim that at trial the District Court erred by not suppressing (1) evidence obtained pursuant to an overbroad warrant to search Amerindo’s New York office; (2) evidence seized in a search of Amerindo’s London storage facility; and (3) testimony concerning statements made by Renata Tanaka, Tanaka’s wife, who worked in Amerindo’s London office. When considering a district court’s order denying a motion to suppress evidence, “we review the district court’s factual findings for clear error, viewing the evidence in the light most favorable to the government,” and review its legal conclusions de novo. United States v. Moreno, 701 F.3d 64, 72 (2d Cir.2012) (internal quotation marks and brackets omitted). We review a district court’s rulings about the admissibility of trial evidence for “abuse of discretion,” United States v. Coplan, 703 F.3d 46, 80 (2d Cir.2012), which means that we set aside its decision if “it based its ruling on an erroneous view of the law or on a clearly erroneous assessment of the evidence, or rendered a decision that cannot be located within the range of permissible decisions,” In re Sims, 534 F.3d 117, 132 (2d Cir.2008) (internal quotation marks and citation omitted) (explaining term of art “abuse of discretion”).

A. The U.S. Search

1. Background

On May 25, 2005, Magistrate Judge Frank Maas signed a search warrant for Amerindo’s office in New York City. The warrant permitted authorities to seize broad categories of documents, including all corporate records and client files, without any temporal limitation. The next day, investigators executed the warrant and seized approximately 170 boxes of documents, as well as 30 computers. Several hours into the search, counsel to Amerindo arrived at the office and indicated that he would cooperate with the government’s investigation. He offered to put into place a preservation policy for Amerindo’s documents and suggested that, because it appeared that the search would not be completed in a day, Amerindo would agree to accept service of a grand jury subpoena for the documents; Amerindo could then, in his view, disclose the requested documents in an orderly fashion. By early afternoon, the government had faxed the grand jury subpoena and Amerindo’s attorney had accepted service. In return for this acceptance, the investigators stopped their search.

But Amerindo did not comply with the subpoena. Instead, Vilar and Tanaka filed a motion to quash the subpoena and suppress any evidence obtained during the search. In a thorough and well-reasoned Opinion and Order, Judge Kenneth M. Karas, who was then the presiding judge, determined that, although there was probable cause to search the New York office, certain portions of the warrant were not supported by probable cause and lacked sufficient particularity. See United States v. Vilar, No. S3 05-CR-621(KMK), 2007 WL 1075041, at *19-23 (S.D.N.Y. Apr. 4, 2007) (“Warrant Decision ”). Judge Karas went on to conclude that the evidence obtained could not be rescued from suppression by the good faith of the executing officers, but that certain valid portions of the warrant could be severed, and evidence seized pursuant to those valid portions would be admissible. Id. at *23-24, *31-34. Finally, Judge Karas found that the grand jury subpoena was not an improper extension of the search and, after modifying the subpoena to address certain areas that were overbroad, insufficiently particular, or overly burdensome, he denied the motion to quash. Id. at *39-50. In practical terms, the government was permitted to obtain the documents from Amerindo’s New York office through its grand jury subpoena.

The saga of the evidence obtained from Amerindo’s New York office did not end there, however. Prior to trial, Vilar and Tanaka moved to exclude the documents produced pursuant to the grand jury subpoena on the ground that these documents represented so-called fruits of the unlawful search. Judge Sullivan, who by then had taken over the case, disagreed and held that both the “inevitable discovery” and “independent source” doctrines permitted the admission of the documents obtained through the grand jury subpoena. See United States v. Vilar, 530 F.Supp.2d 616, 626-34 (S.D.N.Y.2008) (“Subpoena Decision ”).

2. Analysis

Vilar and Tanaka now argue that Judge Karas erred in severing the valid portions of the warrant and that Judge Sullivan erred in admitting the evidence obtained pursuant to the grand jury subpoena. We need not address Judge Karas’s invalidation of parts of the warrant, nor the independent source doctrine, because it is clear that Judge Sullivan properly admitted all of the evidence pursuant to the inevitable discovery doctrine.

As a preliminary matter, Vilar and Tanaka contend, as they did before Judge Sullivan, that the government forfeited its claim that the materials obtained under the subpoena were admissible pursuant to the inevitable discovery doctrine. In particular, they argue that the documents admitted pursuant to the subpoena were the same ones suppressed pursuant to the overbroad warrant and, therefore, the government was required to assert the inevitable discovery doctrine before Judge Karas in opposition to Vilar and Tanaka’s motion to suppress evidence obtained by the warrant. This argument neglects the fact that the government explained its position on the admissibility of the documents to Judge Karas, see Subpoena Decision, 530 F.Supp.2d at 622; indeed, Judge Karas permitted the government to move forward with the subpoena, recognizing that the admissibility of the documents might be subject to challenge at a future date, see id. at 622-23. Even if the government did not incant the phrase “inevitable discovery” when defending before Judge Karas the admissibility of the documents seized pursuant to the warrant, Vi-lar and Tanaka have advanced no plausible authority for the notion that it was not perfectly appropriate to reserve those arguments for the time when Vilar and Ta-naka challenged the admissibility of the subpoenaed evidence itself. In short, the government did not waive its “inevitable discovery” argument in the proceedings before Judge Karas.

Vilar and Tanaka’s substantive arguments fare no better. It is correct, of course, that the so-called exclusionary rule, “when applicable, forbids the use of improperly obtained evidence at trial.” Herring v. United States, 555 U.S. 135, 139, 129 S.Ct. 695, 172 L.Ed.2d 496 (2009). But “[u]nder the ‘inevitable discovery’ doctrine, evidence obtained during the course of an unreasonable search and seizure should not be excluded ‘if the government can prove that the evidence would have been obtained inevitably’ without the constitutional violation.” United States v. Heath, 455 F.3d 52, 55 (2d Cir.2006) (quoting Nix v. Williams, 467 U.S. 431, 447, 104 S.Ct. 2501, 81 L.Ed.2d 377 (1984)). Put another way, whether this exception to the exclusionary rule applies depends on whether “the disputed evidence inevitably [would] have been found through legal means ‘but for’ the constitutional violation[.]” Id.

To prevail under the inevitable discovery doctrine, the government must prove “by a preponderance of the evidence” presented to the district judge that the evidence inevitably would have been discovered. Nix, 467 U.S. at 444, 104 S.Ct. 2501. In United States v. Cabassa, 62 F.3d 470 (2d Cir.1995), we acknowledged that using the preponderance-of-the-evidence standard to prove inevitability creates a problem of probabilities, and observed that even if each event in a series is individually more likely than not to happen, it still may be less than probable that the final event will occur. Id. at 474. For this reason, we subsequently explained “that illegally-obtained evidence will be admissible under the inevitable discovery exception to the exclusionary rule only where a court can find, with a high level of confidence, that each of the contingencies necessary to the legal discovery of the contested evidence would be resolved in the government’s favor.” Heath, 455 F.3d at 60. In other words, the government must prove that each event leading to the discovery of the evidence would have occurred with a sufficiently high degree of confidence for the district judge to conclude, by a preponderance of the evidence, that the evidence would inevitably have been discovered.

. Judge Sullivan, in a careful and clear Memorandum and Order of January 17, 2008, found that (1) the subpoena was not issued on the basis of any information unlawfully seized from Amerindo’s New York office; (2) the government was actively investigating Amerindo and inevitably would have conducted a substantial search of the New York office; (3) Amerindo’s attorney inevitably would have raised the alternative of a grand jury subpoena; (4) the government inevitably would have issued the grand jury subpoena; and (5) Vilar and Tanaka inevitably would have produced the documents requested by the subpoena (which they, in fact, did). See Subpoena Decision, 530 F.Supp.2d at 627-32. We identify no error in these findings, let alone clear error. See Moreno, 701 F.3d at 72.

Indeed, we can be confident that this sequence is what would have happened, because it did happen. This case presents the unusual scenario where the actual events played out exactly as they would have “but for” the over-breadth of the warrant, because the government actually obtained the evidence through alternative means that did not depend on any invalidity of the warrant. As Judge Sullivan noted, “it is beyond doubt that the Government had a lawful basis to be present in Amerindo’s office on the date of the search in order to execute the lawful portions of the Warrant,” Subpoena Decision, 530 F.Supp.2d at 627, because, as Judge Karas found—and Vilar and Tanaka do not contest—there was “[c]learly” probable cause to conduct a search of Amerindo’s New York office, Warrant Decision, 2007 WL 1075041, at *20. Further, the offer of Amerindo’s counsel to accept a grand jury subpoena had nothing to do with any illegality in the warrant; at the time, he thought the warrant was valid. The record, therefore, confirms that the government would have validly discovered the documents produced pursuant to the subpoena “but for” the over-breadth of the warrant.

