
    UNITED STATES of America, Appellee, v. Irving STITSKY, Mark Alan Shapiro, Appellants.
    Nos. 10-2767-cr(L), 10-4426-cr(Con).
    United States Court of Appeals, Second Circuit.
    Oct. 17, 2013.
    
      James M. Branden, Esq., New York, NY, for Irving Stitsky.
    Katherine Alfieri, Esq., New York, NY, for Mark Alan Shapiro.
    Marc P. Berger (Emil J. Bove, III, Michael A. Levy, on the brief), Assistant United States Attorneys, for Preet Bhar-ara, United States Attorney for the Southern District of New York, New York, NY, for Appellee.
    PRESENT: REENARAGGI, CHRISTOPHER F. DRONEY, Circuit Judges, JOHN F. KEENAN, District Judge.
    
    
      
       The Honorable John F. Keenan, of the United States District Court for the Southern District of New York, sitting by designation.
    
   SUMMARY ORDER

Defendants Irving Stitsky and Mark Alan Shapiro, who were found guilty after a jury trial on substantive and conspiratorial counts of securities fraud, mail fraud, and wire fraud, see 15 U.S.C. §§ 78j(b), 78ff; 18 U.S.C. §§ 371, 1341, 1343, appeal their convictions and 85-year prison sentences on numerous grounds discussed herein. We assume the parties’ familiarity with the underlying facts and the record of prior proceedings, which we reference only as necessary to explain our decision to affirm.

1. Challenges to Indictment

a. Constructive Amendment and Prejudicial Variance

Defendants argue that testimony about investors who did not purchase “Units” in certain limited liability companies formed by defendants’ real estate company, Cobalt Capital Company (“Cobait”), but rather invested with Cobalt through other means, constituted a constructive amendment of or a prejudicial variance from the indictment. On de novo review, see United States v. D’Amelio, 683 F.3d 412, 416 (2d Cir.2012), we reject defendants’ claim as without merit.

To establish constructive amendment, defendants must show that the trial evidence or 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. Rigas, 490 F.3d 208, 227 (2d Cir.2007) (internal quotation marks omitted). “Where a generally framed indictment encompasses the specific legal theory or evidence used at trial, there is no constructive amendment.” Id. at 228 (alteration and internal quotation marks omitted). “[W]e have consistently permitted significant flexibility in proof, provided that the defendant was given notice of the core of criminality to be proven at trial.” Id. (emphasis in original; footnote and internal quotation marks omitted). A constructive amendment is a per se violation of the Grand Jury Clause of the Fifth Amendment, which requires reversal. See id. at 226. By contrast, a 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.” Id. (internal quotation marks omitted). “A defendant alleging variance must show substantial prejudice to warrant reversal.” Id. (internal quotation marks omitted).

While the two substantive securities fraud counts of the indictment were specifically limited to the purchase of Units, the conspiracy, wire fraud, and mail fraud counts were not so limited. Indeed, the conspiracy counts charge that defendants engaged in a broad “scheme to defraud investors by soliciting millions of dollars of funds under false pretenses, failing to invest investors’ funds as promised, and misappropriating and converting investors’ funds to their own benefit and the benefit of others without the knowledge or authorization of the investors.” Superseding Indict. ¶¶ 13, 40, 42. Those counts further charge that defendants fraudulently induced victims to invest with Cobalt by utilizing a number of deceptive means, such as “(a) misrepresenting Cobalt’s operating history; (b) failing to inform prospective investors that Cobalt was owned and controlled by [defendants], both convicted felons; and (c) misrepresenting and causing others to misrepresent to prospective investors Cobalt’s purported ownership interests in certain properties.” Id.

The testimony by two of the witnesses at issue, Stanley Gruber and Charles Agule, related to Shapiro’s fraudulent inducement of investors to purchase certain partnership interests in Cobalt using the same deceptive means alleged in the indictment. The testimony of the third witness at issue, Steven May, a Washington Mutual loan officer, described Shapiro’s use of a false financial statement in an effort to secure a $5 million loan on behalf of Cobalt and his failure to disclose his prior conviction in connection with his loan application. The fraudulent acts described by these witnesses, although not specifically identified in the indictment as overt acts in furtherance of the scheme to defraud, “fall[ ] squarely within the charged scheme,” and thus their testimony did not constructively amend the conspiracy, wire fraud, and mail fraud counts. United States v. Salmonese, 352 F.3d 608, 621 (2d Cir.2003) (concluding that there was no constructive amendment where prosecution proved “unalleged overt acts” in furtherance of charged scheme); see United States v. Dupre, 462 F.3d 131, 140-41 (2d Cir.2006) (holding that prosecution did not constructively amend indictment “because the evidence at trial concerned the same elaborate scheme to defraud investors as described in the indictment”).

Nor did this testimony amount to a prejudicial variance in the proof on those counts, especially as defendants were on notice prior to trial of the substance of the witnesses’ testimony. See United States v. Salmonese, 352 F.3d at 621-22 (stating that variance is not prejudicial where pleading and proof “substantially correspond,” variance could not have misled defendant at trial, and variance would not deprive accused of protection against double jeopardy).

Further, the district court properly instructed the jury that defendants could not be convicted on the substantive securities fraud counts based on the testimony of Gruber and May. Thus, their testimony does not support a constructive amendment or prejudicial variance claim on those counts. See United States v. Williams, 690 F.3d 70, 77 (2d Cir.2012) (presuming “that jurors follow their instructions”). Defendants did not request a limiting instruction with respect to Agule’s testimony. But considering the limited nature of his testimony, and defense counsel’s unrebutted summation argument that his testimony could not support conviction on the substantive securities fraud counts, any error in the district court’s failure sua sponte to provide a limiting instruction does not manifest plain error warranting reversal. See United States v. Marcus, 560 U.S. 258, 130 S.Ct. 2159, 2164, 176 L.Ed.2d 1012 (2010) (setting forth plain error criteria); United States v. Desimone, 119 F.3d 217, 225 (2d Cir.1997) (applying plain error review where “trial court failed to give a jury instruction that was not specifically requested”).

b. Multiplicity

Defendants contend that the two substantive securities fraud counts were multiplicitous. We review this unpre-served claim for plain error, see United States v. Marcus, 130 S.Ct. at 2164, which we do not identify here.

“An indictment is multiplicitous when a single offense is alleged in more than one count.” United States v. Jones, 482 F.3d 60, 72 (2d Cir.2006) (internal quotation marks omitted). “A claim of multiplicity cannot succeed, however, unless the charged offenses are the same in fact and in law.” Id. (internal quotation marks omitted).

