SECURITIES AND EXCHANGE COMMISSION, Plaintiff-Appellee, v. Tomo RAZMILOVIC, Defendant-Appellant, Symbol Technologies, Inc., Kenneth Jaeggi, Leonard Goldner, Brian Burke, Michael DeGennaro, Frank Borghese, Christopher DeSantis, James Heuschneider, Gregory Mortenson, James Dean, Robert Donlon, Defendants, 738 F.3d 14

KEARSE, Circuit Judge: Defendant Tomo Razmilovic appeals from so much of a judgment of the United States District Court for the Eastern District of New York, Sandra J. Feuerstein, Judge, as orders him to disgorge to plaintiff Securities and Exchange Commission (“SEC”) $41,753,623.04, plus prejudgment interest in the amount of $27,260,953.99, and to pay a civil penalty of $22,876,811.52, for violations of various provisions of the Securities Act of 1933 (the “Securities Act”) and the Securities Exchange Act of 1934 (the “Exchange Act”) (collectively the “1933 and 1934 Acts”).

The district court entered a default against Razmilovic as a sanction for his refusal to comply with an order to appear for his deposition in the United States; the court ordered Razmilo-vic to pay the above amounts following an evidentiary hearing. On appeal, Razmilo-vic contends principally that the district court (1) abused its discretion in imposing a default, rather than a less severe sanction, for his refusal to appear for his deposition, and (2) erred in its calculations of the disgorgement, prejudgment interest, and statutory penalty amounts.

Razmilo-vic also contends, principally in connection with the proceedings on relief, that the district judge exhibited bias in favor of the SEC and against Razmilovic and should have recused herself. For the reasons that follow, we find no error or abuse of discretion in the entry of the default, the denial of Razmilovic’s recusal motion, and the disgorgement award. However, we remand for recalculation of prejudgment interest and for the clerical correction of a discrepancy between the amount of the civil penalty ordered in the district court’s ruling and the amount of the penalty awarded in the judgment. I.

BACKGROUND This is a civil enforcement action brought by the SEC against defendant Symbol Technologies, Inc. (“Symbol”), a supplier of mobile information systems using handheld electronic devices for barcode and other data capture technology, and various officers and employees of Symbol, alleging that the defendants engaged in fraudulent and manipulative practices in violation of, inter alia, § 10(

b) of the Exchange Act and Rule 10b-5 thereunder, § 13(b)(5) of the Exchange Act and § 17(

a) of the Securities Act, and various rules promulgated under the latter- sections. The complaint’s well-pleaded allegations as to Razmilovic’s liability, which, in light of his default, are deemed admitted, see Greyhound Exhibitgroup, Inc., v. E.L.U.L. Realty Corp., 973 F.2d 155, 158 (2d Cir.1992), cert. denied, 506 U.S. 1080, 113 S.Ct. 1049, 122 L.Ed.2d 357 (1993), include the following.

Razmilovic was Symbol’s president and chief operating officer (“COO”) from 1995 through June 2000, its President and Chief Executive Officer (“CEO”) from July 2000 until February 2002, and a member of its board of directors from 1995 to February 2002. “From at least 1998 until as recently as February 2003,” Razmilovic and others “engaged in a wide array of fraudulent accounting practices and other misconduct that had a cumulative net impact of over $230 million on Symbol’s reported revenue and'over $530 million on its reported pretax earnings.” (Complaint ¶ 1.) That conduct included entering into artificial swap transactions and other fraudulent schemes, publishing false reports of earnings, issuing fraudulent press releases, and filing false reports or registration statements with the SEC. (See, e.g., id. ¶¶ 44-48, 143.) Razmilovic regularly authorized changes to quarterly reports in order to conform Symbol’s reported results to management’s prior forecasts.

For example, on one occasion, management’s prediction was matched by making fraudulent adjustments, authorized by Razmilovic, that made a $2.5 million quarterly loss appear to be a $13.4 million gain. (See Complaint ¶ 40(f).) The frauds are described in greater detail in the district court’s Memorandum of Decision dated September 30, 2011, and reported at 822 F.Supp.2d 234 (“September 2011 Opinion”), familiarity with which is assumed. Razmilovic received bonuses and other compensation directly related to Symbol’s performance.

He also profited from the frauds because they artificially inflated Symbol’s stock price, and he had received as compensation for his employment thousands of Symbol stock options that he was able to exercise at prices well below the inflated market price and to sell at that market price.

