SUMMARY ORDER

We assume the parties’ familiarity with the underlying facts and procedural history of this case. Defendant-Appellant Patrick Marzo (“Marzo”) appeals the judgment of conviction entered on October 30, 2006 by the United States District Court for the Southern District of New York (Jones, J.). A jury convicted Marzo, a former foreign currency trader employed by Société Générale (“SocGen”), on one count of conspiracy to commit bank and wire fraud and ten counts of substantive wire fraud, arising from his participation in a scheme to engage in currency transactions at unauthorized, off-market rates in exchange for cash kickbacks (the “points-for-cash” scheme).

Marzo first argues that the government constructively amended his indictment during trial, or in the alternative, subject*357ed it to a prejudicial variance. He contends that “the government retreated from its touted points-for-eash scheme presented to the jury thus far, and instead characterized the cash prong as merely motive and not an essential part of the charged scheme.”

We review de 'novo a constructive amendment challenge. United States v. Rigas, 490 F.3d 208, 225 (2d Cir. 2007). A constructive amendment claim requires a defendant to “demonstrate that either the proof at trial or the trial court’s jury instructions so altered an essential element of the charge that, upon review, it is uncertain whether the defendant was convicted of conduct that was the subject of the grand jury’s indictment.” United States v. Milstein, 401 F.3d 53, 65 (2d Cir. 2005) (per curiam) (quoting United States v. Salmonete, 352 F.3d 608, 620 (2d Cir. 2003)). A prejudicial variance “occurs when the charging terms of the indictment are left unaltered, but the evidence offered at trial proves facts materially different from those alleged in the indictment.” Rigas, 490 F.3d at 226 (quoting Salmonete, 352 F.3d at 621). “However, we will reverse on account of a variance only if it prejudices the defendant by infringing on the ‘substantial rights’ that indictments exist to protect — ‘to inform an accused of the charges against him so that he may prepare his defense and to avoid double jeopardy.’ ” United States v. Kaplan, 490 F.3d 110, 129 (2d Cir. 2007) (quoting United States v. Dupre, 462 F.3d 131, 140 (2d Cir. 2006)).

Marzo fails to establish that either a constructive amendment or prejudicial variance occurred. The record does not reflect that the government “abandoned” its factual theory that Marzo engaged in off-market trades in exchange for kickbacks. Rather, the government simply sought to clarify, for the purpose of charging the jury, the legal elements of bank and wire fraud, which do not include personal profit to the perpetrator of the fraud.2 The jury charge itself referred to the alleged kickbacks and to “points-for-cash.” There is no indication that the government altered its factual theory of the case during the trial, or that any essential element of the charges against Marzo was impermissibly altered during the trial or in the jury charge.

Marzo next claims that he received ineffective assistance of counsel. He must establish that the representation was unreasonable under “prevailing professional norms,” and that, but for counsel’s incompetence, there is a reasonable probability that “the result of the proceeding would have been different.” Strickland v. Washington, 466 U.S. 668, 688, 694, 104 S.Ct. 2052, 80 L.Ed.2d 674 (1984). When confronted with an ineffective assistance claim, “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. Gaskin, 364 F.3d 438, 468 (2d Cir. 2004) (quoting United States v. Morris, 350 F.3d 32, 39 (2d Cir. 2003)).

*358Marzo contends that his trial counsel was ineffective in failing to realize, when advising him to admit to at least four instances of off-market trades, that Marzo could properly be found guilty on that conduct alone, without proof that he accepted cash kickbacks. We are not entirely convinced that Marzo’s counsel’s advice to admit to some off-market trades was unreasonable, rather than a reasonable strategic choice. See, e.g., Bell v. Miller, 500 F.3d 149, 156 (2d Cir. 2007) (holding that a defendant claiming ineffective assistance “ ‘must overcome the presumption that, under the circumstances, the challenged action might be considered sound trial strategy”’) (quoting Strickland, 466 U.S. at 689, 104 S.Ct. 2052). However, in the absence of a more fully developed record on this point, or the proffer of an affidavit by Marzo’s trial counsel, we conclude that this issue would be better addressed in the first instance by the district court, and dismiss this claim without prejudice to being raised under 28 U.S.C. § 2255. See, e.g., Gaskin, 364 F.3d at 467-68.

Marzo’s claim regarding his attorney’s failure to investigate the date of a high school football game lacks merit and may be denied without further development of the factual record. The duty to investigate “does not ... compel defense counsel to investigate comprehensively every lead or possible defense.” Greiner v. Wells, 417 F.3d 305, 321 (2d Cir. 2005). Marzo’s assertion at trial that he and Sweeney met in September '2003 to settle a bet on a football game was only a minor component of his defense, which focused principally on denying that he had performed the trades and on his lack of criminal intent. Further, we have never held, and decline to do so here, that an attorney is ineffective when he does not bolster his client’s testimony by supplying dates that the client could not independently recollect.

We also disagree with Marzo’s contention that the government’s theory of prosecution failed to constitute a crime under the federal fraud statutes. We find that the jury was adequately instructed as to the intent and materiality elements of wire and bank fraud, and that it could not convict Marzo unless the government proved these elements beyond a reasonable doubt. See, e.g., Dist. Council 37, Am. Fed’n of State, County & Mun. Employees, AFL-CIO v. New York City Dep’t of Parks & Recreation, 113 F.3d 347, 356 (2d Cir. 1997) (“It has long been held that we assume that a jury follows jury instructions as given.”).

Finally, we detect no error in the jury instructions or in the district court’s response to the jury’s questions during deliberations. Because Marzo apparently did not object to these instructions at trial, we review them under the plain error standard, “examin[ing] the challenged language in context by looking at the instructions as a whole to determine if the jury was given a correct interpretation of the law.” United States v. Goldstein, 442 F.3d 777, 781 (2d Cir. 2006). If we find an error that is plain and affects substantial rights, “we may exercise our discretion to review the error, but only if it seriously affects the fairness, integrity, or public reputation of the judicial proceedings.” Id.

We disagree with Marzo that the “ultimate harm” instruction here was improper. The case upon which Marzo relies, United States v. Rossomando, 144 F.3d 197 (2d Cir. 1998), is distinguishable. The district court’s instruction in this case more clearly highlighted the requirement of intent, and there was a sufficient factual predicate for the instruction. Specifically, while Marzo did argue that he completely lacked intent to defraud, he also testified at trial that even if he did engage in some off-market trades, SocGen did not ultimately suffer any harm because he could *359make up the trades later with Sweeney or with some other broker, or because his actions would increase goodwill with the brokers. Because there was an arguable factual predicate for the “ultimate harm” instruction, the district court did not commit plain error in giving it. See, e.g., United States v. Koh, 199 F.3d 632, 641 (2d Cir. 1999); United States v. Berkovich, 168 F.3d 64, 67 (2d Cir. 1999).

Finally, we conclude that the district court did not commit plain error in responding to the jury’s questions. The supplemental instructions were legally correct and well within the court’s “broad discretion” in giving supplemental charges. United States v. Civelli, 883 F.2d 191, 195 (2d Cir. 1989).

We have considered Marzo’s remaining arguments and find them to be without merit.

For the foregoing reasons, the judgment of conviction is AFFIRMED.