Here, each securities fraud count charged defendants with the sale of separate securities: count two alleged fraud in the sale of Units in Cobalt Capital Partners I, LLC (“CCP”), while count three charged fraud in the sale of Units in Cobalt Multifamily Investors I, LLC (“CMF”). Because transactions in separate securities constitute separate offenses, the counts are not multiplicitous. See United States v. Dioguardi, 492 F.2d 70, 83 (2d Cir.1974) (“[E]ach transaction in a securities fraud constitutes a separate offense.”); see also United States v. Langford, 946 F.2d 798, 803 (11th Cir.1991) (stating that “allowable unit of prosecution” under 15 U.S.C. § 78j(b) is “any false statement of material fact in connection with a discrete purchase or sale of a security”).

In urging otherwise, defendants argue that the CCP Units eventually merged into CMF Units, and thus sale of the CCP Units constituted the same transaction as sale of the CMF Units. The record, however, reflects that Cobalt offered CCP Unit holders the option to convert their CCP Units to CMF Units; it does not reflect that the two securities were identical. Thus, the separate sale of those securities supports separate fraud charges, and the two securities fraud counts are not multiplicitous.

2. Evidentiary Challenges

a. Denial of Suppression

Defendants challenge the district court’s denial of Shapiro’s motion to suppress evidence seized from Cobalt’s offices in Great Neck, New York and Springfield, Massachusetts on December 1, 2005, pursuant to search warrants purportedly obtained on false or incomplete information. They argue that the district court wrongfully denied them a hearing on this claim. See United States v. Falso, 544 F.3d 110, 125 (2d Cir.2008) (citing Franks v. Delaware, 438 U.S. 154, 98 S.Ct. 2674, 57 L.Ed.2d 667 (1978)) (recognizing defendant’s right to hearing if he can make “substantial preliminary showing that a deliberate falsehood or statement made with reckless disregard for the truth was included in the warrant affidavit and the statement was necessary to the judge’s finding of probable cause” (internal quotation marks omitted)). Insofar as it is an open question in this circuit whether we review the denial of a Franks hearing de novo or for clear error, see id. at 126 n. 21, we need not resolve that question here because Shapiro’s challenge fails under even the more rigorous de novo standard of review, see Hoffler v. Bezio, 726 F.3d 144, 151-52 (2d Cir.2013).

To determine whether a misstatement or omission is necessary to the finding of probable cause, i.e., whether it is material, we look to a hypothetical “corrected affidavit,” produced by adding to the original warrant affidavit the omitted information highlighted by defendants, as well as any other pertinent omitted information. United States v. Canfield, 212 F.3d 713, 718 (2d Cir.2000). “If the corrected affidavit supports probable cause, the inaccuracies were not material to the probable cause determination and suppression is inappropriate.” Id.

The question of whether the corrected affidavit demonstrates probable cause is a legal question that we review de novo. See id. Probable cause to search exists where circumstances indicate a “fair probability that contraband or evidence of a crime will be found in a particular place.” Illinois v. Gates, 462 U.S. 213, 238, 103 S.Ct. 2317, 76 L.Ed.2d 527 (1983); see Florida v. Harris, — U.S.-, 133 S.Ct. 1050, 1055, 185 L.Ed.2d 61 (2013) (observing that probable cause is “practical,” “commonsensical,” “all-things-considered” standard).

Both the Great Neck and Springfield warrants were supported by the November 30, 2005 affidavit of FBI Special Agent Jennifer May. May’s affidavit was based on her personal knowledge and on information obtained from (1) conversations with a cooperating witness (“CW”), who had provided reliable information to law enforcement in the past; (2) conversations with other law enforcement officers and witnesses; and (3) May’s review of bank, telephone, and Cobalt business records. Based on this information, May stated that there was probable cause to believe that, from approximately May 2004 to November 2005, defendants engaged in a “boiler room” investment fraud scheme in which more than 50 people had been induced to invest more than approximately $10 million. She further stated that there was probable cause to believe that evidence of this scheme was present at Cobalt’s Great Neck and Springfield offices.

In support of her conclusion, May cited, inter alia, (1) phone records showing tens of thousands of short-duration, long-distance telephone calls in a pattern that, based on her training and experience, she believed was consistent with boiler room and cold-call solicitation efforts frequently used in investment scams; (2) the omission of defendants’ true positions at Cobalt and their prior criminal convictions from Cobalt’s July and December 2004 private placement memoranda (“PPM”); (3) a false statement in the December 2004 PPM that Shapiro received degrees from the University of Miami and Harvard University; (4) a recording between the CW and Shapiro, in which Shapiro admitted that he was running Cobalt from a “tertiary position” because of “his personal situation,” May Aff. ¶ 21 (internal quotation marks omitted); (5) a recording between the CW and Shapiro in which Shapiro stated that his salesman would “say anything, do anything, [and] use anything” to sell investments, id. ¶ 27 (alteration in original); (6) bank records indicating that Shapiro had misappropriated investor funds for personal use; and (7) her training and experience that individuals involved in fraudulent investment schemes maintain various records for substantial periods of time evincing their operation of such schemes.

Despite these facts, defendants claim that when May’s affidavit is corrected to add omitted facts regarding the CW — such as the nature of his past convictions, i. e., fraud and perjury; the loss of his law license; and his alleged efforts to compete with Cobalt — probable cause is negated. We disagree. May’s affidavit made clear that the CW had been convicted of federal crimes. Moreover, the CW’s information about Cobalt was corroborated through recordings and bank, business, and telephone records, and the CW was known to be reliable, insofar as he had previously testified on behalf of the government in a case that led to a conviction. Thus, the nature of the CW’s crimes and the other facts highlighted by defendants would not have discredited the CW’s account of the fraudulent scheme so as to defeat probable cause. See United States v. Wagner, 989 F.2d 69, 73 (2d Cir.1993) (stating that “information provided by an informant from whom the government has received consistently reliable information in the past is likely to be sufficiently reliable to establish probable cause” and that informant’s entire account may be credited where “corroborated in material respects”). The remaining misrepresentations and omissions alleged by defendants raise de minimis issues that do not negate probable cause when included in a corrected affidavit.

Because defendants have not identified any material misrepresentations in or omissions from May’s affidavit that could negate probable cause, we identify no error in the district court’s determination that Shapiro failed to make the substantial preliminary showing necessary to justify a Franks hearing. Nor do we identify any error in its denial of Shapiro’s motion to suppress.

b. Prior Convictions

Defendants argue that the district court erred in denying Shapiro’s motion in limine under Fed.R.Evid. 403 and 404(b) to preclude the government from offering proof of their prior convictions. We review the district court’s evidentiary rulings for abuse of discretion, see United States v. Nektalov, 461 F.3d 309, 318 (2d Cir.2006), and we identify no such abuse here.