In the present action, commenced in June 2004, the SEC sought— and largely won — a judgment that would, inter alia, enjoin Razmilovic from further violations of the securities laws, bar him from again serving as an officer or director of any public company, require him to disgorge all executive compensation he had received from Symbol from 1998 onward and all profits from his securities violations, plus prejudgment interest on those sums, and order him to pay penalties authorized by the 1933 and 1934 Acts. As to the relief ordered by the district court, only the monetary awards are at issue on this appeal. A.

The Criminal Case and Razmilovic’s Default in the Present Case In mid-2004, prior to the filing of the present complaint, an indictment was handed down in the United States District Court for the Eastern District of New York against Razmilovic and his codefen-dants, charging them with violations of the securities laws. Razmilovic, who was in Europe at the time, has not since returned to the United States. He is considered a fugitive by the United States Department of Justice (“Justice Department”). In 2004 in the present case, Judge Leonard D.

Wexler, to whom the case was then assigned, granted a motion by those defendants who were not fugitives for a stay of these proceedings pending resolution of the criminal case. Razmilovic’s motion for that relief was denied on the ground of his fugitivity, and he timely filed an answer, denying the material allegations of the complaint; the SEC agreed to postpone discovery until the stay granted by the district court was lifted. In September 2007, the case was reassigned to Judge Feuerstein, who lifted the stay in October 2007. In July 2009, the court set a tentative date for trial in January 2010.

Promptly thereafter, the SEC served Razmilovic with notice that his deposition would be taken at the SEC’s office in New York City on September 28, 2009. In a letter dated September 11, 2009, Razmilovic’s counsel informed the SEC that Razmilovic was “abroad,” and asked the SEC to “let us know whether you wish to make arrangement to take Mr. Razmilo-vic’s deposition abroad, either in person or by videoconference or telephone.” (Letter from Jeffrey B. Coopersmith to Todd D. Brody dated September 11, 2009.) The SEC rejected these alternatives.

Razmilo-vic’s counsel informed the SEC that Raz-milovic would not come to the United States. On September 29, 2009, after Razmilovic failed to appear for the scheduled September 28 deposition, the SEC moved for an order compelling him to appear for his deposition in New York. Razmilovic cross-moved to have his deposition taken via videoconference pursuant to Fed.R.Civ.P. 30(b)(4). In an Order dated October 9, 2009 (“October 2009 Order”), the district court granted the SEC’s motion and denied that of Razmilovic.

The court ordered Razmi-lovic “to appear in person, on a mutually agreeable date on or before October 22, 2009, as provided in plaintiffs notice of deposition.” October 2009 Order at 1. The court warned that “[fjailure of Mr. Razmi-lovic to appear in person for a deposition on or before October 22, 2009 may result in sanctions being imposed against him and/or his attorneys pursuant to Rule 37(b)(2)(A), including a default judgment being entered against him.” October 2009 Order at 1. The SEC thereafter proposed to Razmi-lovic several alternative dates for his deposition.

On October 15, Razmilovic informed the SEC that, despite the court’s October 2009 Order, he would not appear for the deposition. On December 10, the SEC moved pursuant to Fed.R.Civ.P. 37(b)(2)(A)(vi) for entry of a default judgment against Razmilo-vic as a sanction for his refusal to obey the court’s order to appear for his deposition. Razmilovic opposed the motion.

He acknowledged that his violation of the court order “may result in some form of sanction” but argued that a default judgment was drastic, the “harshest of sanctions,” and was not warranted because “lesser, effective sanctions may be imposed.” (Razmilovic Memorandum of Law in Opposition to Motion for Sanctions (“Razmilovic Sanctions Memorandum”) at 4-5.) Razmi-lovic proposed, for example, that he instead be barred from disputing certain facts or asserting certain defenses, or be required to appear for his deposition in Sweden and to pay for the expenses of the deposition. (See id. at 5-6.) Razmilovic also argued that a default judgment would be improper because, in his view, the Supreme Court, in Degen v.

United States, 517 U.S. 820, 116 S.Ct. 1777, 135 L.Ed.2d 102 (1996), had “rejected automatic disen-titlement” of fugitives in civil cases. (Raz-milovic Sanctions Memorandum at 9.) He argued that imposing a default “as the sanction for the sole discovery transgression of failing to attend an in-person deposition in the United States as ordered would be the same as automatic disentitlement.” (Id.) In an order announced on the record at the ensuing status conference, the district court granted the SEC’s motion and imposed a default against Razmilovic (“Default Order”). (See Status Conference Transcript, December 22, 2009 (“Conf.

