
660 F.3d 454 (2011)
UNITED STATES of America, Plaintiff-Appellee,
v.
Gregory L. REYES, Defendant-Appellant.
No. 10-10323.
United States Court of Appeals, Ninth Circuit.
Argued and Submitted May 10, 2011.
Filed October 13, 2011.
*458 Amber S. Rosen, Assistant United States Attorney (argued), Brian J. Stretch, *459 Attorney for United States, Barbara J. Valliere, Chief, Appellate Division, Adam A. Reeves, Assistant United States Attorney, San Jose, CA, for plaintiff-appellee United States.
Seth P. Waxman (argued), Peters G. Neiman, Edward C. DuMont, Micah S. Myers, Sue-Yun Ahn, Shivaprasad Nagaraj, Wilmer Cutler Pickering Hale and Dorr LLP, Washington, D.C., for defendant-appellant Gregory L. Reyes.
Before: RONALD M. GOULD and MILAN D. SMITH, JR., Circuit Judges, and ALGENON L. MARBLEY, District Judge.[*]

OPINION
M. SMITH, Circuit Judge:
Defendant-Appellant Gregory Reyes, the former Chief Executive Officer of Brocade Communications (Brocade, or the Company), appeals his conviction in a second criminal trial for (1) securities fraud and making false filings with the Securities and Exchange Commission (SEC) in violation of 15 U.S.C. §§ 78j(b) and 78ff, and 17 C.F.R. § 240.10b-5; (2) falsifying corporate books and records in violation of 15 U.S.C. §§ 78m(b)(2)(A) and 78ff, and 17 C.F.R. § 240.13b2-1; and (3) making false statements to auditors in violation of 15 U.S.C. § 78ff and 17 C.F.R. § 240.13b2-2. Reyes was previously convicted of violating these statutes, but we vacated that conviction because of prosecutorial misconduct, and remanded for a new trial. United States v. Reyes, 577 F.3d 1069 (9th Cir. 2009). In this appeal, Reyes contends that his second conviction should also be vacated, and the case dismissed, because of (a) prosecutorial misconduct, (b) insufficient evidence of materiality to support his conviction, and (c) various evidentiary and instructional errors at trial. We affirm.

FACTUAL BACKGROUND

Backdated Stock Options
Brocade develops and sells data switches for networks. It became a publicly traded company in 1999. Reyes was hired in 1998, and during his tenure served as CEO and Chairman of the Company's Board of Directors (Board). Brocade offered stock options to its newly hired employees, and its employees generally could also earn stock options through annual incentive programs. These options gave employees the right to purchase Brocade stock at a fixed exercise (strike) price on or after a specific vesting date. A stock option is "in-the-money" if the strike price is below the stock's current market value. "Backdating" stock options means that an option's grant date and strike price are recorded retroactively. During the relevant time period, backdating of Brocade stock options was not illegal as long as the benefit to Brocade employees was recorded on the Company's financial records as a non-cash compensation expense to Brocade. See Reyes, 577 F.3d at 1073. This accounting treatment was required by the then-applicable Accounting Principles Board Opinion No. 25 (APB 25).[1] It is *460 undisputed that the stock options relevant to this appeal were backdated, and were not properly entered in the Company's books, as then required by APB 25.
Reyes approved grants of stock options to Brocade employees from 2000 through 2004. Company policies permitted Reyes (as a sort of one-person committee) to approve grants of stock options to non corporate officer employees. However, a committee of outside directors, who comprised the Compensation Committee, was required to approve the grant of stock options to Company officers and the full Board of Directors was required to approve the grant of stock options to non-officer directors. Committee minutes or unanimous written consents were used to document the number of options granted to specific employees as of a particular date.

Procedural history
In 2004, Brocade's Board of Directors began investigating some of the Company's accounting practices with respect to the granting of stock options to new employees. In early 2005, Brocade changed some of its accounting practices, and announced that Reyes had resigned as CEO and Chairman. Concerned, the SEC and Department of Justice undertook a joint investigation into Brocade's option accounting, which led to the SEC filing civil complaints against Reyes and several others involved in the granting of stock options and accounting practices at Brocade.
On August 10, 2006, the Government charged Reyes with committing criminal securities fraud, mail fraud, falsifying corporate books and records, and violating related statutes and regulations. In August 2007, Reyes was found liable on all counts except the mail fraud charge, which was dismissed before trial. On appeal, we vacated Reyes's conviction and remanded for a new trial after finding prosecutorial misconduct. Reyes, 577 F.3d at 1078-79. Specifically, we held that the prosecution knew that several employees of Brocade's Finance Department had given pre-trial statements to the Federal Bureau of Investigation acknowledging that the Finance Department knew about Reyes's and the Company's stock option backdating practices, but that during closing argument, the prosecution knowingly and falsely claimed that the Finance Department did not know about the stock option backdating. Id. at 1076-77. We held that this deception was material because it went to Reyes's defense that he relied on others. Id. at 1078.