Rule 403 authorizes the exclusion of relevant evidence if its “probative value is substantially outweighed by a danger of ... unfair prejudice.” Fed.R.Evid. 403. Rule 404(b) permits the admission of uncharged crimes, wrongs, or other acts for purposes other than proving propensity. See Fed.R.Evid. 404(b); United States v. LaFlam, 369 F.3d 153, 156 (2d Cir.2004) (adopting inclusionary approach to Rule 404(b) evidence).

In this case, defendants’ prior convictions were direct proof of the charged scheme to defraud. Part of the government’s theory at trial was that defendants fraudulently induced victims to invest in Cobalt by failing to disclose their leadership roles in the company and their prior convictions, facts that investors would have considered material in making their investment decisions. See Basic Inc. v. Levinson, 485 U.S. 224, 231-32, 108 S.Ct. 978, 99 L.Ed.2d 194 (1988) (stating that omitted fact is material if reasonable investor would view it to have “significantly altered the total mix of information made available” (internal quotation marks omitted)); see also United States v. Abdulwahab, 715 F.3d 521, 533-34 (4th Cir.2013) (upholding mail and securities fraud convictions based in part on defendant’s failure to disclose his criminal history). Under these circumstances, the district court acted well within its discretion in concluding that proof of defendants’ prior convictions was more probative than prejudicial under Rule 403. Moreover, because defendants’ prior convictions were direct evidence of the charged offense, they were not subject to Rule 404(b). See United States v. Carboni, 204 F.3d 39, 44 (2d Cir.2000); United States v. Thai, 29 F.3d 785, 812 (2d Cir.1994); United States v. Concepcion, 983 F.2d 369, 392 (2d Cir.1992). Even if they were subject to that rule, though, because they were offered for a purpose other than to prove propensity, the district court did not abuse its discretion in admitting that evidence.

c. Amato’s Testimony

In their pro se supplemental briefs, defendants challenge the admission of testimony by Shapiro’s probation officer, Jennifer Amato, under Rules 403 and 404(b). Because defendants did not object to this testimony below, we review only for plain error, see United States v. Marcus, 130 S.Ct. at 2164, which we do not identify here.

Amato testified that, under the terms of Shapiro’s supervised release, he was not permitted to associate with other convicted felons without prior approval of his probation officer. She further testified that Shapiro (1) did not inform her of his contact with Stitsky, (2) failed to tell her about his employment at Cobalt prior to October 2004, and (3) misrepresented certain other facts about his employment and financial holdings. Amato’s testimony was evidence of Shapiro’s intent to defraud investors because it supported an inference that Shapiro knew he was engaged in impermissible activities with Cobalt and, therefore, deliberately failed to disclose his position and criminal history to investors. Under these circumstances, Amato’s testimony was admissible under Rule 403. Further, because her testimony was direct evidence of the charged conduct, see United States v. Carboni 204 F.3d at 44, and offered for a purpose other than propensity, see United States v. LaFlam, 369 F.3d at 156, it presents no Rule 404(b) concern.

d. Limits on Cross-Examination

Defendants complain that the district court impermissibly limited the scope of their cross-examination at trial of Special Agent Robert Lauria and former Cobalt employee Jeffrey Clark. We review their preserved objection with respect to Clark’s testimony for abuse of discretion, see United States v. Treacy, 639 F.3d 32, 42 (2d Cir.2011), and their unpreserved objection with respect to Lauria for plain error, see United States v. Marcus, 130 5.Ct. at 2164. Under either standard, however, we conclude that the district court did not err.

The limits at issue — the district court’s general instruction not to repeat direct testimony on cross-examination, its preclusion of repetitive and argumentative questions to Lauria, and its preclusion of questions to Clark about personal bankruptcies that would only confuse the jury — all fell within the court’s discretion and did not violate the Sixth Amendment’s Confrontation Clause. See United States v. Figueroa, 548 F.3d 222, 227 (2d Cir.2008) (recognizing district court may place “reasonable limits” on defense cross-examination based on concerns such as harassment, prejudice, confusion of issues, witness safety, or repetitive or irrelevant interrogation (internal quotation marks omitted)).

e. Mazzella Stipulation

Defendants’ Sixth Amendment challenge to stipulated testimony from FBI Financial Analyst Joan Mazzella, who was ill and unable to testify, was not raised below. Here, however, we do not review even for plain error because the stipulation effectively waived defendants’ right of confrontation. See United States v. Plitman, 194 F.3d 59, 64 (2d Cir.1999) (recognizing that “defense counsel may waive a defendant’s Sixth Amendment right to confrontation where the decision is one of trial tactics or strategy that might be considered sound”).

Mazzella’s testimony related to her conversion of voluminous bank records into summary spreadsheets. Defendants claim that the spreadsheets contain errors about which Mazzella should have been cross-examined, making counsel’s stipulation unsound. We are not persuaded. Defendants fail to show that the errors could not have been effectively exposed through other witnesses and arguments. Thus, even if we were not to find waiver, we would identify no plain error.

3. Jury Instructions

Defendants contend that the district court erred in failing to instruct the jury that actual victim reliance on defendants’ material misrepresentations or omissions was necessary to prove securities fraud. That argument is now foreclosed by United States v. Vilar, 729 F.3d 62, 87-90 (2d Cir.2013) (rejecting argument that government must demonstrate actual reliance to prove securities fraud).

4. Sufficiency of the Evidence

Defendants claim that trial evidence was insufficient to satisfy the fraudulent intent element of each count of conviction. See United States v. Novak, 443 F.3d 150, 156 (2d Cir.2006) (stating that mail fraud requires proof that defendant had fraudulent intent and “contemplated” or “intended” some harm to victims (internal quotation marks omitted)); United States v. Guadagna, 183 F.3d 122, 129 (2d Cir.1999) (same for wire fraud); SEC v. First Jersey Sec., Inc., 101 F.3d 1450, 1467 (2d Cir.1996) (stating that “[sjcienter, as used in connection with the securities fraud statutes, means intent to deceive, manipulate, or defraud”). A defendant raising a sufficiency challenge “bears a heavy burden because a reviewing court must consider the evidence ‘in the light most favorable to the prosecution’ and uphold the conviction if ‘any rational trier of fact could have found the essential elements of the crime beyond a reasonable doubt.’” United States v. Aguilar, 585 F.3d 652, 656 (2d Cir.2009) (quoting Jackson v. Virginia, 443 U.S. 307, 319, 99 S.Ct. 2781, 61 L.Ed.2d 560 (1979) (emphasis in original)). Defendants have failed to carry this burden.

a. Shapiro

Trial evidence showed, inter alia, that Shapiro (1) hid from investors his role as a founder, 40% shareholder, and top executive at Cobalt by failing to disclose it in the December 2003 and July 2004 PPMs and by misrepresenting it in the December 2004 PPM; (2) failed to disclose his criminal convictions to investors; (3) reviewed and approved marketing materials containing material misrepresentations about Cobalt’s experience in the real estate industry, such as brochures (a) asserting that Cobalt was founded in 1980 when, in fact, it was established in 2003; (b) containing a line graph falsely depicting Cobalt’s successful investment returns from 1997 to 2003; and (c) identifying prominent investment professionals as associated with Cobalt even though they had no relationship with the company; (4) misrepresented his educational background in the December 2004 PPM; (5) falsely informed investors that Cobalt owned and had developed certain properties, such as the Mercury and Simone Hotels; and (6) misappropriated investor funds for personal use. From this evidence, we easily conclude that a rational jury could have found Shapiro’s fraudulent intent established beyond a reasonable doubt.