Tr.”), at 5.) The court noted that the SEC was entitled, except in circumstances not present here, to choose the location for depositions it wished to take and that Raz-milovic had offered “no excuse for his failure to appear at the deposition which was ordered other than his [own] convenience.” (Id. at 2.) The court found that Razmilo-vic’s refusal to appear was “willful and intentional.” (Id. at 3; see also id. at 4-5 (“Considering the factors that courts are to consider in cases of this type, there is no question that Razmilovic’s noncompliance with this court’s October 9th order was willful....”).) Although Razmilovic argued that Degen foreclosed entry of a default against him under the fugitive disentitlement doctrine, the court pointed out that the SEC was not invoking that doctrine: The SEC sought a default judgment not because Razmilovic was a fugitive from the criminal case but solely because he had willfully violated the court’s October 2009 Order to appear for his deposition in the present case. (Id. at 3.) Quoting from its October 2009 Order, the district court also pointed out that Razmilovic had been “specifically warned” that if he failed to comply with that order “ ‘to appear in person for a deposition on or before October 22, 2009,’ ” he could be subject to sanctions, “ ‘including a default judgment.’ ” (Id. at 5.) The court noted that Razmilovic himself, in opposition to the SEC’s Rule 37 motion, “admits that he should be sanctioned” (id. at 3), and it rejected his request for a sanction less severe than the entry of a default.

The court found that Razmilovic’s proposal that the court should simply order him to have his deposition taken in Sweden — given that this was what Razmilovic had proposed all along — could hardly be considered a “sanction” at all. (Id.) Given the facts that Razmilovic had received an explicit warning that his failure to comply with the October 2009 Order could result in a default, that the SEC’s motion papers described evidence indicating that there was a factual basis for finding that Razmilovic had violated the securities laws (see id. at 4), and that Razmilovic’s refusal to comply with the October 2009 Order was willful and intentional, the court concluded that the entry of a default was appropriate (see id. at 5).

Razmilovic moved for reconsideration, largely reiterating his Degen argument and his contention that lesser sanctions would be more appropriate, and arguing that the district court had failed to assess whether Razmilovic had a meritorious defense to the complaint’s allegations. In an order dated February 25, 2010 (“February 2010 Order”), the district court denied the motion, stating, inter alia, that a motion for a default judgment under Rule 37(b)(2)(A)(vi) does not require determination of the merits of the complaint.

The court noted that Razmilovic’s other arguments had been previously raised and rejected, and there was neither an intervening change of controlling law nor a clear error by the court warranting a different result. B. The Proceedings With Respect to Relief With Razmilovic’s liability established by the default, the district court held a trial to determine the relief to which the SEC was entitled against Razmilovic. (All of Razmi-lovic’s codefendants reached settlements with the SEC.) 1.

The Expert Evidence With Regard to Disgorgement With respect to the SEC’s request for disgorgement of the profits gained by Raz-milovic as a result of his fraud, Razmilovic and the SEC submitted expert reports (see

Part II.B.2. below) principally addressing how to calculate the total amount of Raz-milovic’s fraud-related profits from stock transactions. In order to determine the value by which Symbol’s share price was inflated due to Razmilovic’s fraud, both the SEC’s expert, Edward S.

O’Neal, and Raz-milovic’s expert, Denise Neumann Martin, used “event-study methodology.” That is, assuming that the company’s share price has been affected by prior fraud, the economist seeks to quantify that effect by looking at changes in the stock’s prices in the one or two days after the public availability of new information suggesting a fraud, and comparing those changes to the changes that would have been predicted based solely on market or industry factors. The two experts differed in their applications of that methodology.

O’Neal identified three statistically significant events which publicly disclosed or suggested that Symbol’s profitability had previously been overstated and which were followed by declines in Symbol’s share price. O’Neal opined that as a result of Razmilovic’s prior frauds, Symbol’s share price, prior to the first of these events, had been inflated by a total of $11.54.

Martin, in contrast, found eleven statistically significant events — only one of which was among the three identified by O’Neal — and she opined that much of the stock price movement following the events she cited was attributable to industry trends. She thus calculated that the frauds had inflated Symbol’s share price by a total of only $3.42. ' 2. The District Court’s Decision In its September 2011 Opinion, the district court ruled, to the extent pertinent to this appeal, that Razmilovic should disgorge $41,753,623.04, plus prejudgment interest, and pay a civil penalty of $20,876,811.52 [sic ].

See 822 F.Supp.2d at 284. With respect to the SEC’s request that Razmilovic be required to disgorge all of the compensation he received from Symbol from the time his fraudulent conduct began, the district court disagreed, ruling that he should disgorge only so much as was causally related to the fraud. The court found that since Razmilovic’s promotion from COO to CEO occurred shortly after an announcement of Symbol’s increased revenue “which indisputably resulted from the fraud,” the part of his salary that should be disgorged. was the difference between his salaries as COO and CEO. Id. at 255-56.