After a second five-week jury trial in February 2010, Reyes was acquitted on a conspiracy charge but convicted on all other counts, including: (1) securities fraud and making false filings with the Securities and Exchange Commission (SEC) in violation of 15 U.S.C. §§ 78j(b) and 78ff, and 17 C.F.R. § 240.10b-5; (2) falsifying corporate books and records in violation of 15 U.S.C. §§ 78m(b)(2)(A) and 78ff, and 17 C.F.R. § 240.13b2-1; and (3) making false statements to auditors in violation of 15 U.S.C. § 78ff and 17 C.F.R. § 240.13b2-2. Reyes was sentenced to 18-months imprisonment, two years of supervised release, and was fined $15,000,000. Reyes timely appeals.

JURISDICTION AND STANDARDS OF REVIEW
We have jurisdiction under 28 U.S.C. § 1291.
*461 We review the district court's rulings on alleged prosecutorial misconduct for an abuse of discretion. United States v. Steele, 298 F.3d 906, 910 (9th Cir. 2002); see also United States v. Murillo, 288 F.3d 1126, 1140 (9th Cir. 2002) (applying abuse of discretion standard to the denial of a motion for new trial based on prosecutorial misconduct). Issues of prosecutorial misconduct involving mixed questions of fact and law are reviewed de novo. United States v. Bracy, 67 F.3d 1421, 1433 (9th Cir. 1995). Harmless error review applies when a defendant timely objects to prosecutorial misconduct. United States v. Blueford, 312 F.3d 962, 973-74 (9th Cir. 2002). When reviewing for prosecutorial misconduct, we consider in the context of the entire trial "whether it is more probable than not that the prosecutor's conduct materially affected the fairness of the trial." United States v. McKoy, 771 F.2d 1207, 1212 (9th Cir. 1985).
Plain error review applies when a defendant fails to object to alleged prosecutorial misconduct before the district court. United States v. Sullivan, 522 F.3d 967, 982 (9th Cir. 2008); United States v. Geston, 299 F.3d 1130, 1134 (9th Cir. 2002). To establish plain error, a defendant must establish that (1) there was error, (2) the error was plain, and (3) the error affected his "substantial rights." Geston, 299 F.3d at 1135. "Under this standard, a conviction can be reversed only if, viewed in the context of the entire trial, the [claimed] impropriety seriously affected the fairness, integrity, or public reputation of judicial proceedings, or where failing to reverse a conviction would result in a miscarriage of justice." Id. (citation omitted).
We review de novo the question of whether a trial court's jury instruction accurately states the law. United States v. Hopper, 177 F.3d 824, 831 (9th Cir. 1999). We review for abuse of discretion a district court's formulation of jury instructions. United States v. Franklin, 321 F.3d 1231, 1240-41 (9th Cir. 2003), cert. denied, 540 U.S. 858, 124 S.Ct. 161, 157 L.Ed.2d 106 (2003). Thus, while the question of whether the district court's instructions adequately covers a defense theory is reviewed de novo, we "look to the instructions as a whole and a refusal to give a proper specific instruction can be remedied by other instructions that cover the subject." United States v. Thomas, 612 F.3d 1107, 1122 (9th Cir. 2010) (internal citations omitted).
There must be sufficient evidence to constitutionally support a criminal conviction. See Jackson v. Virginia, 443 U.S. 307, 319, 99 S.Ct. 2781, 61 L.Ed.2d 560 (1979). The evidence must be viewed in the light most favorable to the Government to determine whether any rational trier of fact could have found the essential elements beyond a reasonable doubt. Id.; United States v. Nevils, 598 F.3d 1158, 1163-64 (9th Cir. 2010) (en banc). We "may not usurp the role of the finder of fact by considering how it would have resolved the conflicts, made the inferences, or considered the evidence at trial." Nevils, 598 F.3d at 1164. Evidence is sufficient where it "is adequate to allow `any rational trier of fact [to find] the essential elements of the crime beyond a reasonable doubt.'" Id. (quoting Jackson, 443 U.S. at 319, 99 S.Ct. 2781).

DISCUSSION

I. Prosecutorial Misconduct
A. Reyes claims that the Government asserted a new, false theory at his second trial; specifically, that Reyes "grant[ed] ... in-the-money options to himself" to "pad his own pocket." Reyes argues it was prosecutorial misconduct to focus on this theory when, as the prosecution *462 knew, Reyes could not grant himself options because the Compensation Committee had to approve all options granted to him. In particular, Reyes objects to testimony and exhibits highlighted at trial by the Government where Reyes's name was listed next to other employees to whom he granted options.