In urging to the contrary, Shapiro argues that the evidence did not show his intent to harm Cobalt’s investors, as required to prove mail and wire fraud, but rather showed that he sought to make a profit for investors through Cobalt. We are not persuaded. The evidence was sufficient to prove that Shapiro intended fraudulently to induce investors to entrust him with their money. Shapiro’s intent to cause that immediate loss to his victims is sufficient to sustain his mail and wire fraud convictions, regardless of whether he intended ultimately to generate a return on their investments. See United States v. Ferguson, 676 F.3d 260, 280 (2d Cir.2011) (“Where some immediate loss to the victim is contemplated by a defendant, the fact that the defendant believes (rightly or wrongly) that he will ultimately be able to work things out so that the victim suffers no loss is no excuse for the real and immediate loss contemplated to result from defendant’s fraudulent conduct.” (alteration and internal quotation marks omitted)).

b. Stitsky

Trial evidence showed, inter alia, that Stitsky (1) was a founding member of Cobalt along with Shapiro and held a 40% equity share of the company; (2) reviewed misleading marketing materials, such as a PowerPoint presentation to Cobalt salespeople and investors falsely stating that Cobalt (a) was founded in 1988; (b) made investments that had outperformed other benchmark indexes from 1997 to 2003; and (c) began renovating the Mercury Hotel in 1998 and completed it in 2000; (3) asked a Cobalt consultant to misrepresent his role with the company to an investor; (4) asked his son to create a résumé misrepresenting his length of experience in the mortgage business; (5) admitted to a Cobalt employee that his name was not listed in the PPMs due to his criminal history; (6) instructed a Cobalt employee not to tell the FBI he was a partner at Cobalt; (7) falsely told the FBI that he was only a consultant for Cobalt and did not have direct contact with investors; and (8) lied to investors about Cobalt’s ownership interest in certain properties. From this evidence, a rational jury could have concluded that Stitsky acted with the requisite intent.

Although Stitsky argues that the evidence supports inferences that he did not, in fact, have a leadership role at Cobalt; was not aware of the material misrepresentations in the marketing materials; encouraged “favorable spin but did not flat-out tell others to lie,” Stitsky Reply Br. 4; and concealed his role at Cobalt from investors with the approval of counsel, the jury was free to reject Stitsky’s view of the evidence, see United States v. Hasan, 586 F.3d 161, 166 (2d Cir.2009). The evidence amply supports the contrary inferences urged by the government, which we must credit in reviewing the sufficiency of the evidence. See United States v. Aguilar, 585 F.3d at 656.

Insofar as Stitsky argues that he did not intend to cause harm to Cobalt’s investors, we reject this claim for reasons already stated in rejecting Shapiro’s analogous argument. See United States v. Ferguson, 676 F.3d at 280.

5. Recusal

Defendants argue that the district judge should have sua sponte recused herself due to personal bias against defendants and bias stemming from her handling of five related civil cases. We review defendants’ claim for plain error, see United States v. Bayless, 201 F.3d 116, 128-29 (2d Cir.2000), which is not present here.

A judge is required to disqualify herself “in any proceeding in which [her] impartiality might reasonably be questioned,” 28 U.S.C. § 455(a), and also where she “has a personal bias or prejudice concerning a party, or personal knowledge of disputed evidentiary facts concerning the proceeding,” id. § 455(b)(1). Section 455(a) is “commonly limited to those circumstances in which the alleged partiality stems from an extrajudicial source.” United States v. Carlton, 534 F.3d 97, 100 (2d Cir.2008) (alteration and internal quotation marks omitted). Opinions held by judges as a result of what they learned in a different case involving the same defendant and the same set of facts are “not ordinarily a basis for recusal.” Id.

Here, defendants have pointed to no facts that would have warranted recusal. Their attempt to locate personal bias in the judge’s (1) efforts to control defense counsel’s duplicative cross-examination, (2) manner towards defense counsel, and (3) adverse evidentiary rulings is unconvincing. See Liteky v. United States, 510 U.S. 540, 556, 114 S.Ct. 1147, 127 L.Ed.2d 474 (1994) (rejecting bias claim based on district judge’s questioning of certain witnesses, alleged “anti-defendant tone,” and limitations on testimony regarding defendants’ state of mind (internal quotation marks omitted)). Moreover, the district judge’s knowledge and opinions based on facts presented in related civil cases did not compel her recusal. See United States v. Carlton, 534 F.3d at 100.

In sum, we reject defendants’ various challenges to their convictions as uniformly meritless.

6. Sentencing Challenges

a. Procedural Error

Defendants assert that the district court committed procedural error by (1) miscalculating their Guidelines ranges as the statutory maximum of 85 years (reduced from life imprisonment pursuant to U.S.S.G. § 5Gl.l(a)), and (2) failing to consider the 18 U.S.C. § 3553(a) factors. See United States v. Gavera, 550 F.3d 180, 190 (2d Cir.2008) (en banc) (stating that district court commits procedural error, inter alia, where it miscalculates Guidelines or does not consider § 3553(a) factors). To the extent the argument faults district court determinations that were primarily legal in nature, our review is de novo; to the extent it faults determinations that were primarily factual, we review only for clear error. See United States v. Hsu, 669 F.3d 112, 120 (2d Cir.2012).

i. Loss Calculation

Defendants fault the district court’s application of a 22-level enhancement to their Guidelines offense levels based on a purportedly erroneous loss calculation of $23,152,235. See U.S.S.G. § 2B1.1(b). “In calculating the amount of loss under the Guidelines, a sentencing court ‘need only make a reasonable estimate of the loss.’ ” United States v. Rigas, 583 F.3d 108, 120 (2d Cir.2009) (quoting U.S.S.G. § 2B1.1 cmt. n. 3(C)); see United States v. Bryant, 128 F.3d 74, 75 (2d Cir.1997) (“[T]he Guidelines do not require that the sentencing court calculate the amount of loss with certainty or precision.”).