The district court also ordered disgorgement of, inter alia, Razmilovic’s performance bonuses and severance payment, finding that both had been dependent on Symbol’s fraudulently inflated success. See id. at 256-59. The court found that the amount of executive compensation Razmilovic should disgorge totaled $7,883,647.84. As to the SEC’s request that Razmilovic be required to disgorge his profits from transactions in Symbol stock, measured simply by the difference between his sales price and his purchase price, the district court again disagreed.

It ruled that his unlawful gains from the stock transactions should be measured by the “amount by which the value of Symbol’s stock was inflated as a result of the fraud.” Id. at 261. In determining the amount of that inflation, the court credited the .calculation by the SEC’s expert, O’Neal, over that of Razmilovic’s expert, Martin. The court noted that Martin lacked “prior experience with disgorgement eases involving the exercise of stock options,” that she failed to base her opinions on economic literature, and that she failed to follow her own described procedures. Id. at 262-63.

The court concluded that the frauds in which Razmilovic participated had inflated Symbol’s stock price by $11.54 per share. See id. ■ at 261-66.

On that basis, the court calculated that with respect to Razmilovic’s stock transactions — including his exerciseof stock options by selling fraudulently inflated shares to Symbol to fund the exercise of options having far lower prices; “zero-cost collar” transactions (i.e., offsetting put and call options), that Razmilovic entered into while fraudulently representing to the other party that he had no material, non-public information concerning Symbol; and his sales of Symbol stock on the open market while its price was inflated — Razmilovic’s fraudulent gains totaled $33,869,975.20.

Thus, the court concluded that, given his fraud-related gains in executive compensation and stock transactions, Razmilovic should disgorge a total of $41,753,623.04. Id. at 276. As discussed in

Part II.C.l. below, the district court ruled that Razmilovic should pay prejudgment interest on that dis-gorgeable amount “from the time of his unlawful gains to the entry of judgment,” 822 F.Supp.2d at 278. The court rejected Razmilovic’s contention that he should not be required to pay such interest because the Justice Department had caused $17.4 million of his funds in Swiss bank accounts to be frozen in 2004, denying him access to those funds since that time. See id. at 277-78. The court directed the SEC “to file a proposed judgment including the amount of prejudgment interest calculated in accordance with this order.” Id. at 279. Finally, as discussed in

Part II.C.2. below, the district court imposed a statutory penalty pursuant to § 20(

d) of the Securities Act, 15 U.S.C. § 77t(d)(l), and § 21(

d) of the Exchange Act, 15 U.S.C. § 78u(d)(3)(A), to the extent of one-half the amount of Razmilovic’s disgorgeable pecuniary gain, or $20,876,811.52. See 822 F.Supp.2d at 279-82. In the proposed judgment submitted by the SEC and entered by the court, however, the penalty figure was $2 million higher, $22,876,811.52. II. DISCUSSION On appeal, Razmilovic argues principally that the district court’s imposition of a default judgment was an abuse of discretion and that its disgorgement, penalty, and prejudgment interest awards were erroneous.

He also contends that the district judge should have recused herself from the case, arguing that her rulings evinced partiality toward the SEC. We reject Razmilovic’s contentions except to the extent that Razmilovic was ordered to pay prejudgment interest on funds that had been frozen at the behest of the United States government, and except to the extent that the judgment must be corrected to have the civil penalty match the amount awarded by the district court in its September 2011 Opinion. A.

The Entry of Default Rule 37 of the Federal Rules of Civil Procedure provides in part that if a party “fails to obey an order to provide ... discovery, ... the court where the action is pending may issue further just orders,” including (

i) directing that the matters embraced in the order or other designated facts be taken as established for purposes of the action, as the prevailing party claims; (ii) prohibiting the disobedient party from supporting or opposing designated claims or defenses, or from introducing designated matters in evidence; (iii) striking pleadings in whole or in part; (iv) staying further proceedings until the order is obeyed; (

v) dismissing the action or proceeding in whole or in part; (vi) rendering a default judgment against the disobedient party; or (vii) treating as contempt of court the failure to obey.... Fed.R.Civ.P. 37(b)(2)(A). Clearly, the most severe of these sanctions for a disobedient plaintiff is the dismissal of his action; the most severe for a disobedient defendant is the imposition of a default. “[Djismissal or default” should be ordered “only when the district judge has considered lesser alternatives.” Southern New England Telephone Co. v. Global NAPs Inc., 624 F.3d 123, 144 (2d Cir.2010)(“SNET ”).