Reyes concedes that he did not object at trial to the prosecutor's allegedly improper conduct of introducing evidence that Reyes granted himself stock options. Accordingly, we review this aspect of Reyes's claim of prosecutorial misconduct for plain error. Geston, 299 F.3d at 1134.
We review Reyes's claims of prosecutorial misconduct in the light of clearly established legal principles. The "prosecutor's job isn't just to win, but to win fairly, staying well within the rules." United States v. Kojayan, 8 F.3d 1315, 1323 (9th Cir. 1993). "[I]t is improper for the government to present to the jury statements or inferences it knows to be false or has very strong reason to doubt." Reyes, 577 F.3d at 1077.
It is certainly within the bounds of fair advocacy for a prosecutor, like any lawyer, to ask the jury to draw inferences from the evidence that the prosecutor believes in good faith might be true. But it is decidedly improper for the government to propound inferences that it knows to be false, or has very strong reason to doubt, particularly when it refuses to acknowledge the error afterwards to either the trial court or this court and instead offers far-fetched explanations of its actions.
Blueford, 312 F.3d at 968. Faithful adherence to these principles is particularly important because a "prosecutor's opinion carries with it the imprimatur of the Government" and making false or misleading assertions "may induce the jury to trust the Government's judgment rather than its own view of the evidence." Reyes, 577 F.3d at 1077 (quoting United States v. Young, 470 U.S. 1, 18-19, 105 S.Ct. 1038, 84 L.Ed.2d 1 (1985)).
Viewed in the light of these authorities, Reyes fails to establish that there was prosecutorial misconduct at his second trial regarding this aspect of his claim. What the Government argued at the second trial was that Reyes's motivation for engaging in a fraudulent scheme, in part, was to personally profit. To substantiate its theory, the Government introduced evidence showing the significant number of stock options Reyes received (thirteen million), the value of those options (approximately $130 million for eleven million in-the-money options), that he made almost $2 million from exercising some of his backdated options and that Reyes received almost six times the amount of options granted to any other officer or employee of the Company.
The Government also presented evidence that Reyes was involved in the process of granting stock options to himself because he signed lists of grant options with his name on them. For example, Reyes several times signed lists of stock option grants, which included his own name along with those of non-officer employees. By signing his name to the lists, Reyes was also able to influence the date of his grants to match those of certain non-officer employees. In one instance, Reyes received almost $4 million in options for an April 17, 2001 stock price, the same date as the date applicable to the stock grants he made to certain non-officer employees, even though he did not obtain the Compensation Committee's final approval for, or ratification of, the grant until May 2001. Presenting this evidence did not rise to the level of prosecutorial misconduct because the Government was not pursuing an invalid theory of the case, but rather was showing *463 Reyes's involvement in the process of granting backdated stock options. Moreover, the Government clarified any confusion that might have flowed from the referenced setting by proffering testimony from its own expert that technically, in accordance with Brocade's own internal rules, the Compensation Committee was required to approve stock options granted to Reyes.
In short, the evidence the Government presented was not false (Reyes did sign off on the lists showing grants of backdated stock options to himself and to certain non-officer employees), and the Government did not impermissibly ask the jury to draw false inferences from the evidence presented at trial about Reyes's role in the process of granting backdated stock options to himself because the prosecution acknowledged that ultimately the approval of the Compensation Committee was required, even if that approval was simply pro forma. Cf. Reyes, 577 F.3d at 1078. In this way, the Government sought to show that Reyes knowingly benefitted from the scheme by approving the dates and lists, some of which included his name as a backdated stock option recipient. Without evidence of the Government's relying on known false or misleading statements, Reyes's allegations of this type of prosecutorial misconduct do not rise to the level of improper conduct that "so affected the jury's ability to consider the totality of the evidence fairly that it tainted the verdict and deprived [Reyes] of a fair trial." United States v. Weatherspoon, 410 F.3d 1142, 1151 (9th Cir. 2005) (quoting United States v. Smith, 962 F.2d 923, 935 (9th Cir. 1992)).
B. Reyes also asserts that the Government's introduction of evidence that between 2000 and 2004 Reyes received eleven million backdated options (out of a total of thirteen million), worth approximately $130 million, and that he exercised 40,000 of his backdated options in September 2000, for a gain of approximately $2 million (collectively, the Option Gains Evidence), was irrelevant, unduly prejudiced the jury, and constituted prosecutorial misconduct. We disagree.