The challenged loss calculation here was based on a chart prepared by a court-appointed receiver, which indicated that the total amount of money invested by the 352 victims of defendants’ fraudulent scheme was $23,152,235. The district court’s reliance on this sum to estimate loss was reasonable under our precedent. See United States v. Hsu, 669 F.3d at 122 (stating Guidelines “provide that when an investor puts money into a fraudster’s hands, and ultimately receives nothing of value in return, his loss is measured by the amount of principal invested”); United States v. Byors, 586 F.3d 222, 226 (2d Cir.2009) (concluding that district court did not err in calculating loss based on victims’ total $9 million investment); see also United States v. Rutkoske, 506 F.3d 170, 178 (2d Cir.2007) (stating that our review of district court’s loss calculation is limited to determining whether its “method of calculating the amount of loss was legally acceptable” (internal quotation marks omitted)).

Defendants nevertheless assert that individuals who invested with Cobalt through methods other than purchasing Units are not victims of the charged crimes and, thus, their investments should not be included in the loss amount. This argument fails because, as discussed supra with respect to defendants’ constructive amendment argument, those individuals were, in fact, victims of the fraudulent scheme charged in the indictment.

Nor are we persuaded by defendants’ argument that investments made in Cobalt following November 30, 2005, the date of an amendment to the December 2004 PPM that disclosed defendants’ criminal convictions, should not be counted in the loss amount. Defendants were convicted pursuant to an indictment charging a fraudulent scheme that lasted until March 27, 2006. Their argument that the November 2005 amendment terminated the fraudulent scheme earlier than that date is unavailing. Indeed, as we have already explained, the wide-ranging fraud at Cobalt was not limited to defendants’ failure to disclose their criminal convictions; it also involved other misrepresentations, such as false statements about Cobalt’s properties, its history in the real estate business, and its past investment performance. Thus, because defendants have not established that the investments Cobalt received following the November 2005 amendment were not fraudulently induced, the district court did not err as a matter of law or fact in including them in its loss calculation. Defendants also argue that their fraud victims received securities with some value, i.e., the Units, in exchange for their investment in Cobalt, and thus the loss amount should be offset by the value of those securities. See U.S.S.G. § 2B1.1 cmt. n. 3(E)(i) (stating that loss should be offset by “money returned, and the fair market value of the property returned and the services rendered, by the defendant ... to the victim before the offense was detected”). The district court, however, found that investors had been left with “nothing of value when the fraud was uncovered” and, specifically, that the Units “conferred no value at all on the investors,” because the “few buildings that Cobalt purchased were all highly leveraged with multiple mortgages” and “Cobalt did not have the funds or ability to renovate these properties.” Stitsky Sent. Tr. 17:6-12, Stitsky App. 517. Defendants fail to demonstrate that this factual determination is clearly erroneous. Indeed, even if some of Cobalt’s properties retained value at the time the fraud was uncovered, as defendants contend, the district court reasonably concluded that the Cobalt securities had no value because there was no realistic possibility that Cobalt would be able to generate a positive return for investors. See United States v. Leonard, 529 F.3d 83, 93 (2d Cir.2008) (“The reasonable valuation of ... illiquid assets is an exercise best committed to the sound discretion of the district court.”).

Defendants’ argument for loss to be offset by Cobalt’s legitimate expenditures fares no better because the “Guidelines do not require a loss to be offset by any legitimate expenditures.” United States v. Byors, 586 F.3d at 226 (citing U.S.S.G. § 2B1.1 cmt. n. 3(E)(i)). Additionally, the district court reasonably determined that no offset was warranted for losses resulting from changed economic circumstances because Cobalt investors would not have been exposed to such risks had defendants not fraudulently induced them to invest in the first instance.

Accordingly, because investors received nothing of value at the time the fraud was uncovered, the district court reasonably estimated the loss to be the principal amount invested by the victims of defendants’ fraud. See United States v. Hsu, 669 F.3d at 122; United States v. Byors, 586 F.3d at 226; United States v. Leonard, 529 F.3d at 93 n. 10.

ii. Number of Victims

Defendants challenge application of a six-level Guidelines enhancement based on more than 250 fraud victims. See U.S.S.G. § 2Bl.l(b)(2)(C). As this objection was not raised before the district court, we review only for plain error. See United States v. Marcus, 130 S.Ct. at 2164.

Defendants argue that the victim list, created by the court-appointed receiver and adopted by the district court, erroneously identifies 352 victims by including (1) non-Unit investors with Cobalt and (2) post-November 2005 investors. We have already rejected these arguments in other contexts, and the same conclusion obtains here. Insofar as defendants also argue that the list is duplicative, an independent review of the list refutes that claim. Thus, the district court did not err in applying the challenged victim enhancement.

iii. Sophisticated Means

Defendants challenge the two-level enhancement applied for sophisticated means. See U.S.S.G. § 2Bl.l(b)(10)(C). The Guidelines define “sophisticated means” to be “especially complex or especially intricate offense conduct pertaining to the execution or concealment of an offense.” U.S.S.G. § 2B1.1 cmt. n. 8(B). The district court concluded that defendants’ scheme was “very sophisticated” because it (1) “lasted several years”; (2) “reflected very careful planning”; (3) included a “careful effort to conceal the fraud by lying” to business partners, lawyers, and investors; (4) “relied on creating and disseminating marketing publications that contained material misrepresentations”; and (5) involved the “creation of fictitious documents for the purpose of convincing investors to give money or not to redeem their money from Cobalt.” Shapiro Sent. Tr. 25:6-20, Shapiro App. 373; see Stitsky Sent. Tr. 18:19-20:4, Stitsky App. 518-20 (noting that scheme also involved “fictitious corporate officer” and call scripts containing material misrepresentations). Defendants have failed to demonstrate that these findings are clearly erroneous. See United States v. Jackson, 346 F.3d 22, 25 (2d Cir.2003) (“[Ejven if each step in the scheme was not elaborate, the total scheme [may be] sophisticated [when] all the steps [are] linked together.”). Indeed, the Guidelines’ example of sophisticated means, a telemarketing scheme in which the scheme’s main office is located in one jurisdiction but its soliciting operations are in another, see U.S.S.G. § 2B1.1 cmt. n. 8(B), closely parallels Cobalt’s operations out of its Springfield and Great Neck offices.

iv. Aggravating Role

Defendants challenge the application of a four-level leadership-role enhancement pursuant to U.S.S.G. § 3Bl.l(a) (stating that enhancement is warranted if defendant “was an organizer or leader of criminal activity that involved five or more participants or was otherwise extensive”).