No sanction should be imposed without giving the disobedient party notice of the particular sanction sought and an opportunity to be heard in opposition to its imposition. See, e.g., Reilly v. NatWest Markets Group Inc., 181 F.3d 253, 270 (2d Cir.1999), cert. denied, 528 U.S. 1119, 120 S.Ct. 940, 145 L.Ed.2d 818 (2000); United States Freight Co. v. Penn Central Transportation Co., 716 F.2d 954, 955 (2d Cir.1983) (“U.S. Freight ”). We review a district court’s imposition of sanctions for abuse of discretion. See, e.g., National Hockey League v.

Metropolitan Hockey Club, Inc., 427 U.S. 639, 642, 96 S.Ct. 2778, 49 L.Ed.2d 747 (1976) (“NHL ”); Agiwal v. Mid Island Mortgage Corp., 555 F.3d 298, 302 (2d Cir.2009) (“Agiwal”);. U.S. Freight, 716 F.2d at 955; Sieck v.

Russo, 869 F.2d 131, 134 (2d Cir.1989) (“Sieck ”). “[S]everal factors may be useful in evaluating a district court’s exercise of discretion” to impose sanctions pursuant to this rule, including “(1) the willfulness of the non-compliant party or the reason for noncompliance; (2) the efficacy of lesser sanctions; (3) the duration of the period of noncompliance, and (4) whether the non-compliant party had been warned of the consequences of noncompliance.” SNET, 624 F.3d at 144 (quoting Agiwal 555 F.3d at 302).

Because the text of the rule requires only that the district court’s orders be “just,” however, and because the district court has “wide discretion in imposing sanctions under Rule 37,” Shcherbakovskiy v. Da Capo Al Fine, Ltd., 490 F.3d 130, 135 (2d Cir.2007) (internal quotation marks omitted), these factors are not exclusive, and they need not each be resolved against the party challenging the district court’s sanctions for us to conclude that those sanctions were within the court’s discretion. SNET, 624 F.3d at 144.

In Sieck, we affirmed the entry of defaults against defendants who “elected to defy” two court orders to attend their depositions. 869 F.2d at 134. We noted that [t]he mere availability of softer sanctions ... does not bar a court from imposing the default sanction.

As the Supreme • Court recognized, here, as in other areas of the law, the most severe in the spectrum of sanctions provided by statute or rule must be available to the district court in .appropriate cases, not merely to penalize those whose conduct may be deemed to warrant such a sanction, but to deter those who might be tempted to such conduct in the absence of such a deterrent.

Sieck, 869 F.2d at 134 (quoting NHL, 427 U.S. at 643, 96 S.Ct. 2778); see also NHL, 427 U.S. at 640, 642, 96 S.Ct. 2778 (extreme sanction of dismissal of complaint justified where failure to comply with court’s order was due to plaintiffs’ willfulness and bad faith); Agiwal, 555 F.3d at 302 (“dismissal with prejudice is a harsh remedy to be used only in extreme situations, and then only when a court finds willfulness, bad faith, or ... fault by the non-compliant litigant” (internal quotation marks omitted)); id. (“[wjhether a litigant was at fault or acted willfully or in bad faith are questions of fact”).

An abuse of discretion may consist of an erroneous view of the law, a clearly erroneous assessment of the facts, or a decision that cannot be located within the range of permissible decisions. See, e.g., Agiwal, 555 F.3d at 302 n. 2; Sims v. Blot, 534 F.3d 117, 132 (2d Cir.2008). “A district court would necessarily abuse its discretion if it based its ruling on an erroneous view of the law or on a clearly erroneous assessment of the evidence.” Cooter & Gell v. Hartmarx Corp., 496 U.S. 384, 405, 110 S.Ct. 2447, 110 L.Ed.2d 359 (1990) (reviewing sanction imposed pursuant to Fed.R.Civ.P. 11).

But in the absence of such an error, “[t]he question, of course, is not whether [the reviewing court] would as an original matter have [imposed the sanction in question]; it is whether the District Court abused its discretion in so doing.” NHL, 427 U.S. at 642, 96 S.Ct. 2778; see, e.g., SNET, 624 F.3d at 143. In the present case, we see no error of law nor any clearly erroneous finding of fact with respect to the district court’s decision to impose on Razmilovic the sanction of default.