Reyes does not explain how the admission of such allegedly irrelevant or unfairly prejudicial evidence constitutes prosecutorial misconduct, and we fail to see independently how it does. See Fed. R.Evid. 401, 403; see also, e.g., Greenwood v. FAA, 28 F.3d 971, 977 (9th Cir. 1994) ("We will not manufacture arguments for [a party]...."). The Option Gains Evidence was based on facts and testimony introduced at trial and the inferences that flowed therefrom were linked to Reyes's motives. See Reyes, 577 F.3d at 1077. Moreover, because we conclude below that the Options Gains Evidence was properly admitted, Reyes cannot rely on the admission of that evidence to demonstrate prosecutorial misconduct. See United States v. Hinton, 31 F.3d 817, 824 (9th Cir. 1994).
Tellingly, Reyes also did not object to the introduction of the Options Gains Evidence on prosecutorial misconduct grounds; he simply raised an evidentiary objection to its admission. "Evidentiary rulings will be reversed for abuse of discretion only if such nonconstitutional error more likely than not affected the verdict." United States v. Tran, 568 F.3d 1156, 1162 (9th Cir. 2009) (citation omitted). The district court permitted the introduction of the Options Gains Evidence because it related to motive, knowledge, and intent, and because it demonstrated that Reyes made money in the backdating scheme. On the other hand, the district court showed sensitivity to undue prejudice concerns when it forbade the introduction of evidence that Reyes made $500 million from the sale of Brocade stock, *464 reasoning that such evidence was unduly prejudicial, whereupon the parties agreed that the jury would be told only that Reyes sold "a significant amount of Brocade stock" between 2000 and 2004.
The Government was not permitted to introduce evidence simply to show that Reyes was wealthy. See, e.g., United States v. Mitchell, 172 F.3d 1104, 1108-09 (9th Cir. 1999) ("A rich man's greed is as much a motive to steal as a poor man's poverty. Proof of either, without more, is likely to amount to a great deal of unfair prejudice with little probative value."). However, the Government was allowed to introduce evidence about Reyes's motivation for his involvement in the backdating scheme, his scienter, even if such evidence is generally not sufficient, standing alone, to prove intent to defraud. Cf. Tellabs, Inc. v. Makor Issues & Rights, Ltd., 551 U.S. 308, 325, 127 S.Ct. 2499, 168 L.Ed.2d 179 (2007) ("While it is true that motive can be a relevant consideration, and personal financial gain may weigh heavily in favor of a scienter inference, we agree ... that the absence of a motive allegation is not fatal."); Livid Holdings Ltd. v. Salomon Smith Barney, Inc., 416 F.3d 940, 948 (9th Cir. 2005) (mere motive to commit fraud is insufficient to adequately plead scienter); United States v. Quattrone, 441 F.3d 153, 187 (2d Cir. 2006) (permitting evidence of executive compensation where the introduction of the evidence was for the limited purpose of demonstrating motive and not simply wealth).
Consistent with these authorities, the district court permitted the introduction of relevant and not unfairly prejudicial evidence related to Reyes's motive. Reyes's gains from backdated options permitted the jury to draw a reasonable inference that he knew what he was doing, and how the scheme operated to his benefit. Reyes also fails to demonstrate that the Government sought a verdict from the jury based on Reyes's wealth, instead of with respect to his conduct related to backdated stock options. The jury was properly instructed as to the elements of the relevant crimes, including specific willfulness and intent on Reyes's part to defraud, a heightened standard from mere motive. There was also significant evidence in the record that Reyes knowingly participated in a scheme that he recognized was illegal.
The jury was also presented with evidence by both parties showing the amount of gain actually made by Reyes, approximately $2 million, and that he did not exercise or receive the full potential gain of $130 million that could have been realized on his backdated options. Under these circumstances, we conclude the Options Gains Evidence constituted probative evidence of Reyes's motive, knowledge, and intent to participate in the backdating scheme, and its admission into evidence fell far short of meeting the level required to find unfair prejudice. See United States v. Mende, 43 F.3d 1298, 1302 (9th Cir. 1995) ("Under the terms of the rule, the danger of prejudice must not merely outweigh the probative value of the evidence, but substantially outweigh it."); United States v. Patterson, 819 F.2d 1495, 1505 (9th Cir. 1987) (stating that Rule 403 is "an extraordinary remedy to be used sparingly").
C. Reyes further argues that the Government committed prosecutorial misconduct in its questioning of two witnesses. Specifically, Reyes contends that through the testimony of Stephen Beyer, a former employee in Brocade's Human Resources department, the Government furthered the false impression that Brocade's options-pricing process was "secretive and unusual." Reyes similarly objects to the introduction of the testimony of Carol Bowie, a consultant with ISS Governance Services, *465 who discussed Brocade's governance and compensation practices.