Vilar and Tanaka nonetheless insist that this material should have been excluded because the subpoena was issued after the government began its search pursuant to the (partly) invalidated warrant. They rely on our decision in United States v. Eng, 971 F.2d 854 (2d Cir.1992), in which we cautioned that, “[particular care is appropriate where ... subpoenas are issued after or at the time of the unlawful search,” and “subpoenas must not serve as an after the fact insurance policy to validate an unlawful search under the inevitable discovery doctrine.” Id. at 860-61 (internal quotation marks omitted). Put simply, Vilar and Tanaka assert that the inevitable discovery doctrine cannot apply where the subpoena was sought after the government initiated its partly unlawful search. We cannot agree.

First, Eng created no such rule and, in fact, it rejected a per se rule “that the subpoena power never may be relied upon by the government to meet the inevitable discovery burden of proof.” Id. at 860. Indeed, we explained quite clearly that we could find “no reason why the government may not rely upon the subpoena power as one way it might meet the burden of proving inevitable discovery by a preponderance of the evidence.” Id.

Second, based on the facts of this case, the temporal or causal relationship between the search of Amerindo’s New York office and the issuance of the subpoena has no bearing on whether “the disputed evidence inevitably [would] have been found through legal means ‘but for’ the constitutional violation[.]” Heath, 455 F.3d at 55. And, as we have explained, there is no doubt that the government would have discovered the evidence through the grand jury subpoena, irrespective of the invalidity of parts of the warrant.

Accordingly, we identify no error in the admission of the documents from Amerin-do’s New York office.

B. The Search in the United Kingdom

1. Background

On October 13 and 14, 2005, British and American authorities searched the Cado-gan Tate warehouse in London for documents stored by Amerindo U.K. Warrant Decision, 2007 WL 1075041, at *17. In order to gain access to Amerindo’s documents in the United Kingdom, American authorities first filed a “Mutual Legal Assistance Treaty” (“MLAT”) request, in which they sought the assistance of U.K. law enforcement. Id. at *12.

After receiving the request, a U.K. detective conducted his own investigation to ensure that any warrant application would comport with U.K. law and that it would be based on sufficient information to justify the issuance of a warrant. Id. at *11-13. Once these prerequisites had been satisfied, the detective sought and obtained a valid warrant from a magistrate. Id. at *16. As part of his normal procedure, the detective requested that American officials attend the search to provide advice on what materials were relevant. Id. at *13. Although American investigators did attend the search and offered their opinions on the relevance of various documents, Judge Karas found-—and we have no reason to doubt—that the authority to determine what documents could validly be seized under U.K. law remained at all times with the U.K. authorities. Id. at *16-17.

Vilar and Tanaka subsequently sought to suppress the evidence obtained at the Cadogan Tate warehouse. Judge Karas, then presiding, denied their motion, holding (1) that the Fourth Amendment’s warrant requirement did not apply because the search was executed abroad, and (2) that the evidence did not have to be suppressed because the search was valid under U.K. law and was reasonable. See id. at *51-58. Vilar and Tanaka now renew their challenge to the admission of the evidence obtained in the United Kingdom.

2. Analysis

After Judge Karas issued his opinion, we clarified the law applicable to searches of United States citizens conducted abroad by United States authorities, holding “that the Fourth Amendment’s warrant requirement does not govern searches conducted abroad by U.S. agents; such searches of U.S. citizens need only satisfy the Fourth Amendment’s requirement of reasonableness.” In re Terrorist Bombings of U.S. Embassies in E. Africa, 552 F.3d 157, 167 (2d Cir.2008) (“In re Terrorist Bombings ”). “To determine whether a search is reasonable under the Fourth Amendment, we examine the ‘totality of the circumstances’ to balance ‘on the one hand, the degree to which it intrudes upon an individual’s privacy and, on the other, the degree to which it is needed for the promotion of legitimate governmental interests.’ ” Id. at 172 (quoting Samson v. California, 547 U.S. 843, 848, 126 S.Ct. 2193, 165 L.Ed.2d 250 (2006)).

Judge Karas’s undisputed factual findings provide ample support for the conclusion that the U.K. search was reasonable, and that the Cadogan Tate materials were therefore properly admitted. Indeed, Vilar and Tanaka’s only substantive challenge to this determination is a misguided effort to confine In re Terrorist Bombings to its facts. They contend that “[t]he interest in obtaining evidence of possible white collar crimes—particularly involving only a handful of investors—cannot compare to the national security interest in preventing murderous, terrorist attacks, the interest at stake in Terrorist Bombings.” Tanaka Br. 86-87. In re Terrorist Bombings was not limited to cases of suspected terrorism or instances of similarly horrific crime. We could not have been clearer in stating that “the Fourth Amendment’s warrant requirement does not govern searches conducted abroad by U.S. agents.” In re Terrorist Bombings, 552 F.3d at 167. The government has demonstrated that the U.K. search was reasonable; it need do no more. For this reason, the District Court properly admitted the evidence obtained in the U.K.

C. Statements of Renata Tanaka

The final evidentiary claim of Vilar and Tanaka may also be disposed of readily. They protest the admission of statements made by Renata Tanaka, the wife of defendant Tanaka, who worked at Amerindo U.K., to Stephen Gray, the attorney for several GFRDA clients. Judge Sullivan permitted Gray to relate the statements pursuant to Federal Rule of Evidence 801(d)(2)(D), which excludes from the definition of hearsay any statement “offered against an opposing party” that “was made by the party’s agent or employee on a matter within the scope of that relationship and while it existed.” Vilar and Tana-ka each argue that Renata Tanaka was not his agent and that the statements were not made within the scope of any agency relationship. However, after a lengthy colloquy, Judge Sullivan found, by a preponderance of the evidence, that Renata Tanaka was, in fact, an agent of both Vilar and Tanaka, and that the challenged statements were made within the scope of that relationship. See Tanaka App’x 345-61. We identify no error, let alone clear error, in Judge Sullivan’s findings, see Coplan, 703 F.3d at 80, nor in his conclusion that these findings satisfied the requirements of Rule 801(d)(2)(D), see United States v. Lauersen, 348 F.3d 329, 340 (2d Cir.2003).

IV. Jury Instructions

Defendants charge two main errors in the District Court’s jury instructions. First, they both argue that the District Court erroneously omitted a reliance element from the charges for securities fraud (Counts Two and Three). Second, Vilar (only) claims that the District Court improperly permitted the jury to convict him of mail fraud (Count Five) without proving that the mailing contained false or fraudulent material.

As we recently explained,

we review a properly preserved claim of error regarding jury instructions de novo, reversing only where, viewing the charge as a whole, there was a prejudicial error. The trial court enjoys broad discretion in crafting its instructions, which is only circumscribed by the requirement that the charge be fair to both sides. A defendant challenging a district court’s refusal to give a requested jury instruction carries the heavy burden of showing that his proposed charge accurately represented the law in every respect, and that the charge actually given, viewed as a whole, prejudiced him.

Coplan, 703 F.3d at 87 (internal quotation marks, brackets, ellipses, and citations omitted). By contrast, where a defendant fails to make a specific and timely objection to a district court’s jury charge, those instructions are subject to review only for plain error. See United States v. Nouri, 711 F.3d 129, 138 (2d Cir.2013); see also Marcus, 130 S.Ct. at 2164 (explaining plain error standard); Part I.A., ante (same).

A. Securities Fraud (Counts Two and Three)

First, Vilar and Tanaka protest the District Court’s refusal to instruct the jury that, to prove a violation of Section 10(b) and Rule 10b-5, “the government must prove beyond all reasonable doubt that the alleged victim did in fact rely upon the alleged device, scheme, or practice in purchasing or selling shares of the alleged listed securities.” Gov’t Supp. App’x 53. Reliance, however, is not an element of a criminal case brought by the government under Section 10(b) or Rule 10b-5. Accordingly, the District Court did not err in deciding not to issue this charge.

