SUMMARY ORDER
The appellants in this appeal were convicted by a jury of violating Section 10b of the Securities Exchange Act of 1934, 15 U.S.C. §§ 78j(b) & 78ff(a), by willfully violating Securities Exchange Act Rule lob-5, 17 C.F.R. § 240.10b-5. The appellants appeal their convictions, and one appellant, Newman, also appeals his sentence.
The fraud of which the appellants were accused involved what is colloquially known as a “pump and dump” scheme, in which a person artificially raises the market price of a security in which he or she has an interest (the “pump”) so that he or she can sell the security at a profit (the “dump”). The appellants were stock brokers employed by Kensington Woods, a now-defunct brokerage, which fraudulently manipulated the market for securities in companies whose initial public offerings it had underwritten.
The defendant brokers were charged with one count of conspiring to violate Section 10b of the Securities Exchange Act of 1934, 15 U.S.C. §§ 78j(b) & 78ff(a), by violating Securities Exchange Act Rules 10b-5 and 10b-6 (rescinded Jan. 7, 1997), and one count of violating Section 10b by violating Rule 10b-5. Each defendant was acquitted of the first count, and convicted of the second.
During summation, the government argued that the appellants were guilty on the second count because they had violat*128ed Rule 10b-6. The jury was instructed that it could convict if it found that the appellants had violated Rule 10b-6 for the purpose of manipulating the market. On appeal, the appellants argue that the instruction and summation constructively amended the indictment to permit the jury to convict if it found that the appellants had violated Rule 10b-6, when they had only been indicted on the second count of violating Rule 10b-5. A constructive amendment “occurs when the government’s presentation of evidence and the district court’s jury instructions combine to ‘modify essential elements of the offense charged to the point that there is a substantial likelihood that the defendant may have been convicted of an offense other than the one charged by the grand jury.’ ” United States v. Wozniak, 126 F.3d 105, 109 (2d Cir.1997) (quoting United States v. Vebeliunas, 76 F.3d 1283, 1290 (2d Cir.1996)). Because the appellants failed to object on this ground at trial, we review the claim for plain error. Fed. R.Civ.P. 52(b).
The framework of the analysis for plain error pursuant to Rule 52(b) is the four-pronged test set forth in United States v. Olano, 507 U.S. 725, 732, 113 S.Ct. 1770, 123 L.Ed.2d 508 (1993). Before an appellate court can correct an error not raised at trial, there must be (1) error, (2) that is plain, and (3) that affects substantial rights. If all three conditions are met, an appellate court may then exercise its discretion to notice a forfeited error, but only if (4) the error seriously affects the fairness, integrity, or public reputation of judicial proceedings.
United States v. Thomas, 274 F.3d 655, 667 (2d Cir.2001) (in banc) (citations, internal quotation marks, and alterations omitted).
While it is “clear” that an indictment may not be constructively amended without violating the grand jury clause, see, e.g., Stirone v. United States, 361 U.S. 212, 217, 80 S.Ct. 270, 4 L.Ed.2d 252 (1960), applying this established rule to the particular facts here does not result in an error that was either clear or obvious. The Rule 10b-5 count under which the appellants were convicted incorporated by reference those acts of pre-selling alleged in support of the indictment’s charge that the appellants conspired to violate Rule 10b-6, and they therefore had notice that acts of pre-selling in violation of Rule 10b-6 would be used by the prosecution to prove the 10b-5 charge. Violations of Rules 10b-5 and 10b-6, moreover, are violations of the same criminal provision, Section 10b of the Securities Exchange Act of 1934, and carry the same sentence. See 15 U.S.C. § 78ff(a); U.S.S.G. § 2B1.1 (2002); id. § 2F1.1 (1998); Goldstein v. Regal Crest, 62 F.R.D. 571, 574 (E.D.Pa.1974). Parenthetically, the only case to date of which we are aware that has addressed the question of whether Rule 10b-5 is violated when a defendant violates Rule 10b-6 with the intent of manipulating the market held in the affirmative. See Pappas v. Moss, 257 F.Supp. 345, 364 & n. 6 (D.N.J.1966) (citing SEC v. Scott Taylor & Co., 183 F.Supp. 904, 906-09 (S.D.N.Y.1959)). We therefore conclude that it is not clear or obvious that the indictment charged an offense other than the one the jury instruction and government’s summation allowed the jury to convict for.
Further, the charge also required the jury to find that the conduct was done with the purpose of defrauding buyers or sellers of securities. Because the district court charged the jury that it had to find an intent to defraud to convict on Count 2, and also told the jury that in “the context of market manipulation, to defraud means intentional or willful conduct that is designed to defraud or deceive investors by artificially controlling or fraudulently af*129fecting the price of securities,” the jury necessarily had to find that defendants intentionally engaged in conduct manipulative of the market and deceptive of investors — the essence of a criminal Rule 10b-5 violation — in order to return a verdict against the defendants on Count 2. Even if it was error to instruct the jury that it could convict on Count 2 if it found a violation of either Rules 10b-5 or 10b-6, then, this error would not have been plain error.
Appellants’ alternate contention, that their counsel were constitutionally ineffective for failing to object to the inclusion of Rule 10b-6 in the jury, charge fails for similar reasons. We have held that counsel is ineffective for failing to object to a jury instruction when “precedent supported a ‘reasonable probability" that a higher court would rule in [the] defendant’s favor,” Bloomer v. United States, 162 F.3d 187, 193 (2d Cir.1998), but there is no such precedent here. The appellants have not, under the first prong of Strickland v. Washington, 466 U.S. 668, 688-89, 104 S.Ct. 2052, 80 L.Ed.2d 674 (1984), defeated the “strong presumption that counsel’s conduct falls within the wide range of reasonable professional assistance,” or established that counsel’s performance “fell below an objective standard of reasonableness.” Even if failing to object to the erroneous inclusion of Rule 10b-6 in the charge on Count Two fell below an objective standard of reasonableness, moreover, because the charge required a showing of intent to manipulate the market, we conclude that no showing of prejudice has been made under Strickland’ s second prong, “that there is a reasonable probability that, but for counsel’s [allegedly] unprofessional errors, the result of the proceeding would have been different.” Id.