Reyes fails to show how the introduction of the Beyer or Bowie evidence constitutes prosecutorial misconduct. Reyes does not demonstrate that Beyer gave any false testimony related to his experience with accounting practices at KLA-Tencor, and then Brocade. Beyer testified on direct examination that he was instructed not to use email at Brocade to discuss backdating stock options, in order to avoid an "audit trail" for an "incorrect practice." Defense counsel then cross-examined Beyer about his work at KLA-Tencor, and that company's practice of backdating stock options. Defense counsel then introduced evidence of emails sent to Beyer at KLA-Tencor showing a list of backdated stock options to undermine Beyer's credibility and to show that backdating was a common practice. On redirect, the Government sought to distinguish KLA-Tencor's process of pricing stocks with the backdating process at Brocade.
Approximately a week after Beyer's testimony, defense counsel raised an objection to his testimony on prosecutorial misconduct grounds. According to Reyes, the Government's effort to distinguish the two practices was prosecutorial misconduct, because the Government surely knew that backdating was occurring at KLA-Tencor. The district court denied the objection on the ground that the witness did not give false testimony because the questions posed on redirect were related to Beyer's own knowledge of the practices at KLA-Tencor.[2]
The district court did not abuse its discretion in finding that there was no prosecutorial misconduct based on the Government's questioning of Beyer on redirect. Beyer's direct testimony dealt with his concerns about Brocade's stock option practices, when compared with his experiences at KLA-Tencor. The defense sought to impeach Beyer on the grounds that he was not a credible witness and that he had lied about his experience at KLA-Tencor, in order to show that he did not actually have concerns about Brocade's practices. On redirect, the Government asked questions that were specifically related to Beyer's personal knowledge about KLA-Tencor's practices, and did not seek an inference that, regardless of any knowledge Beyer may have had, the KLA-Tencor never backdated its stock options. Because there is no evidence that Beyer knowingly offered false testimony, or that the Government sought to draw false inferences beyond Beyer's personal knowledge testimony, Reyes fails to show prosecutorial misconduct. See Reyes, 577 F.3d at 1077 (finding prosecutorial misconduct where the Government made statements that it knew, or had very strong reasons to doubt, that such statements were accurate).
Moreover, even if the district court did err in permitting Beyer's testimony, it was harmless. See Blueford, 312 F.3d at 973-74. Three other witnesses from Brocade's Human Resources department testified that they thought the backdating practices at Brocade were improper. The jury was specifically instructed that backdating was not in and of itself *466 illegal. The jury also heard other testimony that a significant number of other companies had engaged in backdating as a routine practice. Accordingly, whether the jury knew specifically about KLA-Tencor's backdating practices from Beyer was unlikely to substantially affect the jury's verdict. See McKoy, 771 F.2d at 1212.
The district court also did not abuse its discretion when it denied defense counsel's motion to strike Carol Bowie's testimony. United States v. Martinez-Rodriguez, 472 F.3d 1087, 1091 (9th Cir. 2007). Bowie testified that investors care how companies compensate employees and that granting stock options is the equivalent of granting equity in the company. She also testified about materiality, see infra, and about a report finding that Brocade had a "disturbing pattern" of granting stock options to Reyes when the stock price dropped.
Reyes strongly objects to Bowie's "arresting" testimony that his compensation (through the grant of stock options, most of which were not exercised) increased 1,896% at the same time that Brocade's stock prices were falling. Reyes claims that this evidence is irrelevant and unfairly prejudicial because it relies on biases and class prejudice.
Notably, Reyes does not explain how the introduction of Bowie's testimony constitutes prosecutorial misconduct. Reyes does not demonstrate that such testimony was false, or that the Government sought to draw improper inferences based on its admission. See Reyes, 577 F.3d at 1077. As previously noted, while it would be improper to admit this evidence simply to show Reyes's wealth, the evidence is relevant to Reyes's motives for the backdating scheme, since he had a financial interest in the process of backdating options. See Mitchell, 172 F.3d at 1108-09. The 1,896% compensation increase figure is not so "arresting" as to make it unfairly prejudicial because this figure was tied to potential gain had Reyes exercised all of the stock options. Fed.R.Evid. 403. The record reflects that Reyes did not exercise all of his stock options, and the jury was clearly informed of that fact. Under these circumstances, the district court did not abuse its discretion by permitting Bowie's testimony.