To prevail in a civil case under Section 10(b) and Rule 10b-5, the government must “prove that in connection with the purchase or sale of a security the defen-, dant, acting with scienter, made a material misrepresentation (or a material omission if the defendant had a duty to speak) or used a fraudulent device.” VanCook v. SEC, 653 F.3d 130, 138 (2d Cir.2011). In order to impose criminal liability, the government must- also prove that the defendant willfully violated the law. 15 U.S.C. § 78ff(a); see also O’Hagan, 521 U.S. at 665-66, 117 S.Ct. 2199; note 7, ante.

Conspicuously absent from this list of elements is “reliance.” Indeed, it has long been the law that the government, as opposed to a private plaintiff, need prove only materiality, meaning that “there is a substantial likelihood that a reasonable investor would find [the omission or misrepresentation] important in making an investment decision,” United States v. Contorinis, 692 F.3d 136, 143 (2d Cir.2012), and not that a victim did, in fact, rely on it. See SEC v. Apuzzo, 689 F.3d 204, 213 (2d Cir.2012) (“Thus, while a plaintiff must prove reliance ... in a private securities fraud suit, there is no such requirement in an SEC enforcement action.”) (internal citation omitted); United States v. Gleason, 616 F.2d 2, 28 (2d Cir.1979) (relying on SEC v. Texas Gulf Sulphur Co., 401 F.2d 833, 860 (2d Cir. 1968)). That is because, as explained earlier, see Part I.B.l.ii, ante, reliance is relevant only to the identification of the private persons entitled to bring suit. See Cent. Bank of Denver, N.A., 511 U.S. at 173, 114 S.Ct. 1439; see also United States v. Marino, 654 F.3d 310, 320 (2d Cir.2011) (noting that reliance is “required in a private Rule 10b-5 action” (emphásis supplied)).

Despite Vilar and Tanaka’s argument to the contrary—which is’ based on language from a non-precedential summary order, see United States v. Schlisser, 168 Fed.Appx. 483, 486 (2d Cir.2006)—the long-established law of our Circuit, and nearly every other circuit, is that, when the government (as opposed to a private plaintiff) brings a civil or criminal action under Section 10(b) and Rule 10b-5, it need only prove, in addition to scienter, materiality, meaning a substantial likelihood that a reasonable investor would find the omission or misrepresentation important in making an investment decision, and not actual reliance.

The explanation for this discrepancy, as the Supreme Court explained in the context of mail fraud, is that because the statute prohibits “the ‘scheme to defraud,’ rather than the completed fraud, [inferring] the elements of reliance and damage would clearly be inconsistent with the statutes Congress enacted.” Neder v. United States, 527 U.S. 1, 24-25, 119 S.Ct. 1827, 144 L.Ed.2d 35 (1999); see also SEC v. N. Am. Research & Dev. Corp., 424 F.2d 63, 84-85 (2d Cir.1970). Accordingly, we find no error in the District Court’s refusal to instruct the jury on reliance.

B. Mail Fraud (Count Five)

Second, Vilar alone argues that the District Court’s instructions concerning mail fraud “lowered the government’s burden of proof,” and were therefore erroneous. Vilar Br. 150. The indictment alleged a single act giving rise to the mail fraud count: that Vilar and Tanaka “sent and caused to be sent and delivered via a private and commercial interstate carrier a false and fraudulent account statement from London, England,” to Lily Cates in New York. Tanaka App’x 117. When instructing the jury, the District Court repeated this allegation verbatim, Trial Tr. 5589, but went on to state that, “[i]nciden-tally, the mailed letter need not itself be fraudulenta f]or example, the mailed matter need not contain any fraudulent representations, and indeed may be completely innocent,” id. at 5594.

The government responds that this instruction contains no error because it is accurate—the mailing itself need not contain false information for a defendant to commit fraud by mail. See, e.g., Schmuck v. United States, 489 U.S. 705, 715, 109 S.Ct. 1443, 103 L.Ed.2d 734 (1989) (explaining that “ ‘innocent’ mailings—ones that contain no false information—may supply the mailing element”). Though correct as to the law, the government’s answer misunderstands the nature of Vilar’s objection. In substance, Vilar claims that the jury charge constructively amended the indictment because the indictment charged that Vilar sent a specific false account statement, but the District Court’s instruction permitted the jury to convict based on an accurate account statement sent in support of a scheme to defraud.

As stated earlier, see Part II, ante, an indictment is constructively amended when “the terms of the indictment are in effect altered by the presentation of evidence and jury instructions which so modify essential elements of the offense charged that there is a substantial likelihood that the defendant may have been convicted of an offense other than that charged in the indictment.” D’Amelio, 683 F.3d at 416 (internal quotation marks omitted; emphasis in original). “Although constructive amendment is viewed as a per se violation of the Grand Jury Clause, sufficient to secure relief without any showing of prejudice, this court has proceeded cautiously in identifying such error, consistently permitting significant flexibility in proof, provided that the defendant was given notice of the core of criminality to be proven at trial.” United States v. Agrawal, 726 F.3d 235, 259-60 (2d Cir.2013) (internal quotation marks and brackets omitted).

The dispositive question is whether the District Court’s instruction affected the “core of criminality.” We recently tried to clarify this phrase in United States v. D Amelio, where we described it as “the essence of a crime,” not “the particulars of how a defendant effected the crime.” 683 F.3d at 418. Relying on Stirone v. United States, 361 U.S. 212, 80 S.Ct. 270, 4 L.Ed.2d 252 (1960), and our prior holdings, we explained that the distinction between a constructive amendment and a permissible variation in the government’s proof “lies in whether the jury convicted based on a complex of facts distinctly different from that which the grand jury set forth in the indictment, or whether the indictment charged a single set of discrete facts from which the government’s proof was at most a non-prejudicial variance.” D'Amelio, 683 F.3d at 419 (internal quotation marks and citation omitted).

In D Amelio, the government charged the defendant with enticing a minor using a computer and the Internet. Id. at 414. The core of his criminality was his enticement of a minor, which “did not encompass a specific facility and a specific means of interstate commerce employed by [the defendant] in connection with the crime.” Id. at 421. Accordingly, we held that the indictment was not constructively amended when the district court instructed the jurors that they could convict if the defendant used the Internet or telephone. See id. at 421-22. We explained that the government’s proof and the jury instructions did not “supportf ] a theory ... that was distinctly different from the one charged,” because the variance from the indictment would not have caused the defendant to be surprised by the introduction “of different and unrelated proof adduced at trial,” and because the differences between the indictment and proof were not “extreme.” Id. at 421. Put another way, the defendant in D Amelio was convicted of the very enticement of a minor he was charged with, even if the district court permitted the jury to find that the means of enticement was a telephone instead of a computer.

Guided by these principles, we conclude that the jury instructions of Judge Sullivan did not impermissibly amend the mail fraud count or improperly broaden the basis for Vilar’s conviction on that count. In cases where the crime charged concerns the making of false statements, we have described the “core of criminality” as “knowingly making false statements.” United States v. Bernstein, 533 F.2d 775, 787 (2d Cir.1976); see also United States v. Sindona, 636 F.2d 792, 797 (2d Cir.1980). A fair reading of the mail fraud count, which incorporated the previous allegations in the indictment, makes clear that the scheme to defraud consisted of inducing Cates to transfer funds to Amerindo by misrepresenting the nature and quality of the SBIC investment. These were the false statements that Vilar knowingly made, and it was his mailing in support of this scheme that constituted the essential element of the mail fraud. It was, therefore, entirely unnecessary for the government also to prove that the account statement itself was false, and it has long been held that it is no constructive amendment “to drop from an indictment those allegations that are unnecessary to an offense that is clearly contained within it....” Miller, 471 U.S. at 144, 105 S.Ct. 1811; see also United States v. Rosenthal, 9 F.3d 1016, 1023 (2d Cir.1993) (“While it is the Government’s burden to prove the essential elements of a charged crime, allegations in an indictment that go beyond the essential elements which are required for conviction do not increase the Government’s burden.”).

Accordingly, we do not understand the jury instructions as “supporting] a theory ... that was distinctly different from the one charged,” nor do we think that Vilar would have been surprised by the introduction “of different and unrelated proof adduced at trial.” D'Amelio, 683 F.3d at 421. Indeed, the mailing specified in the indictment was the very mailing for which Vilar was convicted. In other words, the indictment informed the defendant as to the specific time and place of the criminal conduct for which he could be held liable, such that the “core of criminality” was clear. See, e.g., United States v. Danielson, 199 F.3d 666, 670 (2d Cir.1999); United States v. Knuckles, 581 F.2d 305, 312 (2d Cir.1978). For these reasons, the indictment “fairly inform[ed the] defendant of the charge against which he [had to] defend,” and was not constructively amended. United States v. Resendiz-Ponce, 549 U.S. 102, 108, 127 S.Ct. 782, 166 L.Ed.2d 591 (2007).