(a) Shapiro

Shapiro does not dispute leadership; he challenges only the finding that the scheme involved more than five “participants” or was “otherwise extensive.” Id. This argument merits little discussion. At Shapiro’s sentencing, the district court identified seven individuals by name as knowing participants in the scheme, and the record amply supports that determination. See U.S.S.G. § 3B1.1 cmt. n. 1 (defining “participant” as “person who is criminally responsible for the commission of the offense, but need not have been convicted”). In the alternative, the district court concluded that the scheme was otherwise extensive because of the large number of unknowing and knowing participants who provided services “peculiar and necessary to the criminal scheme.” Shapiro Sent. Tr. 26:9-13, Shapiro App. 374. Considering that Cobalt employed numerous individuals, including a cadre of salespersons, in furtherance of its fraudulent scheme, the district court’s determination is not clearly erroneous. See United States v. Manas, 272 F.3d 159, 166 (2d Cir.2001) (“[U]nknowing or unwitting participants in a criminal scheme ... may be counted in ascertaining whether it was otherwise extensive” (internal quotation marks omitted)); U.S.S.G. § 3B1.1 cmt. n. 3 (“[A] fraud that involved only three participants but used the unknowing services of many outsiders could be considered extensive.”). This record is “sufficiently specific to permit meaningful appellate review” and to permit a conclusion of no error. United States v. Ware, 577 F.3d 442, 452 (2d Cir.2009).

(b) Stitsky

Stitsky challenges his leadership role in the fraudulent scheme. The district court’s leadership-role determination was properly informed by “the exercise of decision making authority, the nature of participation in the commission of the offense, the recruitment of accomplices, the claimed right to a larger share of the fruits of the crime, the degree of participation in planning or organizing the offense, the nature and scope of the illegal activity, and the degree of control and authority exercised over others.” U.S.S.G. § 3B1.1 cmt. n. 4.

The district court determined, inter alia, that Stitsky (1) “was an equity partner in the scheme,” Stitsky Sent. Tr. 26:8-9, Stitsky App. 526; (2) “was involved from the start in planning the Cobalt business scheme”; (3) “worked with [William] Foster and Shapiro to execute the fraudulent scheme”; (4) “personally oversaw Cobalt’s fundraising arm”; (5) “was fully aware of the most pertinent aspects of the fraud,” id. at 18:8-18, Stitsky App. 518; (6) along with Shapiro, recruited Foster to serve as the “front man for Cobalt so that investors would not learn the truth about [his] and Shapiro’s criminal past and their leadership role at Cobalt,” id. at 19:8-9, Stitsky App. 519; (7) “directed [Charles] Hartman to make misleading and false statements for the purpose of marketing Cobalt to investors,” id. at 20:14-15, Stitsky App. 520; and (8) “directed other Cobalt employees to lie to investors,” id. at 19:22-23, Stitsky App. 519. We identify no clear error in these findings of fact nor in the leadership conclusion the district court derived therefrom.

Contrary to Stitsky’s assertion, that Shapiro may have “played a larger role in the day-to-day management of the criminal activity in this case does not foreclose a finding that [Stitsky] was also a leader of the activity.” United States v. Wisniewski 121 F.3d 54, 58 (2d Cir.1997) (internal quotation marks omitted).

v. Abuse of Trust

Defendants challenge the two-level abuse-of-trust enhancement. See U.S.S.G. § 3B1.3 (providing for enhancement where defendant “abused a position of public or private trust ... in a manner that significantly facilitated the commission or concealment of the offense”). A position of trust is “characterized by professional or managerial discretion (ie., substantial discretionary judgment that is ordinarily given considerable deference).” Id. § 3B1.3 cmt. n. 1. For this enhancement to apply, the position of trust “must have contributed in some significant way to facilitating the commission or concealment of the offense (e.g., by making the detection of the offense or defendant’s responsibility for the offense more difficult).” Id. The district court concluded that Shapiro “possessed enough managerial discretion at Cobalt to enable him to perpetrate a difficult-to-detect fraud by siphoning money out of Cobalt for his own use.” Shapiro Tr. 26:17-20, Shapiro App. 374. With respect to Stitsky, the district court found that he was “a high-level manager in a company with discretionary authority that assisted him in keeping essential information from investors and provided him the freedom to commit a difficult-to-detect wrong.” Id. at 21:21-25, Stitsky App. 521. These conclusions find ample support in the record.

Shapiro submits that this enhancement should not apply to him because Cobalt did not hold him out as someone in a position of trust. But the district court did not clearly err in determining otherwise based on trial. For example, one investor testified that Shapiro specifically told her he was the owner and president of Cobalt.

Stitsky’s contention that he lacked the necessary discretion to warrant application of this enhancement also fails. As discussed supra with respect to his leadership-role enhancement, Stitsky was a founding member of Cobalt who oversaw the company’s fundraising arm and knew the details of the fraudulent scheme. Thus, the district court’s conclusion that he exercised discretion is fully supported by the record.

vi. Overlapping Enhancements

Defendants argue that the district court erred in refusing to apply a downward departure based on overlapping Guidelines enhancements. The accumulation of overlapping enhancements, “when imposed upon a defendant whose adjusted offense level translates to a high sentencing range, ... permits a sentencing judge to make a downward departure.” United States v. Lauersen, 348 F.3d 329, 344 (2d Cir.2003) (citation omitted). The denial of such a departure, however, is “generally not appealable,” absent “clear evidence” that the “sentencing court misapprehended the scope of its authority to depart or the sentence was otherwise illegal.” United States v. Stinson, 465 F.3d 113, 114 (2d Cir.2006) (internal quotation marks omitted).

Here, the district court explicitly considered and rejected Stitsky’s argument for a downward departure based on cumulative enhancements, and the record admits no the conclusion that the district court misapprehended the scope of its departure authority. Accordingly, its downward-departure decision is not appealable.

vii. Section 3553(a) Factors

Defendants contend that the district court failed adequately to consider the § 3553(a) factors. The record belies this argument. During both Shapiro’s and Stitsky’s sentencing hearings, the district court explicitly considered the § 3553(a) factors, including the nature and circumstances of the offense, the history and characteristics of defendants, general deterrence, and specific deterrence. Moreover, the court specifically rejected Shapiro’s claim that the Guidelines range would result in unwarranted sentencing disparities among individuals with similar criminal records. Thus, the record affords no basis for concluding that the district court failed to consider the § 3553(a) factors. See United States v. Fernandez, 443 F.3d 19, 30 (2d Cir.2006) (“[W]e presume, in the absence of record evidence suggesting otherwise, that a sentencing judge has faithfully discharged her duty to consider the statutory factors.”).

b. Substantive Reasonableness

Defendants contend that their respective 85-year prison sentences are substantively unreasonable. They bear “a heavy burden because our review of a sentence for substantive reasonableness is particularly deferential.” United States v. Broxmeyer, 699 F.3d 265, 288-89 (2d Cir. 2012). “[Wjhile appellate courts have a role to play in patrolling the boundaries of reasonableness, we do so modestly, not substituting our own judgment for that of district courts, but rather, identifying as substantively unreasonable only those sentences that are so shockingly high, shockingly low, or otherwise unsupportable as a matter of law that allowing them to stand would damage the administration of justice.” Id. (alteration, citations, and internal quotation marks omitted). This is not such a case.

i. Shapiro

The district court found that Shapiro was the key architect and leader of a sophisticated fraudulent scheme, in which 352 victims lost a total of approximately $23,152,000. The district concluded that the scheme “resulted in devastating injury,” particularly for many older victims whose “life savings” were wiped out “at the end of their fives when they no longer had the ability to earn substantial amounts of money.” Shapiro Sent. Tr. at 27:2-5, Shapiro App. 375.