D. Reyes also maintains that the district court erred in admitting public statementsin the form of two press releases and a civil pleading (answer)made by his first defense counsel to the effect that Reyes did not engage in backdating options at Brocade (collectively, the Prior Case Evidence). Specifically, Reyes argues that the admission of the Prior Case Evidence was irrelevant to establishing his guilt and was unfairly prejudicial because it was introduced as evidence of his guilt.[3]
The district court did not abuse its discretion in admitting the Prior Case Evidence. At his second trial, Reyes's defense strategy was to admit that he backdated stock options, but deny that he had knowledge and responsibility for misreporting the compensation expenses. To show that Reyes understood that he was engaged in illegal conduct, the Government introduced the testimony of an attorney who conducted an internal investigation of Brocade's practices, at the Company's request. The attorney testified *467 that Reyes told him that he never backdated stock options. Defense counsel sought to discredit the attorney by questioning the attorney's memory and bias. To corroborate the attorney's testimony, the Government introduced Reyes's first defense counsel's press releases and his answer in the civil enforcement suit brought by the SEC. For example, the press releases quoted Reyes's first counsel, who claimed that "Mr. Reyes did not backdate options." Reyes's answer to the SEC's civil complaint made similar denials. Reyes objected to these admissions.
The statements were relevant because they were inconsistent with Reyes's position at his second trial, to the effect that he engaged in backdating, and were used to corroborate another Government witness's testimony that Reyes told him that he did not backdate. The Prior Case Evidence was also relevant to Reyes's guilty state of mind. See United States v. Perkins, 937 F.2d 1397, 1402 (9th Cir. 1991) (false exculpatory statements can be considered as evidence of consciousness of guilt).
E. Reyes also asserts that the prosecution unduly focused on a theme of corporate responsibility whereby Reyes was ultimately responsible for any misconduct because he was CEO of Brocade. In particular, Reyes points to prosecution's references to corporate culture and that Reyes signed the SEC filings. Reyes also contends that the district court erred by not giving proposed defense jury instructions directing the jury not to give any significance to Reyes's position as CEO of the Company, or to the legal concept of respondeat superior liability.[4] We disagree.
Reyes did not object at trial to the introduction of evidence related to Reyes's responsibilities as CEO of the Company. Moreover, the district court did not plainly err when it allowed the introduction of evidence that Reyes, in his role as CEO, signed the financial statements and representation letters which formed the basis of the Government's charges that Reyes falsified Company books and records, and lied to Company auditors. See Geston, 299 F.3d at 1134; 15 U.S.C. §§ 78m(b)(2)(A) and 78ff, 17 C.F.R. § 240.13b2-1 (falsifying corporate books and records); 15 U.S.C. § 78ff, 17 C.F.R. § 240.13b2-2 (making false statements to auditors). In further clarification of the purpose of the evidence, the Government argued that as CEO of the Company, Reyes knew about what was occurring at Brocade regarding the granting of stock options, not that he should be held liable simply because he was the CEO.
The district court also did not abuse its discretion when it rejected defense counsel's proposed jury instruction that a corporate officer is not criminally responsible for the acts of subordinates. The issue arose after the district court received a question from a juror part way through trial asking the court if Reyes was individually liable, or liable as a CEO. In response, the court told the jury that it would be instructed on the issue at the end of the trial.
Reyes's claim that the district court's given instructions did not adequately cover his theory of defense is reviewed de novo. United States v. Howell, 231 F.3d 615, 629 (9th Cir. 2000). The district court has wide discretion in formulating the instructions to the jury, see, e.g., United *468 States v. Echeverry, 759 F.2d 1451, 1455 (9th Cir. 1985), and we review its decision for an abuse of discretion. Franklin, 321 F.3d at 1240-41. The court did not commit reversible error by refusing to give a separate instruction where "other instructions, in their entirety, adequately cover that defense theory." See Thomas, 612 F.3d at 1120 (9th Cir. 2010).
The jury was properly instructed before closing arguments and the commencement of jury deliberations. The trial court properly instructed the jury as to the required elements of each of the crimes charged. Jurors are presumed to follow the court's instructions. Zafiro v. United States, 506 U.S. 534, 540, 113 S.Ct. 933, 122 L.Ed.2d 317 (1993). From the instructions given, it was clear that the jury could not find Reyes guilty simply due to his position as CEO of Brocade. Therefore, the district court's refusal to give the requested instruction regarding that aspect of the defense's theory did not constitute reversible error. See, e.g., United States v. Reed, 575 F.3d 900, 925 (9th Cir. 2009) (alteration in original) ("A district court may properly refuse to give a `mere presence' instruction when the government's case rests on `more than just a defendant's presence, and the jury is properly instructed on all elements of the crime....") (quoting United States v. Negrete-Gonzales, 966 F.2d 1277, 1282 (9th Cir. 1992)).