V. Sufficiency of the Evidence

The defendants advance a legion of challenges to the sufficiency of the evidence marshaled against them at trial. Although we review sufficiency challenges de novo, United States v. Desposito, 704 F.3d 221, 226 (2d Cir.2013), 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,” United States v. Chavez, 549 F.3d 119, 124 (2d Cir.2008) (internal citations, alterations and quotation marks omitted). “[A] defendant challenging the sufficiency of the evidence that led to his conviction at trial bears a heavy burden,” Coplan, 703 F.3d at 62 (internal quotation marks omitted), because we must uphold the judgment of conviction if “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). We consider in turn the claims of insufficiency as to each count of conviction.

A. Conspiracy (Count One)

Count One charged the defendants with conspiring to (1) carry out the GFRDA scheme, and (2) cover up the collapse of the GFRDAs by paying off GFRDA investors with money taken from Lily Cates through the SBIC scheme. Vilar and Ta-naka contend that the evidence introduced at trial was insufficient to support a finding of a single conspiracy. Instead, according to Vilar and Tanaka, the evidence at most proved the existence of two smaller conspiracies to defraud—one to sell the GFRDAs and a separate conspiracy to conceal the earlier fraud.

Vilar and Tanaka’s argument was not persuasive for “duplicity” purposes, see Part II, ante, and it is not persuasive from a sufficiency-of-the-evidence standpoint either. In short, sufficient evidence supports the jury’s finding that a single conspiracy existed here. See United States v. Eppolito, 543 F.3d 25, 48 (2d Cir.2008) (“[A] single conspiracy is not transformed into multiple conspiracies merely by virtue of the fact that it may involve two or more phases or spheres of operation, so long as there is sufficient proof of mutual dependence and assistance.”). Most notably, the evidence demonstrates that Cates’s money was transferred at the same time that Vilar and Tanaka settled debts arising from the GFRDA scheme. See Trial Tr. 4129-35; Gov’t Supp. App’x 742-52, 883. Based on the evidence put forth at trial, a rational juror could have found that Vilar and Tanaka entered into a conspiracy in 1986 with the objective of defrauding customers by causing them to believe that GFRDAs were safe and liquid investments. The specific methods they used may have evolved, but the objective of the conspiracy remained the same.

B. Securities Fraud (Counts Two and Three)

As set out at length above, see Part IV.A, to convict a defendant of securities fraud under Section 10(b) and Rule lob-5, the government must prove that in connection with a domestic purchase or sale of a security the defendant willfully made a material misrepresentation (or a material omission if the defendant had a duty to speak) or used a fraudulent device. See 15 U.S.C. §§ 78j (b), 78ff(a); 17 C.F.R. § 240.10b-5; see also O’Ha-gan, 521 U.S. at 665-66, 117 S.Ct. 2199; VanCook, 653 F.3d at 138. A misrepresentation or omission is material “when there is a substantial likelihood that a reasonable investor would find [the omission or misrepresentation] important in making an investment decision.” Conto-rinis, 692 F.3d at 143.

1. The SBIC Fraud (Count Two)

Vilar alone contends that the evidence is insufficient to support his conviction relating to the SBIC fraud because there is inadequate evidence (1) that he conveyed any misrepresentation to Lily Cates; (2) that he intended to steal from Lily Cates; and (3) that he used the mails or instru-mentalities of interstate commerce in connection with Cates’s SBIC purchase. We need not dwell long on these claims.

The record contains more than enough evidence for a reasonable juror to find, beyond a reasonable doubt, that Vilar lied to Cates about the nature of her SBIC investment, and in particular about the status of the SBIC license. Most notably, Cates testified to these exact facts. See Trial Tr. 2100-02. Although Vilar attempts to discredit her testimony as “unclear,” Vilar Br. 76, and “disjointed,” id. at 80, her testimony was clear enough to permit the jury to credit it and rely on her account of what happened.

Vilar next declares that his conviction is invalid because the evidence does not demonstrate that he intended to “steal” from Cates. Id. at 83. This argument misses the mark because the government was under no obligation to prove that he wanted to steal Cates’s money, only that he intended to defraud her in connection with his sale of the SBIC investment. See United States v. Kelley, 551 F.3d 171, 175-76 (2d Cir.2009); cf. SEC v. Obus, 693 F.3d 276, 286 (2d Cir.2012) (explaining that scienter under Section 10(b) is “defined as ‘a mental state embracing intent to deceive, manipulate, or defraud’ ” (quoting Ernst & Ernst v. Hochfelder, 425 U.S. 185, 193 & n. 12, 96 S.Ct. 1375, 47 L.Ed.2d 668 (1976))). There is no doubt that there was sufficient evidence of this intent to support the jury’s verdict. See, e.g., Trial Tr. 2101 (testimony of Lily Cates indicated that Vilar told her that the SBIC license was “already done”).

Finally, Vilar contends that the evidence of his use of the mails or an instrumentality of interstate commerce was insufficient to support his conviction. He claims that Cates’s transfer of $5 million to purchase her SBIC investment “was made not by wire or mailing a check, but via a journal entry, a back-office accounting maneuver executed by the Bear Stearns’ New York Office.... ” Vilar Br. 90-91. Even if Vilar were correct that Cates did not use the mails or an instrumentality of interstate commerce to transfer the money, that would have little bearing on the numerous other occasions that Vilar did use the mails and wire transfers to carry out his scheme. See, e.g., Gov’t Supp. App’x 615-17 (letter faxed to Lily Cates stating, inter alia, that Vilar was “very proud of securing” funds from the Small Business Administration and that “we can all go on to make a killing in the SBA Fund”). The jury’s verdict as to Count Two was therefore fully supported by the evidence.

2. The GFRDA Fraud (Count Three)

Vilar and Tanaka argue that the government did not prove that the GFRDA victims invested based on the fraudulent terms contained in the offering memoran-da and circulars because it failed to prove that those documents were in fact sent to GFRDA investors. Vilar and Tanaka suggest that any misrepresentations contained in the offering memoranda and circulars could not, therefore, have been material, inasmuch as no investor could find information of which they were not aware to be important to their investment decision.

This argument fails because it ignores all of the documents containing the same misrepresentations that clearly were received by the Mayers and Lecube-Chavez. Even if we assume that the government did not introduce evidence from which a reasonable juror could infer that the investors received the offering memoranda and circulars, the government introduced other documents that unmistakably conveyed to the investors specific, false representations concerning the investment mix backing the GFRDAs. See, e.g., Gov’t Supp. App’x 878 (1987 letter to Mayer family setting out GFRDA investment ratios). Vilar and Tanaka’s argument also ignores the direct testimony of Lisa Mayer and Graciela Lecube-Chavez. As described at length above, see Part I.B.2, the government offered sufficient evidence for a rational juror to find beyond a reasonable doubt that the defendants made material misrepresentations in connection with the sale of the GFRDAs.

C. Investment Adviser Fraud (Count Four)

The defendants challenge the sufficiency of the government’s evidence on the investment adviser fraud count on two grounds: first, that Amerindo was not an investment adviser within the meaning of the statute because it did not charge fees for its services; and second, that there was insufficient proof of a mailing or use of an instrumentality of interstate commerce. These claims are wholly without merit. First, a letter from Vilar to Cates’s attorney in 2004 discussed fees that would be due to Amerindo. See Gov’t Supp. App’x 708-09. Although the letter did not specify that the fees were for Amerindo’s investment advisory services, the jury could reasonably have inferred that fact. Second, it is clear from the record that numerous communications with Cates, including the solicitation of her investment into the fraudulent SBIC account, were conducted using the mails and telephones. See, e.g., id. at 755-57. The evidence therefore was sufficient to support the jury’s verdict as to the investment adviser fraud count.

D. Wire Fraud (Counts Six and Seven)

In order to prove wire fraud, “the government must establish the existence of a scheme to defraud, that money or property were the object of the scheme, and that defendant used interstate wires in furtherance of that scheme.” United States v. Guadagna, 183 F.3d 122, 129 (2d Cir.1999). Vilar challenges his wire fraud convictions on the basis that the wire transfers at issue, by which Cates’s money was transferred from Amerindo’s account to Vilar’s account, occurred after Cates had transferred her $5 million to the SBIC fund. Vilar argues that these wire transfers cannot satisfy the “in furtherance” requirement because the scheme was complete once Amerindo obtained the funds.