The district court further determined that Shapiro, who had been convicted of other fraud crimes in 1998 and was in Guidelines Criminal History Category III, was a recidivist who seemed not to hold himself “accountable for the devastating harm he inflicts on victims,” id. at 28:23-25, Shapiro App. 376, and who continued to pose a significant threat to society. In this regard, the court noted that Shapiro was in prison when he hatched the Cobalt scheme with Stitsky and on supervised release when engaged in the scheme.

Although the court acknowledged Shapiro’s childhood hardships, it accorded them little mitigating weight given the “extensive harm” caused by his crimes. Id. at 28:2-5, Shapiro App. 376. The court concluded, in light of Shapiro’s long history of criminal conduct, his likely recidivism, and the need for general deterrence, that an 85-year sentence was warranted.

The “particular weight” that a district court affords “aggravating and mitigating factors is a matter firmly committed to [its] discretion.” United States v. Broxmeyer, 699 F.3d at 289 (internal quotation marks omitted). Our appellate task is only to ensure that each factor “can bear the weight assigned it under the totality of circumstances in this case.” Id. (internal quotation marks omitted). While the challenged sentence is severe, it is within the applicable Guidelines range, and we cannot conclude that the factors identified by the district court do not adequately support its sentencing decision in this case. See United States v. Friedberg, 558 F.3d 131, 137 (2d Cir.2009) (stating that “in the overwhelming majority of cases, a Guidelines sentence will fall comfortably within the broad range of sentences that would be reasonable in the particular circumstances”); United States v. Jones, 531 F.3d 163, 174 (2d Cir.2008) (recognizing that in “great majority of cases, a range of sentences — frequently extending well beyond the narrow ranges prescribed by the Guidelines — must be considered reasonable”). Accordingly, we conclude that Shapiro’s sentence was substantively reasonable.

ii. Stitsky

The district court determined that Stit-sky was also an architect and a leader of a sophisticated scheme that defrauded hundreds of “not particularly sophisticated” people out of more than $23 million. Stitsky Sent. Tr. 16:7-10, Stitsky App. 516. The court identified as victims of Stitsky’s fraud a single working mother who lost funds intended to help her son pay for college, a couple who could no longer pay their mortgage, and retirees who lost their entire IRA funds.

The district court further noted that this was Stitsky’s third conviction for securities fraud, with prior frauds bearing some similarities to the Cobalt scheme and having ties to organized crime. Incarceration for past convictions had not deterred Stitsky from the Cobalt scheme, which he engaged in shortly after release from prison and while still under supervision. Based on these facts and Stitsky’s Criminal History Category of IV, the district court concluded that he was an “inveterate conman” who was unlikely to be deterred by additional prison time. Id. at 16:16, Stitsky App. 516. Accordingly, the court concluded that the “goal” of its sentence was to “provide general deterrence to criminal conduct, as well as to protect the public from further crimes of Mr. Stitsky.” Id. at 16:21-23, Stitsky App. 516. It therefore imposed an 85-year term of imprisonment.

Again, while the district court’s sentence is severe, the facts it identified in support of its within-Guidelines sentence adequately bear the weight assigned to them. Through the Cobalt scheme, which he helped create, Stitsky caused significant harm to hundreds of people, and he posed a particularly high risk of recidivism on release. In these circumstances, Stitsky has not shown that the challenged sentence is substantively unreasonable. See United States v. Broxmeyer, 699 F.3d at 289; United States v. Friedberg, 558 F.3d at 137.

iii. Sentencing Disparities

In arguing that their sentences are substantively unreasonable, defendants also contend that the their sentences yield unwarranted sentencing disparities. See 18 U.S.C. § 3553(a)(6); see also United States v. Mazza-Alaluf, 621 F.3d 205, 214 (2d Cir.2010) (stating that where defendant argues that district court “failed to accord the § 3553(a)(6) factor sufficient mitigating weight, he raises a substantive challenge”). In rejecting this argument by Shapiro, the district court observed that most of the proffered comparators, who received shorter sentences than defendants for fraudulent schemes involving similar or greater loss, did not have extensive criminal histories. Thus, those comparators are not so similarly situated to defendants as to render the challenged sentences substantively unreasonable.

In any event, disparities alone do not necessarily render sentences substantively unreasonable. See United States v. Florez, 447 F.3d 145, 157-58 (2d Cir.2006) (stating that weight to be given sentencing disparities, if properly considered, is within discretion of district court as long as ultimate sentence is reasonable); United States v. Fernandez, 443 F.3d at 32 (“[T]he requirement that a sentencing judge consider an 18 U.S.C. § 3553(a) factor is not synonymous with a requirement that the factor be given determinative or disposi-tive weight in the particular case, inasmuch as it is only one of several factors that must be weighted and balanced by the sentencing judge.” (emphasis in original)). Thus, we cannot conclude that the district court exceeded its sentencing discretion in determining that its articulated concern with defendants’ particular risk of recidivism and the significant harm that they had caused to numerous victims outweighed any disparity concern in this case.

iv. Loss Guidelines

Defendants also argue that their sentences are substantively unreasonable because the loss Guideline under U.S.S.G. § 2B1.1(b)(l) results in excessively harsh sentences. Even assuming that application of § 2Bl.l(b)(l) might result in substantively unreasonable sentences in some cases, this is not one of them in light of defendants’ particular criminal history, risk of recidivism, and harm caused. In any event, “[w]e have never held that a district court is required to reject an applicable Guideline.” United States v. Salim, 690 F.3d 115, 126 (2d Cir.2012). “At most, the judge may give a non-Guidelines sentence where she disagrees with the weight the Guidelines assigns to a factor.” Id. Defendants’ sentences thus are not substantively unreasonable due the district court’s application of § 2Bl.l(b)(l).