To begin with, we reject Razmilovic’s contention that the district court violated the principle established by Degen, i.e., that the fugitive dis-entitlement doctrine should not be applied to prevent a fugitive from a criminal case from participating in a civil case. The fugitive disentitlement doctrine allows an appellate court to, inter alia, “dismiss the appeal of a defendant who is a fugitive from justice during the pendency of his appeal.” Ortega-Rodriguez v. United States, 507 U.S. 234, 239, 113 S.Ct. 1199, 122 L.Ed.2d 581 (1993).

The Degen Court held that this doctrine does not authorize the district court to “strike the filings of a claimant in a forfeiture suit” and enter judgment against him merely “for failing to appear in a related criminal prosecution,” 517 U.S. at 821, 116 S.Ct. 1777, “or otherwise ... resisting[ the] related criminal prosecution,” id. at 823, 116 S.Ct. 1777. In the present case, however, as described in

Part I.A. above, the court rejected Razmilovic’s Degen argument because the SEC did not seek — and the court did not enter — sanctions under the fugitive disentitlement doctrine (see Conf. Tr. 3). Rather, the court entered the default against Razmilovic on the express basis that he had willfully disobeyed the October 2009 Order. (See id. at 3, 4-5.) Further, that basis for imposition of a default was plainly one as to which the Degen Court had indicated approval.

That Court stated that a “District Court has its usual authority to manage discovery in a civil suit, including the power to enter protective orders limiting discovery as the interests of justice require.” 517 U.S. at 826, 116 S.Ct. 1777. The Degen Court added: [0]f course, [the fugitive’s] absence entitles him to no advantage. If his unwillingness to appear in person results in noncompliance with a legitimate order of the court respecting pleading, discovery, the presentation of evidence, or other matters, he will be exposed to the same sanctions as any other uncooperative party.

A federal court has at its disposal an array of means to enforce its orders, including dismissal in an appropriate case. Again, its powers include those furnished by federal rule, see, e.g., Fed. Rules Civ. Proc. 37, 41(b); National Hockey League v. Metropolitan Hockey Club, Inc., 427 U.S. 639 [96 S.Ct. 2778, 49 L.Ed.2d 747] (1976) (per curiam).... Degen, 517 U.S. at 827, 116 S.Ct. 1777 (emphases added). The entry of a default in the present case pursuant to Rule 37(b)(2)(A)(vi) because of Razmilovic’s refusal to comply with the district court’s legitimate discovery order plainly did not run afoul of Degen.

Razmilovic does not even attempt to argue that the court’s finding of willfulness was erroneous. Nor, plausibly, could he. His adamant and express insistence that he would not comply with the October 2009 Order requiring that he appear for his deposition in New York made plain that his disobedience was willful and intentional. None of Razmilovic’s proposed alternative sanctions was likely to lead to his compliance with the court’s order for his deposition as noticed by the SEC or to provide the SEC with the discovery methods to which it was entitled. As indicated in

Part I.A. above, the court had warned that if Razmilovic did not appear for his deposition in accordance with the SEC’s notice he would be exposed to “sanctions ... pursuant to Rule 37(b)(2)(A), including a default judgment being entered against him,” October 2009 Order at 1.

Although Razmilovic disobeyed only that single court order, his adamance in the face of the court’s warning of possible sanctions that included the extreme sanction of default clearly supported an inference that renewed orders to appear would be unavailing and that no lesser sanction would be effective to induce Razmilovic to appear in New York for his deposition. The court was not required to relieve him of that obligation.

Given that “the most severe in the spectrum of sanctions provided by” Rule 37 “must be available to the district court in appropriate cases,” not only to make such discovery orders effective in the case at hand but also “to deter those who might be tempted to [engage in similar disobedience] in the absence of such a deterrent,” NHL, 427 U.S. at 643, 96 S.Ct. 2778, we cannot conclude that the entry of default against Razmilovic in the present case was an abuse of discretion. B. Disgorgement Razmilovic attacks the district court’s disgorgement order on several grounds.

First, he contends that the judge should have recused herself on the ground of what he characterizes as “extreme bias against” him and an abuse of discretion in, inter alia, allowing the SEC to reopen its case-in-ehief in the remedies hearing in order to present expert evidence in support of disgorgement. (Razmilovic brief on appeal at 23.) He urges this Court to vacate the default judgment against him and remand for proceedings before a different district judge.

Second, Razmilovic argues that the court’s calculations of the disgorgeable amounts were without foundation and that the court should have credited the views of Razmilovic’s expert and excluded the report of the SEC’s expert. None of these contentions is persuasive. 1. Recusal. As indicated above, the district court entered thé default against Razmilovic in' December 2009 and denied his motion for reconsideration in February 2010. March 15, 2010, was eventually set as the date for the evidentiary hearing needed to determine the amounts that Razmilovic should be required to disgorge.