The appellants contend that the district court erred in declining to instruct the jury that certain regulatory violations were not violations of Rule 10b-5. The district court ruled that since the prosecution had contended that the violations were “part of the plan and scheme of manipulation ... the government may bring [them] out.” The court later instructed the jury that to convict, it had to find “intentional or willful conduct that [was] designed to defraud or deceive investors by artificially controlling or fraudulently affecting the price of securities.” Defense counsel had an opportunity to argue their position that the regulatory violations were not manipulative of the market to the jury. We conclude that there was no error in the district court’s ruling.
The appellants argue that they were prejudiced by the government’s summation. To require reversal, summation comments must “so infect[ ] the trial with unfairness as to make the resulting conviction a denial of due process.” Gonzalez v. Sullivan, 934 F.2d 419, 424 (2d Cir.1991) (quoting Donnelly v. DeChristoforo, 416 U.S. 637, 643, 94 S.Ct. 1868, 40 L.Ed.2d 431 (1974) (alteration in original)).
Most of the comments complained of were entirely proper, either independently or as appropriate responses to arguments made by the defense. While it was arguably improper for the prosecutor to refer to defense counsel’s argument that violating Rule 10b-6 did not constitute market manipulation as a “neat little trick,” “total bunk,” and requiring “audacity,” since the appellants failed to object to these comments at trial, they are grounds for vacating a conviction only if they constituted “flagrant abuse.” United States v. Rivera, 22 F.3d 430, 437 (2d Cir.1994) (citing United States v. Ortiz, 857 F.2d 900, 904 (2d Cir.1988), cert. denied, 489 U.S. 1070, 109 S.Ct. 1352, 103 L.Ed.2d 820 (1989)). We do not think the comments complained of can properly be described as flagrant abuse.
*130It was also improper as to Newman, Orandello and Mclnerney for the government to point out to the jury that those appellants had previously worked for another brokerage which was notorious for engaging in schemes similar to the one charged, because that evidence had only been admitted against DiFrisco and Jaross. Any prejudice caused by the comment was cured by a limiting instruction given by the district court.
Jaross, Mclnerney and DiFrisco argue that the evidence introduced at trial was insufficient to sustain their convictions. An appellant raising such a claim carries the.“heavy burden,” United States v. Scarpa, 913 F.2d 993, 1003 (2d Cir.1990), of establishing that “reasonable jurors must necessarily have had a reasonable doubt as to [his or her] guilt.” United States v. Brown, 776 F.2d 397, 402 (2d Cir.1985).
The government introduced direct evidence that Jaross, Mclnerney and DiFrisco either pre-sold stock or misrepresented the stock to customers and testimony regarding their knowledge of and participation in the “no net sales” policy and special secret incentives given for selling the company’s shares to investors. Upon review of the evidence introduced at trial, we cannot conclude that a reasonable jury must necessarily have had a reasonable doubt regarding any of the appellants’ guilt.
None of Newman’s arguments on appeal with respect to his sentencing were raised in the district court with sufficient specificity to alert the district court to the nature of Newman’s objections, and we therefore apply plain-error review. See Unites States v. Sofsky, 287 F.3d 122, 125-26 (2d Cir.2002) (plain-error review applies to review of sentencing errors not objected to, with exceptions not relevant here).
Newman contends that the district court improperly calculated the loss attributable to him for sentencing purposes. The district court calculated the difference between the price of the stock during the fraud and its price after the fraud ended and multiplied that sum by the number of shares attributable to Newman.
A district court at sentencing is not required to “determinen the loss with precision[, it need] only make a reasonable estimate of the loss, given the available information.” U.S.S.G. § 2F1.1 cmt. 9 (1998). Newman presented no evidence to the district court to aid it in differentiating between that portion of the decline of the company’s stock price attributable to a decline in its business prospects, if any, as opposed to market manipulation. Whether or not such evidence, had it been presented, would have affected the analysis, the district court calculation based on the evidence before it was not plainly erroneous.
Newman also argues that he is not responsible for manipulation of the market by Kensington Woods’ principals. The government introduced evidence indicating that even if Newman was not aware of all of the methods used to manipulate the price of the securities, he was aware that manipulation was going on. The losses caused by those methods of market manipulation are attributable to Newman for sentencing purposes. See U.S.S.G. § lB1.3(a)(l)(B) (1998).
Newman also argues that Kengsington Woods bore some of the loss when it was forced, as the market-maker, to purchase the company’s stock back from customers who wanted to sell. As we have just noted, a district court at sentencing is not required to “determine[ ] the loss with precisionf, it need] only make a reasonable estimate of the loss, given the available information.” U.S.S.G. § 2F1.1 cmt. 9 (1998). Because Newman introduced no evidence supporting his contention that Kensington Woods bore a portion of the *131loss, the district court’s estimate of the loss, which did not take into account repurchases by the brokerage, was reasonable.
Newman also argues that he should not have to pay $600,000 in restitution to a customer who suffered a portion of his loss after Newman left Kensington Woods. The customer’s loss is attributable to Newman because he personally convinced that customer to purchase the stock.
For the foregoing reasons, the judgments of the District Court are hereby AFFIRMED.