c. Eighth Amendment

Defendants claim that their 85-year sentences violate the Eighth Amendment’s prohibition against cruel and unusual punishment. See U.S. Const, amend. VIII. For the same reasons that their sentences are procedurally and substantively reasonable, we reject defendants’ argument. See United States v. Yousef, 327 F.3d 56, 163 (2d Cir.2003) (“Lengthy prison sentences, even those that exceed any conceivable life expectancy of a convicted defendant, do not violate the Eighth Amendment’s prohibition against cruel and unusual punishment when based on a proper application of the Sentencing Guidelines or statutorily mandated consecutive terms.”).

d. Competency

Shapiro argues that the district court erred in failing sua sponte to hold a competency hearing before sentencing. A district court is required to order a competency hearing “on its own motion, if there is reasonable cause to believe that the defendant may presently be suffering from a mental disease or defect rendering him mentally incompetent.” 18 U.S.C. § 4241(a). We review the district court’s application of § 4241(a) for abuse of discretion. See United States v. Arenburg, 605 F.3d 164, 169 (2d Cir.2010). Shapiro’s psychological evaluation states that his psychological “deficits” were not “of a degree as to render him incompetent to proceed with his case.” Forensic Psychological Report of Sanford L. Drob, Ph.D., Shapiro App. 308. Thus, the district court did not abuse its discretion in declining to order a hearing as to his competency.

We have considered defendants’ remaining arguments on appeal and conclude that they are without merit. Accordingly, the judgment of the district court is AFFIRMED. 
      
      . Although Stitsky and Shapiro submitted separate briefs on appeal, Stitsky has joined in Shapiro’s briefs. See Fed. R.App. P. 28(i). Thus, our resolution of Shapiro's arguments applies to Stitsky as well.
     
      
      . Gruber invested $900,000 in Cobalt. Agule, Cobalt’s lawyer, testified to an investment agreement that he executed with Louis Pap-pas, pursuant to which Pappas invested $2 million in Cobalt. Pappas did not testify at trial due to a recent surgery.
     
      
      . For this reason, defendants’ argument that the district court abused its discretion in admitting this testimony as "other act” evidence pursuant to Fed.R.Evid. 404(b) is meritless. See United States v. Carboni, 204 F.3d 39, 44 (2d Cir.2000) (”[E]vidence of uncharged criminal activity is not considered other crimes evidence under Fed.R.Evid. 404(b) if it arose out of the same transaction or series of transactions as the charged offense, if it is inextricably intertwined with the evidence regarding the charged offense, or if it is necessary to complete the story of the crime on trial.” (internal quotation marks omitted)); United States v. Thai, 29 F.3d 785, 812 (2d Cir.1994) ("When the indictment contains a conspiracy charge, uncharged acts may be admissible as direct evidence of the conspiracy itself.”); United States v. Concepcion, 983 F.2d 369, 392 (2d Cir.1992) ("An act that is alleged to have been done in furtherance of the alleged conspiracy, however, is not an ‘other’ act within the meaning of Rule 404(b); rather, it is part of the very act charged.”).
     
      
      . The affidavit of FBI Special Agent Christopher Dillon submitted in support of the Springfield warrant incorporated May’s affidavit by reference.
     
      
      . We likewise conclude that the district court did not abuse its discretion in denying Shapiro's motion to strike from the indictment the allegations that defendants had previously been convicted of fraud. See Fed.R.Crim.P. 7(d); United States v. Mulder, 273 F.3d 91, 99-100 (2d Cir.2001) ("Motions to strike sur-plusage from an indictment will be granted only where the challenged allegations are not relevant to the crime charges and are inflammatory and prejudicial.” (internal quotation marks omitted)).
     
      
      . We do not, however, foreclose defendants from pursuing an ineffective assistance of counsel challenge on a more developed record pursuant to 28 U.S.C. § 2255. See Massaro v. United States, 538 U.S. 500, 504, 123 S.Ct. 1690, 155 L.Ed.2d 714 (2003); United States v. Plitman, 194 F.3d at 64. At the same time, however, we express no view as to the merits of any such claim.
     
      
      . The evidence at trial indicated that Cobalt created the amendment in mid-January 2006 and backdated it to November 30, 2005, to avoid disclosing that the FBI executed search warrants at Cobalt's Springfield and Great Neck offices on December 1, 2005.
     
      
      . Nor do we identify abuse of discretion in the district court's failure to authorize funds pursuant to the Criminal Justice Act ("CJA”) to retain a real estate appraiser to value Cobalt’s properties. See United States v. Bah, 574 F.3d 106, 118 (2d Cir.2009) (stating that district court "may authorize the expenditure of funds exceeding $500 under the CJA only when ‘necessary for adequate representation’ ” (quoting 18 U.S.C. § 3006A(e)(l),(2))). Contrary to defendants’ assertion, such an appraisal would not have proved that the Units had value, even if it could have demonstrated that the properties had value. Nor would the appraisal have shown that defendants did not intend to harm their victims. See United States v. Ferguson, 676 F.3d at 280.
     
      
      . We also reject defendants’ argument that the district court was required to hold an evidentiary hearing as to the applicable Guidelines enhancements discussed supra. The district court afforded defendants an adequate "opportunity to rebut the Government’s allegations,” and thus no hearing was required. United States v. Phillips, 431 F.3d 86, 93 (2d Cir.2005) ("The district court is not required, by either the Due Process Clause or the federal Sentencing Guidelines, to hold a full-blown evidentiary hearing in resolving sentencing disputes.” (internal quotation marks omitted)).
     
      
      . The court noted that, in connection with his 1998 guilty plea, Shapiro was found to have (1) voided his cooperation agreement by withholding information from and lying to the government and (2) advanced incredible claims of actual innocence and a secret plea agreement with the government in an attempt to withdraw his plea.
     
      
      . This case is unlike United States v. Corsey, 723 F.3d 366 (2d Cir.2013), on which defendants rely. There, we vacated a sentence because the district court committed procedural error by engaging in a perfunctory analysis of the § 3553(a) factors and relying almost exclusively on deterrence to justify its sentence. See id. at 375-77. This case presents no such concerns. Moreover, the fraud at issue in Corsey involved no actual loss, only intended loss, see id. at 374-75, whereas here defendants’ fraud resulted in more than $23 million in loss and caused substantial harm to hundreds of victims.
     
      
      . Insofar as Stitsky argues that his sentence is unreasonable as compared to Shapiro’s and Foster's sentences, that claim is without merit. Section 3553(a) "does not require district courts to consider sentencing disparity among co-defendants.” United States v. Williams, 524 F.3d 209, 216 (2d Cir.2008) (internal quotation marks omitted). Moreover, the district court reasonably concluded that, in light of Stitsky’s more extensive criminal history and high risk of recidivism, his conduct warranted a sentence equivalent to Shapiro’s and much longer than Foster’s.
     
      
      . As Shapiro did not submit his psychological evaluation to the district court until after trial, there was no basis for the district court to order a competency hearing before trial.
     