The fact that the wire transactions at issue occurred after Cates had transferred the funds to the SBIC account is irrelevant. As we have explained, “[a] scheme to defraud is not complete until the proceeds have been received and use of the mail or wires to obtain the proceeds satisfies the jurisdictional element,” which is to say that the jurisdictional element is fulfilled when the defendant uses the mail or wires to convert the money to his own use. Sindona, 636 F.2d at 802 (relying on Pereira v. United States, 347 U.S. 1, 7-9, 74 S.Ct. 358, 98 L.Ed. 435 (1954)). Inasmuch as Vilar used the wire transfers to send the money to his own account, the wire transfers were undoubtedly in furtherance of the scheme to defraud.

E. Money Laundering (Counts Eight, Nine, Ten, and Eleven)

In order to prove that a defendant has committed the crime of money laundering under 18 U.S.C. § 1957(a), the government must “present evidence that the defendant knowingly engaged or attempted to engage in a monetary transaction in unlawful funds.” United States v. Ness, 565 F.3d 73, 78 (2d Cir.2009). Vilar argues that the government has proved neither that he knowingly initiated or agreed to the transfers of Cates’s money from Amerindo’s account to his own account, nor that he knew that the funds were unlawful.

Both of these claims are belied by the sequence of events in this case. As we have already confirmed, the evidence at trial demonstrated that Vilar knowingly and willfully defrauded Cates of millions of dollars by lying to her about the nature of the SBIC investment opportunity. Based on these misrepresentations, Cates transferred her money to an Amerindo account that was previously empty. Immediately thereafter, hundreds of thousands of these dollars were transferred to Vilar’s own account. Based on the evidence of these transfers and their timing, a rational juror could conclude that Vilar knew of the criminal scheme and of the origin of the funds. Accordingly, Vilar’s insufficiency claims as to money laundering are meritless.

VI. Sentencing

Vilar and Tanaka argue that their sentences must be vacated due to errors in the calculation of (1) loss caused by the offense, (2) restitution, and (3) forfeiture. As with any sentencing claim, when considering a challenge to the calculation of loss amount, “[w]e review legal conclusions, such as interpretations of the Guidelines, de novo and findings of fact for clear error.” United States v. Lacey, 699 F.3d 710, 717 (2d Cir.2012). Accordingly, we are “obliged to determine whether the trial court’s method of calculating the amount of loss was legally acceptable,” but we will not disturb a district court’s “reasonable estimate of the loss, given the available information.” United States v. Turk, 626 F.3d 743, 748 (2d Cir.2010) (internal quotation marks and ellipsis omitted). The same standard applies to review of forfeiture determinations. See United States v. Gaskin, 364 F.3d 438, 461-62 (2d Cir.2004). Restitution orders under the Mandatory Victim Restitution Act (“MVRA”), 18 U.S.C. §§ 3663A-3664, are reviewed for “abuse of discretion,” which occurs when the decision rests on an error of law, clearly erroneous finding of fact, or otherwise cannot be located within the range of permissible decisions. See United States v. Zangari, 677 F.3d 86, 91 (2d Cir.2012); see also In re Sims, 534 F.3d at 132. For the following reasons, we agree with Vilar and Tanaka that the cause must be remanded for resentencing.

First, the calculation of the applicable sentencing guidelines must derive from the losses resulting from or intended to result from the criminal “offense.” United States Sentencing Guidelines Manual (“U.S.S.G.”) § 2B1.1 cmt. n.3(A). The District Court calculated the loss caused by Vilar and Tanaka’s scheme to be between $20 million and $50 million, resulting in a twenty-two-level sentencing enhancement. Tanaka App’x 805-06. This finding was based on the losses suffered by Lily Cates, the Mayer family, and Lecube-Chavez, as well as other victims who may have purchased GFRDAs abroad. See id.

As we explained in Part I, ante, conduct in connection with extraterritorial transactions in securities does not constitute an offense under Section 10(b) or Rule 10b-5. However, the parties have not briefed, and the District Court has not had an opportunity to consider, the question of whether losses suffered by victims who purchased GFRDAs abroad may constitute “relevant conduct” under U.S.S.G. §§ lB1.3(a)(l), 2Bl.l(b). Accordingly, we leave it to the District Court to consider this question in the first instance on remand.

Second, the District Court must recalculate restitution. The MVRA requires district courts to order defendants to make restitutions to their victims. 18 U.S.C. § 3663A(a)(l). A “victim” refers to a “person directly and proximately harmed as a result of the commission of an offense for which restitution may be ordered including, in the case of an offense that involves as an element a scheme, conspiracy, or pattern of criminal activity, any person directly harmed by the defendant’s criminal conduct in the course of the scheme, conspiracy, or pattern.” Id. § 3663A(a)(2).

The MVRA’s definition of “victim” reflects an important limiting principle for restitution awards—namely, that Congress has “authorize[d] an award of restitution only for the loss caused by the specific conduct that is the basis of the offense of conviction.” Hughey v. United States, 495 U.S. 411, 413, 110 S.Ct. 1979, 109 L.Ed.2d 408 (1990). As we have previously explained, restitution is not permitted for loss caused by “relevant conduct,” even though such conduct may be “properly included in offense level calculation” under the Sentencing Guidelines. United States v. Lussier, 104 F.3d 32, 33 (2d Cir.1997). It follows, therefore, that the District Court cannot order restitution for investors who purchased GFRDAs abroad, since those investors are not victims of the offense. Accordingly, the District Court must vacate the restitution award and proceed to recalculate restitution with respect to victims who have been “directly harmed by the defendant’s criminal conduct.” 18 U.S.C. § 3663A(a)(2).

Third, we must remand with instructions to vacate the forfeiture order because, as the government concedes and the District Court itself has confessed, due to arithmetical mistakes, the calculation of the final forfeiture amount was clearly erroneous.

In sum, we remand the cause to the District Court with directions to vacate the sentences of Vilar and Tanaka, and to proceed to resentence the defendants in terms consistent with this opinion.

VII. Ineffective Assistance of Counsel

Finally, Vilar contends that his trial counsel was constitutionally ineffective, laying an extensive list of missteps and failures at the feet of his former attorney. Among other things, Vilar charges his trial counsel with (1) inadequate review of discovery; (2) inadequate development of defenses; (3) failure to cross-examine witnesses; (4) failure to advocate for his client in his summation; and (5) failure to challenge the forfeiture order.

We have three options for dealing with a claim for ineffective assistance of counsel raised on direct appeal: We may “(1) decline to hear the claim, permitting the appellant to raise the issue as part of a subsequent petition for writ of habeas corpus pursuant to 28 U.S.C. § 2255; (2) remand the claim to the district court for necessary factfinding; or (3) decide the claim on the record before us.” United States v. Ramos, 677 F.3d 124, 129 (2d Cir.2012) (internal quotation marks omitted). The Supreme Court has indicated that “in most cases a motion brought under § 2255 is preferable to direct appeal for deciding claims of ineffective assistance,” Massaro v. United States, 538 U.S. 500, 504, 123 S.Ct. 1690, 155 L.Ed.2d 714 (2003), and we have expressed our own “baseline aversion to resolving ineffectiveness claims on direct review,” Ramos, 677 F.3d at 130 (internal quotation marks omitted). Particularly in view of the complexity of this case and the absence of any comment from Vilar’s attorney, see Sparman v. Edwards, 154 F.3d 51, 52 (2d Cir.1998), we think it unwise to consider an ineffective assistance claim on direct review. Vilar may pursue this claim, if he chooses, in a subsequent § 2255 petition.