The hearing started on that date; -the SEC rested after presenting evidence of Razmilovic’s executive compensation at Symbol and of the proceeds of his other transactions in Symbol stock after his fraudulent activity began. On March 16, the hearing was resumed but was adjourned without either side presenting evidence; the SEC said it had not decided whether it would call an expert witness in rebuttal to the expert to be called by Razmilovic. The hearing was adjourned until May 10 to allow the parties to produce and exchange information with regard to the reports of their respective experts.

After a further adjournment— and after the district court “denied the parties’ respective motions to exclude the testimony of each other’s expert witness” — the court, over the SEC’s objection, granted Razmilovic’s request that the remaining issues be determined “upon submission of experts’ reports, deposition transcripts and post-hearing briefs.” 822 F.Supp.2d at 242. In the meantime, on April 5, 2010, Raz-milovic moved pursuant to Fed.R.Civ.P. 52(

c) for a judgment on partial findings, dismissing the SEC’s disgorgement claims on the ground that the SEC had failed to introduce evidence of any causal connection between the moneys gained by Razmi-lovic and his fraudulent conduct. .At an unrecorded telephone conference call among the court and the parties on April 9, 2010, the SEC indicated that it wished to reopen its case-in-chief to offer two documents it had inadvertently failed to introduce. The SEC also said it would produce an expert in rebuttal to the evidence anticipated from Razmilovic’s expert.

At that point, counsel for Razmilovic announced that Razmilovic did not intend to put on a defense case. According to Razmilovic, the district court then pointedly asked [SEC counsel] whether the Commission wanted to move to reopen its case-in-chief to present an expert witness. It was the Court, not SEC counsel, that suggested reopening for the purpose of presenting an expert witness. [SEC counsel] hesitated, and then responded that the Commission did want to reopen its case to present an expert witness. (Declaration of Jeffrey B.

Coopersmith dated April 27, 2010 (“Coopersmith Deck”), ¶ 21.) Over Razmilovic’s objection, the court set dates for the making of, and the response to, the SEC’s motion to reopen. The court thereafter granted the SEC’s motion before Razmilovic’s formal response was due.

On April 27, 2010, Razmilovic moved pursuant to 28 U.S.C. § 455 to have the district judge recuse herself from further presiding over the case “on the ground that the Court’s impartiality might reasonably be questioned.” (Razmilovic Memorandum of Law in Support of Motion for Recusal at 1 (internal quotation marks omitted).) The motion, supported also by a declaration of counsel, argued that the court had exhibited bias against Razmilo-vic and in favor of the SEC by, inter alia, granting default as a sanction; denying Razmilovic’s motion to preclude the SEC from presenting any evidence in support of disgorgement or civil penalties because the SEC’s damages statement was filed less than 15 days before the hearing date, in violation of the judge’s individual rules; denying that motion prior to the deadline for Razmilovic’s reply brief in support of his motion; urging the SEC to move to reopen its case-in-chief in order to introduce expert evidence on disgorgement; and granting that motion prior to the deadline the court had set for Razmilovic’s response to the motion. (Id. at 3-5; see also Coopersmith Decl. ¶¶ 10-22.) The SEC opposed the motion for recusal on several grounds.

It argued that the motion principally complained of legal rulings by the court with which Razmilovic disagreed, and that such rulings and disagreements were not a valid basis for a motion to recuse.

The SEC also argued that the motion was untimely: that a litigant must make such a motion “ ‘at the earliest possible moment after obtaining knowledge of facts demonstrating the basis for such a claim,’ ” rather than continuing to participate in the proceedings and waiting to see how the court rules on the various issues, as Razmilovic had done. (SEC Memorandum in Opposition to Raz-milovic Motion for Recusal at 7 (quoting In re International Business Machines Corp., 45 F.3d 641, 643 (2d Cir.1995)).) And the SEC argued that the court had exhibited no bias but had treated the parties even-handedly, overlooking many procedural transgressions by Razmilovic.

In an order dated June 14, 2010, the district court denied Razmilovic’s recusal motion. The court ruled that in large part the motion was based on its legal rulings, which provided no basis for recusal. The court acknowledged that in two instances it had inadvertently ruled on motions prematurely, ascribing those errors to the fact that the court had failed to adhere to its own so-called “Bundle” rule, which required that no motion be filed until all of the papers, for and against, were ready.

The court noted that after denying Razmi-lovic’s preclusion motion prior to the deadline for his reply brief, the court had rectified that mistake by granting his motion for reconsideration and fully considering Razmilovie’s reply brief submitted on reconsideration; the court had adhered to its original decision only after reconsideration. The court also pointed out that Razmilovic had not even bothered to move for reconsideration of the order allowing the SEC to reopen its case-in-chief; he had instead immediately moved for recusal.