Accordingly, we conclude that Reyes has failed to show that the Government made any false or misleading statements based on the evidence introduced, which necessarily means that Reyes failed to show that the Government knowingly made any misrepresentations. See Reyes, 577 F.3d at 1077. As a result, there is no evidence of sufficient facts in this record supporting any allegation of prosecutorial misconduct that would "so infect[] the trial with unfairness as to make the resulting conviction a denial of due process." Darden v. Wainwright, 477 U.S. 168, 181, 106 S.Ct. 2464, 91 L.Ed.2d 144 (1986) (citation omitted).

II. Sufficiency of the Materiality Evidence
A. "[A]ny person who uses or employs a manipulative or deceptive device in connection with the sale of any security commits securities fraud." United States v. Jenkins, 633 F.3d 788, 801-02 (9th Cir. 2011) (citing 15 U.S.C. § 78j(b)), 17 C.F.R. § 240.10b-5(b) (prohibiting "any untrue statement of a material fact"). Materiality is one element of securities fraud. Id. at 802 (citing In re Cutera Secs. Litig., 610 F.3d 1103, 1108 (9th Cir. 2010)) ("Central to a 10b-5 claim is the requirement that a misrepresentation or omission of fact must be material.").
For an omission to be material, "there must be a substantial likelihood that the disclosure of the omitted fact would have been viewed by the reasonable investor as having significantly altered the `total mix' of information made available." Basic Inc. v. Levinson, 485 U.S. 224, 231-32, 108 S.Ct. 978, 99 L.Ed.2d 194 (1988) (citation and internal quotation marks omitted); United States v. Tarallo, 380 F.3d 1174, 1182 (9th Cir. 2004) ("For securities fraud, a statement is material if there is a substantial likelihood that a reasonable investor would consider it important in making a decision."). "[T]he standard of materiality is judged from the perspective of a `reasonable investor,' and is therefore an objective one." Reyes, 577 F.3d at 1075 (rejecting Reyes's argument that witnesses' testimony failed to establish materiality because they made no personal decision to invest in Brocade's stock).
*469 Reyes argues that the prosecution failed to prove that additional disclosures related to the APB 25 non-cash expenses would have been material to investors. In particular, Reyes argues that the testimony of Bowie and Robert McCormick, a lawyer who supervised proxy voting for Fidelity Investments, only related to proxy voting decisions and did not establish that APB 25 expenses could influence a reasonable investor's decision. Reyes also maintains that the two Brocade investors who testified, Kevin Kilgannon and David Ryan, did not establish that they found APB 25 information important.[5] We disagree with Reyes's highly theoretical and distorted reading of the materiality standard.
"We have recognized that information regarding a company's financial condition is material to investment." Id. at 1076 (citing SEC v. Murphy, 626 F.2d 633, 653 (9th Cir. 1980) ("Surely the materiality of information relating to financial condition, solvency and profitability is not subject to serious challenge.")); see also Berson v. Applied Signal Tech., Inc., 527 F.3d 982, 985 (9th Cir. 2008) ("[A] statement is misleading if it would give a reasonable investor the impression of a state of affairs that differs in a material way from the one that actually exists." (Internal citations and quotation marks omitted)). Here, there was substantial evidence for the jury to rely on in finding materiality based on the extent to which Brocade's true financial condition was not disclosed to investors.
In particular, the Government presented evidence that the backdating scheme affected Brocade's reported earnings. Brocade's net income was overstated by almost $1 billion between 2000 and 2004; it reported profits in 2001 and 2002 when it should have reported losses, and underreported losses by almost $500 million in 2003 and 2004. Government expert Fujuimoto testified that APB 25 calculations affected the reported earnings (unlike FAS 123 disclosures). Further, McCormick provided identical testimony to that which he gave at Reyes's first trial that Fidelity's policy was to vote against company plans that allow in-the-money options because it costs the company more money and can affect shareholder returns. Bowie's testimony was consistent with McCormick's. A jury could reasonably conclude based on this testimony that investors would want to know information that affects investment returns.
Further, two actual Brocade investors testified that they cared about accurately stated earnings. Kilgannon testified that, as an investor, whether a company was really suffering a loss but reported profits, would "have been important" to him. He also testified that he sold his remaining Brocade shares after he learned that the company was restating its earnings. Ryan traded on a basis of the stock's price and *470 trading volume. He testified that price follows earnings and that he decided to sell when he heard of Brocade's restated earnings. While the Brocade investors' testimony is not specific to APB 25 non-cash expenses, it is sufficient to help establish materiality in this case because investors care about earnings, which at that time were required to reflect APB 25 non-cash expenses.