CONCLUSION

To summarize, we hold that:

(1) Section 10(b) and Rule 10b-5 do not apply to extraterritorial conduct, regardless of whether liability is sought criminally or civilly. Accordingly, a defendant may be convicted of securities fraud under Section 10(b) and Rule 10b-5 only if he has engaged in fraud in connection with (1) a security listed on an American exchange, or (2) a security purchased or sold in the United States.
(2) Although the District Court erred by failing to require proof of domestic securities transactions, that error was not “plain,” because the evidence in the record demonstrated that Vilar and Tanaka engaged in fraud in connection with a domestic purchase or sale of securities, and therefore, the error did not affect the outcome of the proceedings or affect Vilar and Tanaka’s substantial rights.
(3) The indictment was sufficient. In particular, Count One of the indictment was not “duplicitous” because it charged a single scheme to defraud, and Count Four of the indictment was sufficiently pleaded, insofar as it informed Vilar and Tanaka of the charges to be met and enabled them to plead double jeopardy in the future.
(4) The District Court properly admitted evidence obtained during the U.S. and U.K. searches. First, the District Court correctly concluded that documents obtained from defendants’ office in the United States were admissible pursuant to the “inevitable discovery” doctrine. Second, the U.K. search was reasonable, and therefore, the evidence obtained was properly admitted because evidence obtained in a search by the U.S. government in another country is admissible so long as the search was “reasonable” under the Fourth Amendment.
(5) In a prosecution brought by the government for securities fraud under Section 10(b) or Rule 10b-5, the government does not need to prove that the victims of a scheme to defraud actually relied on the material misrepresentation or omission. Accordingly, the District Court did not err by not instructing the jury on reliance.
(6) Although the mail fraud charge in the indictment specified that the mailing itself was false or fraudulent, the District Court’s instruction permitting the jury to convict based on a mailing that contained no false or fraudulent statement did not “constructively amend” the indictment.
(7) Under the Mandatory Victim Restitution Act, restitution is not permitted for investors who purchased securities abroad, inasmuch as those investors are not victims of an offense under Section 10(b) or 10b-5.
(8) The District Court must, on remand, determine what acts constitute offense conduct for the purposes of calculating loss amount at sentencing, as well as the amount subject to forfeiture.
(9) With the exception of Vilar’s ineffective assistance of counsel claim, which we do not reach, Vilar and Tanaka’s remaining claims are without merit.

The February 8, 2010, and February 10, 2010 judgments of conviction of the District Court are AFFIRMED in all respects, except for the sentences; and the cause is REMANDED to the District Court with instructions to vacate both sentences and proceed to a de novo resentenc-ing consistent with this opinion. 
      
      . The text of Section 10(b), 15 U.S.C. § 78j(b), and of Rule 10b-5, 17 C.F.R. § 240.10b-5, may be found at Note 6, post.
      
     
      
      . Because Vilar and Tanaka appeal from judgments of conviction entered after a jury trial, we draw the facts from the evidence presented at trial, viewed in the light most favorable to the government. See, e.g., Parker v. Matthews, - U.S. -, 132 S.Ct. 2148, 2152, 183 L.Ed.2d 32 (2012); United States v. Rosen, 716 F.3d 691, 694 (2d Cir.2013).
     
      
      . Throughout this opinion we refer generically to Vilar and Tanaka's various joint ventures as "Amerindo.”
     
      
      . The SEC also proceeded against Vilar and Tanaka in a separate civil action. See SEC v. Amerindo Inv. Advisors, Inc., No. 05 Civ. 5231(RJS) (S.D.N.Y. filed June 1, 2005).
     
      
      . We note, as we have many times before, that, prior to the Supreme Court's decision in Johnson, we employed a "modified” plain error analysis when addressing a claimed error that resulted from a supervening legal decision. In those cases, we placed the burden on the government to demonstrate that the error did not affect the defendant’s substantial rights, rather than requiring the defendant to show that it did. See United States v. Needham, 604 F.3d 673, 678 (2d Cir.2010). We have also observed that "it is unclear whether this standard remains in force following the Supreme Court’s decision in Johnson," id., but on at least twenty-two occasions in published decisions, which we refrain from citing on grounds of tedium, we have declined to resolve this question because its answer has never affected the result in any case, see, e.g., United States v. Botti, 711 F.3d 299, 308-10 (2d Cir.2013). Not surprisingly, we have no reason to address the parties' arguments on this issue in this case, as it would have no effect on our decision. Indeed, we cannot help but be skeptical that the allocation of the burden of demonstrating harm will ever be dispositive in this context. We simply add our voice to the chorus of those who warn of this snare in our jurisprudence.
     
      
      . Section 10(b) provides:
      It shall be unlawful for any person, directly or indirectly, by the use of any means or instrumentality of interstate commerce or of the mails, or of any facility of any national securities exchange.... [t]o use or employ, in connection with the purchase or sale of any security registered on a national securities exchange or any security not so registered, or any securities-based swap agreement^] any manipulative or deceptive device or contrivance in contravention of such rules and regulations as the [SEC] may prescribe as necessary or appropriate in the public interest or for the protection of investors.
      15 U.S.C. § 78j(b). Rule 10b-5, which was promulgated pursuant to Section 10(b), provides:
      It shall be unlawful for any person, directly or indirectly, by the use of any means or instrumentality of interstate commerce, or of the mails or of any facility of any national securities exchange,
      (a) To employ any device, scheme, or artifice to defraud,
      (b) To make any untrue statement of a material fact or to omit to state a material fact necessary in order to make the statements made, in the light of the circumstances under which they were made, not misleading, or
      (c) To engage in any act, practice, or course of business which operates or would operate as a fraud or deceit upon any person,
      in connection with the purchase or sale of any security.
      17 C.F.R. § 240.10b-5.
     
      
      . Specifically, Section 32 provides that “[a]ny person who willfully violates any provision of this chapter ..., or any rule or regulation thereunder the violation of which is made unlawful or the observance of which is required under the terms of this chapter” may, upon conviction, be subject to a fine and sentence of imprisonment. 15 U.S.C. § 78ff(a). However, "no person shall be subject to imprisonment under this section for the violation of any rule or regulation if he proves that he had no knowledge of such rule or regulation.” Id.
      
     
      
      . Although the government does observe that "[t]he GFRDA purported to invest in and, in fact, did invest in numerous securities traded in the U.S. markets,” Gov’t Br. 101-02, it provides no legal argument whatsoever for why this fact would render the GFRDA a domestic security within the meaning of Morrison. Accordingly, we deem this claim waived. See, e.g., Viacom Int’l, Inc. v. You-Tube, Inc., 676 F.3d 19, 40 n. 14 (2d Cir.2012) (holding that a "one-sentence argument is insufficient to raise [an] issue for review before this Court” because " ‘[i]ssues not sufficiently argued in the briefs are considered waived and normally will not be addressed on appeal’ ”) (quoting Norton v. Sam’s Club, 145 F.3d 114, 117 (2d Cir.1998)).
     
      
      . Although we presume that Congress did not intend to apply Section 10(b) to extraterritorial conduct, we also presume that Congress did intend to apply Section 10(b) to security transactions occurring in Puerto Rico, since, as the First Circuit has explained, "the default rule presumes the applicability of federal laws to Puerto Rico.” United States v. Acosta-Martinez, 252 F.3d 13, 20 (1st Cir.2001). By statute, the First Circuit reviewed decisions of the Supreme Court of Puerto Rico from 1915 until 1961 and was, absent appeal to the Supreme Court, the final arbiter of the law of Puerto Rico for fifty-six years. See Act of Jan. 28, 1915, Pub.L. No. 63-241, 38 Stat. 803, 803-04 (1915) (providing for appellate jurisdiction in the First Circuit to review final judgments of the Supreme Court of Puerto Rico); Act of Aug. 30, 1961, Pub.L. No. 87-189, 75 Stat. 417, 417 (1961) (withdrawing the same jurisdiction). In light of this historical relationship, the law of the First Circuit has an especially compelling persuasiveness when it comes to the interplay between federal law and the law of Puerto Rico. See United States v. Laboy-Torres, 553 F.3d 715, 719 n. 3 (3d Cir.2009) (according the First Circuit's decisions "great weight” due to its "expertise with Puerto Rican law").
     
      
      . The government also contends that the relevant securities transaction were domestic because (1) “the GFRDA was marketed and sold to customers based in the United States,” and (2) "[(Investors were directed to wire funds to a New York bank, and the custodian of the fund was a New York securities firm.” Gov’t Br. 101. However, we have already held that, assuming such facts to be true, they are insufficient to demonstrate a purchase or sale of a security in the United States for the purposes of Section 10(b). See Absolute Activist, 677 F.3d at 70.
     
      
      . We are aware that in his recent Memorandum and Order granting summary judgment in part to the SEC in the parallel civil action against Vilar and Tanaka, Judge Sullivan declined to grant summary judgment to the SEC on its claim for securities fraud upon the Mayers. Judge Sullivan held that there was a genuine issue of material fact as to whether the Mayers became irrevocably bound in the United States because Vilar may have sent an offer letter from abroad and, arguably, under Puerto Rico law, a contract agreed to by mail " ‘is presumed as executed at the place where the offer was made.’ ” SEC v. Amerindo Inv. Advisors, Inc., No. 05 Civ. 5231(RJS), 2013 WL 1385013, at *7 (S.D.N.Y. Mar. 11, 2013) (quoting 31 L.P.R.A. § 3401). We are not persuaded by Judge Sullivan’s reasoning in the parallel civil action because we do not see how the law of a state or territory governing the place of contract bears on the question, under federal law, of whether "a manipulative or deceptive device or contrivance” was employed "in connection with ... the purchase or sale of any ... security in the United States.” Morrison, 130 S.Ct. at 2888. That question is answered by determining whether "the purchaser incurred irrevocable liability within the United States to take and pay for a security, or ... the seller incurred irrevocable liability within the United States to deliver a security.” Absolute Activist, 677 F.3d at 68. In other words, territoriality under Morrison concerns where, physically, the purchaser or seller committed him or herself, not where, as a matter of law, a contract is said to have been executed. See Morrison, 130 S.Ct. at 2885 (noting that “it is the foreign location of the transaction that establishes (or reflects the presumption of) the Act’s inapplicability” (emphasis in original)).
      We also observe, in passing, that Judge Sullivan did grant summary judgment to the SEC as to the security fraud claims relating to Lecube-Chavez and several other investors in the GFRDA program, as well as Lily Cates, holding that the undisputed facts demonstrated that those investors incurred irrevocable liability in the United States. See Amerindo Inv. Advisors, 2013 WL 1385013, at *6-8.
     
      
      . Vilar and Tanaka argue that, even if some victims purchased securities within the United States, "evidence showed that purchases and sales of GFRDA were deliberately and carefully structured to occur outside the United States.” Vilar Reply 6. In other words, Vilar and Tanaka argue that their very intention to evade U.S. law is evidence of their innocence. We see no reason to rescue fraudsters when they complain that their perfect scheme to avoid getting caught has failed. Morrison is straightforward: When a securities transaction takes place in the United States, it is subject to regulation under Section 10(b), and when a securities transaction takes place abroad, it is not. The parties' intention to engage in foreign transactions is entirely irrelevant.
     
      
      . Federal Rule of Criminal Procedure 8(a) provides:
      Joinder of Offenses. The indictment or information may charge a defendant in separate counts with 2 or more offenses if the offenses charged—whether felonies or misdemeanors or both—are of the same or similar character, or are based on the same act or transaction, or are connected with or constitute parts of a common scheme or plan.
     
      
      . In a related vein, there was no error in the District Court’s decision not to use a multiple conspiracy jury instruction. It is true that "[i]f the evidence at trial supports an inference that there was more than one conspiracy, then, whether multiple conspiracies existed is a question of fact for the jury.” United States v. Vazquez, 113 F.3d 383, 386 (2d Cir.1997). However, "[i]n order to secure a reversal on the ground that the court failed to give a multiple conspiracy charge, a defendant must prove there were two or more groups operating separately from one another, although membership in the groups might overlap, and that failure to give the requested charge prejudiced defendant.” Id. (internal citation omitted). Vilar and Tanaka have shown neither that there were two or more groups operating separately from one another, nor that they were prejudiced by the lack of a multiple conspiracy instruction, since "there was ample proof before the jury for it to find beyond a reasonable doubt that defendant was a member of the conspiracy charged in the indictment.” Id.
      
     
      
      . We note that Vilar and Tanaka did not challenge the sufficiency of the Indictment with regard to Count Four until trial had begun. Where the sufficiency of the indictment is not challenged until trial, "the sufficiency of an indictment should be interpreted liberally in favor of sufficiency.” United States v. Sabbeth, 262 F.3d 207, 218 (2d Cir.2001).
     
      
      .In full, Rule 7(c)(1) provides:
      In General. The indictment or information must be a plain, concise, and definite written statement of the essential facts constituting the offense charged and must be signed by an attorney for the government. It need not contain a formal introduction or conclusion. A count may incorporate by reference an allegation made in another count. A count may allege that the means by which the defendant committed the offense are unknown or that the defendant committed it by one or more specified means. For each count, the indictment or information must give the official or customary citation of the statute, rule, regulation, or other provision of law that the defendant is alleged to have violated. For purposes of an indictment referred to in section 3282 of title 18, United States Code, for which the identity of the defendant is unknown, it shall be sufficient for the indictment to describe the defendant as an individual whose name is unknown, but who has a particular DNA profile, as that term is defined in that section 3282.
     
      
      . Pursuant to the "good faith" exception to the exclusionary rule, "[w]hen police act under a warrant that is invalid for lack of probable cause, the exclusionary rule does not apply if the police acted 'in objectively reasonable reliance’ on the subsequently invalidated search warrant.” Herring v. United States, 555 U.S. 135, 142, 129 S.Ct. 695, 172 L.Ed.2d 496 (2009) (quoting United States v. Leon, 468 U.S. 897, 922, 104 S.Ct. 3405, 82 L.Ed.2d 677 (1984)).
     
      
      . The “inevitable discovery” rule permits unlawfully obtained evidence to be admitted at trial if the government can “establish by a preponderance of the evidence that the information ultimately or inevitably would have been discovered by lawful means.” Nix v. Williams, 467 U.S. 431, 444, 104 S.Ct. 2501, 81 L.Ed.2d 377 (1984).
     
      
      . The "independent source” rule permits the admission of evidence seized pursuant to an unlawful search if that evidence would have been obtained through separate, lawful means. See Murray v. United States, 487 U.S. 533, 537, 108 S.Ct. 2529, 101 L.Ed.2d 472 (1988).
     
      
      . The Mutual Legal Assistance Treaty Between the United States of America and the United Kingdom of Great Britain and Northern Ireland was signed on January 6, 1994. S. Treaty Doc. No. 104-2, 1994 WL 855115. The Treaty provides that the U.S. and U.K. will assist each other in the investigation and prosecution of criminal offenses, including by "executing requests for search and seizures.” Id. at *7.
     
      
      . We note that the government does not contest that the search of the Cadogan Tate warehouse constituted a search by American authorities. If the search was not conducted by the U.S., evidence found would not need to be excluded even if the search was not reasonable because it is "well-established that the Fourth Amendment’s exclusionary rule ... generally does not apply to evidence obtained by searches abroad conducted by foreign officials.” United States v. Lee, 723 F.3d 134, 139 (2d Cir.2013).
     
      
      . Vilar and Tanaka identify three additional supposed errors in the jury instructions: (1) the failure to issue a multiple conspiracies instruction; (2) the failure to require a finding that the events giving rise to the convictions for securities fraud transpired within the statute of limitations; and (3) the failure to require a unanimous finding as to the use of the mails or instrumentality of interstate commerce in furtherance of the securities fraud (Counts Two and Three) and Investment Adviser Fraud (Count Four). We may dispatch these claims in short order.
      First, we have already explained that Vilar and Tanaka have failed to establish that they were entitled to a multiple conspiracies instruction or that the omission of one prejudiced them. See note 14, ante. Second, Vilar and Tanaka did not assert their statute-of-limitations claim before the District Court, and we therefore review it for "plain error.” See United States v. Nouri, 711 F.3d 129, 138 (2d Cir.2013). Even if the omissions described by Vilar and Tanaka were in error—a conclusion we do not reach—they were certainly not plain errors, nor did they affect a substantial right. See Marcus, 130 S.Ct. at 2164. The record contains ample evidence that both the Mayers, see, e.g., Gov’t Supp. App’x 791-92, and Lecube-Chavez, see, e.g., id. at 767-68, invested money in GFRDAs, and that Vilar and Tanaka continued to engage in conduct aimed to reassure investors and prevent them from redeeming their investments within the five-year limitations period, cf. United States v. Scop, 846 F.2d 135, 139 (2d Cir.1988) (holding that “evidence of continued stock purchases and sales at prices affected (or so the jury might find) by the earlier artificial trades, of the mailings of stock certificates, and of the reassurances to customers ... was sufficient to permit a rational jury to conclude that the conspiracy and substantive scheme to defraud continued” into the limitations period). Third, Vi-lar and Tanaka not only failed to raise an objection to the failure explicitly to require a unanimous finding as to the use of the mails or instrumentality of interstate commerce, but they invited such an error (if it was indeed, an error) by proposing jury instructions that required unanimity on certain elements but not on the mail or instrumentality of interstate commerce element. See Gov't Supp. App'x 49-63 (defendants’ proposed jury instructions). Accordingly, we reject this claim on appeal. See United States v. Cherif, 943 F.2d 692, 701 (7th Cir.1991). The same conclusion applies to Tanaka’s contention that the government somehow failed, through the jury instructions as to Count Four, to "mitigate a grave risk” that the jury could have convicted Tanaka for investment adviser fraud for his role in the GFRDA scheme, which was not the conduct underlying that count. Tanaka Br. 57; see also Part II, ante.
      