Taking into account the cumulative testimony of the witnesses regarding the materiality of the Company's misstatement of its earnings, coupled with the information in the Company's financial statements and SEC filings, and viewing the evidence in the light most favorable to the Government, a rational jury could find that Brocade's significantly overstated net income and underreported losses were material to investors. Reyes, 577 F.3d at 1076; Berson, 527 F.3d at 985. Accordingly, we reject Reyes's narrow reading of the materiality standard.
B. Reyes also contends the prosecution improperly suggested to the jury that it could find materiality based on proxy-voting decisions, and that the district court erred because it did not give an instruction that would prevent the jury from being mislead. We disagree.
Reviewing for plain error, Geston, 299 F.3d at 1134, Reyes does not point to any place in the record where we could find that the prosecutors acted in a "well-calculated" manner to "mislead the jury" as to this issue. Having various unconnected references in the record is not sufficient to show prosecutorial misconduct where the Government did not offer the proxy voting to establish materiality. Rather, the voting preferences testimony largely related to the reasons why the witnesses voted against plans permitting in-the-money options, because they can lead to lesser earnings, about which investors do care.
Second, while improper accounting requiring a restatement does not, by itself, establish materiality, it can be used as evidence. See DSAM Global Value Fund v. Altris Software, Inc., 288 F.3d 385, 390 (9th Cir. 2002) ("[T]he mere publication of inaccurate accounting figures, or a failure to follow GAAP, without more, does not establish scienter." (citation omitted)); Gebhardt v. ConAgra Foods, Inc., 335 F.3d 824, 829 (8th Cir. 2003) ("We do not believe that restating earnings makes the original misstatement material per se... [but] those facts are part of the total mix of information available to investors and are deserving of some consideration."). Here, the Government did not argue that Brocade's financial restatement alone, which was required because the Company's accountants found material discrepancies in the financials, rendered Reyes criminally culpable.
The district court did not abuse its discretion by not giving Reyes's proposed jury instruction. The jury was properly instructed as to the materiality requirements under Basic, 485 U.S. at 231-32, 108 S.Ct. 978, and is presumed to follow those instructions, Zafiro, 506 U.S. at 540, 113 S.Ct. 933. That is sufficient, particularly where the context for the testimony related to how granting in-the-money option affects earnings. Further, the trial court gave limiting instructions during trial concerning the materiality of accounting restatements, and gave correct materiality instructions at the end of trial.

CONCLUSION
For the foregoing reasons, we AFFIRM the district court.
NOTES
[*]  The Honorable Algenon L. Marbley, United States District Judge for the Southern District of Ohio, sitting by designation.
[1]  In 2005, Financial Accounting Standards (FAS) 123(R) superseded APB 25 and required that companies use FAS 123 expense amounts in their Generally Accepted Accounting Principles (GAAP) statements. FAS 123 required reporting estimating the economic value of stock options granted to employees during the relevant reporting period and the effect such grants would have had on the Company's earnings, determined pursuant to GAAP, if they had been treated as non-cash compensation expenses.
[2]  The district court also denied defense counsel's proffered limiting jury instructions as "enormously argumentative" and "totally inappropriate." Defense counsel, while objecting to the Government's proposed limiting instructions, and despite the trial court's repeated efforts to solicit input, refused to offer any substantive suggestions that would make the Government's version acceptable. Defense counsel's complete rejection of any limiting instructions except its own does not, per se, make the Government responsible for failing to correct misleading testimony. See Blueford, 312 F.3d at 968.
[3]  Reyes does not explain how the Government engaged in prosecutorial misconduct by introducing the Prior Case Evidence at trial. He does not demonstrate how the evidence is false or how the Government sought to draw false inferences from the facts, and fails to show that the Government knew or should have known that such inferences were false. See Reyes, 577 F.3d at 1077.
[4]  Reyes does not specifically explain how the prosecutors allegedly engaged in misconduct as to this issue.
[5]  Reyes also contends that as a matter of law no jury could find that the omission of APB 25 expenses was matter based on "basic market economics." Reyes's academic theory is that decreased earnings will only lead to lower securities prices if the earnings are cash earnings. GAAP earnings, Reyes maintains, reflect only non-cash accounting and does not affect future cash flows, which "should" not affect stock price. Because APB 25 options expenses are non-cash accounting entries, omitting them "should not affect stock valuations by reasonable investors."

Notwithstanding this theoretical analysis of how the market should behave, the Government proffered testimony suggesting that actual investors do care about earnings prices. Where, as here, the earnings were overstated because of improper accounting at the time, such information affects investors decisions to buy or sell. Moreover, the overarching legal conclusion in Reyes is applicable, as the court concluded that the "false records" could affect a reasonable investor because it produced an "incorrect picture" of Brocade's finances. Reyes, 577 F.3d at 1075-76.