     
      
      . See, e.g., SEC v. Goble, 682 F.3d 934, 942 (11th Cir.2012); McCann v. Hy-Vee, Inc., 663 F.3d 926, 931-32 (7th Cir.2011); United States v. Jenkins, 633 F.3d 788, 802 (9th Cir.2011); SEC v. Tambone, 597 F.3d 436, 447 n. 9 (1st Cir.2010); SEC v. Pirate Investor LLC, 580 F.3d 233, 239 n. 10 (4th Cir.2009); SEC v. Wolfson, 539 F.3d 1249, 1256 (10th Cir.2008); United States v. Haddy, 134 F.3d 542, 544, 549-51 (3d Cir.1998); SEC v. Blavin, 760 F.2d 706, 711 (6th Cir.1985).
     
      
      . Tanaka was not convicted of mail fraud.
     
      
      . Whether an unpreserved claim of constructive amendment is amenable to plain error review is subject to some debate. See D’Amelio, 683 F.3d at 417 n. 2 (declining to decide whether a constructive amendment determination is subject to plain error review); see also United States v. Vebeliunas, 76 F.3d 1283, 1291 (2d Cir.1996) (applying plain error review to a constructive amendment claim after the defendant conceded that such standard applied). We need not resolve that issue here, however, inasmuch as we conclude that the mail fraud count was not constructively amended by the District Court’s jury instructions.
     
      
      
        . The essential elements of a mail fraud charge are “(1) a scheme to defraud, (2) money or property as the object of the scheme, and (3) use of the mails to further the scheme.” United States v. Litwok, 678 F.3d 208, 213 (2d Cir.2012) (internal quotation marks and ellipsis omitted).
     
      
      . For the text of these provisions, see notes 6 and 7, ante.
      
     
      
      . For additional background on the meaning of “willfully” in Section 32, see United States v. Kaiser, 609 F.3d 556, 568-69 (2d Cir.2010); United States v. Dixon, 536 F.2d 1388, 1396-97 (2d Cir.1976).
     
      
      .Tanaka was not convicted on Count Two.
     
      
      . Vilar and Tanaka also contend that the evidence was insufficient to demonstrate that the GFRDA funds were actually invested in risky technology stocks, and Tanaka argues that the evidence was insufficient to prove his intent to defraud. To the contrary, both of these facts were amply supported by direct testimony or documentary evidence. See, e.g., Gov’t Supp. App’x 538-40 (testimony of Am-erindo employee who booked trades indicating that Tanaka chose which trades to execute and that Amerindo only traded in stocks); id. at 786-87 (GFRDA subscription agreement, signed by Tanaka, specifying that 50-75% of funds would be invested in non-stock, high-quality, short-term investments).
     
      
      . Title 15 U.S.C. § 80b-6 provides:
      It shall be unlawful for any investment adviser, by use of the mails or any means or instrumentality of interstate commerce, directly or indirectly—
      (1) to employ any device, scheme, or artifice to defraud any client or prospective client;
      (2) to engage in any transaction, practice, or course of business which operates as a fraud or deceit upon any client or prospective client;
      (3) acting as principal for his own account, knowingly to sell any security to or purchase any security from a client, or acting as broker for a person other than such client, knowingly to effect any sale or purchase of any security for the account of such client, without disclosing to such client in writing before the completion of such transaction the capacity in which he is acting and obtaining the consent of the client to such transaction. The prohibitions of this paragraph shall not apply to any transaction with a customer of a broker or dealer if such broker or dealer is not acting as an investment adviser in relation to such transaction; or
      (4)to engage in any act, practice, or course of business which is fraudulent, deceptive, or manipulative. The Commission shall, for the purposes of this paragraph (4) by rules and regulations define, and prescribe means reasonably designed to prevent, such acts, practices, and courses of business as are fraudulent, deceptive, or manipulative. An "investment adviser” is defined as “any
      person who, for compensation, engages in the business of advising others, either directly or through publications or writings, as to the value of securities or as to the advisability of investing in, purchasing, or selling securities, or who, for compensation and as part of a regular business, issues or promulgates analy-ses or reports concerning securities.” Id. § 80b-2(a)(ll).
     
      
      . Indeed, the letter specifically refers to "The Investment Management Agreement.” Gov't Supp. App'x 708.
     
      
      . In relevant part, 18 U.S.C. § 1957(a) provides: “Whoever ... knowingly engages or attempts to engage in a monetary transaction in criminally derived property of a value greater than $10,000 and is derived from specified unlawful activity, shall be punished as provided in subsection (b).”
     
      
      . Vilar and Tanaka argue that the amount of actual loss should be zero, because (1) the victims received profits from Amerindo during the course of the scheme, and therefore did not actually lose money; and (2) there is enough money in frozen Amerindo accounts to repay each victim. We disagree because defendants should not benefit from attempting to ensure the continuation of their scheme, see United States v. Carrozzella, 105 F.3d 796, 805 (2d Cir.1997), or from inducing investors to reinvest certain interest payments received, see United States v. Hsu, 669 F.3d 112, 122 (2d Cir.2012).
      Nor should defendants’ liability be reduced by the amount of money available in Amerin-do’s bank accounts, because the relevant sentencing guideline permits a sentencing court to credit a defendant with available funds only when those funds are designated as collateral for the debt owed the victim. See U.S.S.G. § 2B1.1, cmt. n.3(E)(ii) ("In a case involving collateral pledged or otherwise provided by the defendant,” the loss shall be reduced by "the fair market value of the collateral. ...”).
     
      
      . In relevant part, the MVRA provides:
      (a)(1) Notwithstanding any other provision of law, when sentencing a defendant convicted of an offense described in subsection (c), the court shall order, in addition to, or in the case of a misdemeanor, in addition to or in lieu of, any other penalty authorized by law, that the defendant make restitution to the victim of the offense or, if the victim is deceased, to the victim’s estate.
      18 U.S.C. § 3663A(a)(l).
     
      
      . Although Hughey interpreted the provisions of the earlier Victim Witness Protection Act (“VWPA”), the relevant language in the VWPA is nearly identical to the MVRA's provisions, and we have therefore applied Hu-ghey in cases addressing restitution under the MVRA. See Marino, 654 F.3d at 319 n. 7.
     
      
      . Our decision in Marino is not to the contrary. In that case, we held that a defrauded investor may be a “victim” for restitution purposes, even if he would not have a private right of action to seek damages in a civil suit. 654 F.3d at 321. The question in this case, however, is whether the investors that purchased GFRDAs abroad were victims of Vilar and Tanaka’s criminal conduct, which, for the reasons spelled out above, they surely were not. See Part I, ante.
      
     
      
      . We expect that on remand Vilar and Tana-ka will renew, and the District Court will consider, their arguments concerning the propriety of calculating restitution awards to include a compounding 9% rate of prejudgment interest. Vilar and Tanaka contend, persuasively, that this rate, which is based on New York State's statutory rate, see N.Y. C.P.L.R. § 5004, will have the effect of benefitting victims of the GFRDA scheme at the expense of innocent investors in non-fraudulent securities. In fact, there is some doubt as to whether it is ever appropriate to award interest at the state rate on federal claims. Cf. Thomas v. iStar Fin., Inc., 629 F.3d 276, 280 (2d Cir.2010) (holding that "judgments that are based on both state and federal law with respect to which no distinction is drawn shall have applicable interest calculated at the federal interest rate”).
     
      
      .We also leave it for the District Court to consider on remand whether the forfeiture amount is affected by the extraterritorial limitations imposed on Section 10(b) by Morrison. See Part I, ante.
      
     
      
      . We leave it to the District Court to consider in the first instance the question of whether bail should be granted pending any petition for certiorari. In the interest of judicial economy, jurisdiction may be restored to this Court for an appeal of the District Court's bail decision, or of the sentences imposed on remand, by letter to the Clerk of this Court. Any such proceedings will be assigned to this panel.
     