As to the merits of its order allowing the SEC to reopen its case-in-chief to present expert evidence, the court noted that Raz-milovic’s Rule 52(

c) motion, which was filed with the Court on April 5, 2010, clearly apprized the SEC of the defects in its evidence, of which it presumably was otherwise unaware. Razmilovic had not yet commenced his presentation of a defense and had previously secured an expert witness. There is nothing improper or inappropriate in permitting a party to reopen its case to remedy the defects in its evidence, particularly absent any prejudice to the opposing party. Order dated June 14, 2010, at 12.

The court concluded that none of the actions attributed to it by Razmilovic could reasonably be perceived as emanating from any bias against Razmilovic or in favor of the SEC, and that recusal would be inappropriate. Razmilovic contends that this conclusion was error. We disagree. A judge is required to recuse herself from “any proceeding in which h[er] impartiality might reasonably be questioned.” 28 U.S.C. § 455(a). The standard for disqualification under 28 U.S.C. § 455(

a) is “an objective” one, ISC Holding AG v. Nobel Biocare Finance AG, 688 F.3d 98, 107 (2d Cir.2012) CISC Holding ”) (internal quotation marks omitted); the question is whether an objective and disinterested observer, knowing and understanding all of the facts and circumstances, could reasonably question the court’s impartiality, see, e.g., id.; In re Drexel Burnham Lambert Inc., 861 F.2d 1307, 1313 (2d Cir.1988), reh’g denied en banc, 869 F.2d 116 (2d Cir.), cert. denied, 490 U.S. 1102, 109 S.Ct. 2458, 104 L.Ed.2d 1012 (1989).

To be disqualifying under § 455, “ ‘[t]he alleged bias and prejudice ... must stem from an extrajudicial source and result in an opinion on the merits on some basis other than what the judge has learned from his participation in the case.’ ” In re International Business Machines Corp., 618 F.2d 923, 927 (2d Cir.1980) (quoting United States v.

Grinnell Corp., 384 U.S. 563, 583, 86 S.Ct. 1698, 16 L.Ed.2d 778 (1966) (emphasis ours)). [Ojpinions formed by the judge on the basis of facts introduced or events occurring in the course of the current proceedings, or of prior proceedings, do not constitute a basis for a bias or partiality motion unless they display a deep-seated favoritism or antagonism that would make fair judgment impossible. Thus, judicial remarks during the course of a trial that are critical or disapproving of, or even hostile to, counsel, the parties, or their cases, ordinarily do not support a bias or partiality challenge. Liteky v.

United States, 510 U.S. 540, 555, 114 S.Ct. 1147, 127 L.Ed.2d 474 (1994). Accordingly, recusal is not warranted where the only challenged conduct “consist[s] of judicial rulings, routine trial administration efforts, and ordinary admonishments ... to counsel and to witnesses,” where the conduct occurs during judicial proceedings, and where the judge “neither (1) reliefs] upon knowledge acquired outside such proceedings nor (2) display[s] deep-seated and unequivocal antagonism that would render fair judgment impossible.” Id. at 556, 114 S.Ct. 1147.

A district judge’s decision not to recuse herself from a proceeding is reviewed under an abuse-of-discretion standard. See, e.g., ISC Holding, 688 F.3d at 107; Diamondstone v. Macaluso, 148 F.3d 113, 120 (2d Cir.1998). It is “rare” for “a district judge’s denial of a motion to recuse” to be “disturbed by an appellate court.” ISC Holding, 688 F.3d at 107 (internal quotation marks omitted). We see no abuse of discretion here. The court found that Razmilovic’s refusal to comply with the court’s order was willful — a finding he does not suggest was in any way erroneous or inaccurate. As discussed in

Part II.A. above, the entry of a default based on that willful choice was well within the proper bounds of the court’s discretion. All of Razmilovic’s complaints about the district judge center on judicial rulings, ordinary trial administration efforts, and relatively routine commentary on the positions and conduct of the parties in the litigation. And although, as the court acknowledged, two administrative errors occurred when the court ruled on two motions before they were fully submitted, we see no objective basis for attributing those errors to bias. Judges are human.

Errors are made; some are corrected; some are not, but are harmless. New are attributable to bias. Nor are we persuaded that the district court’s allowing the SEC to reopen its case-in-chief could reasonably be viewed as emanating from bias. The absence of bias in favor of the SEC is reflected by the fact that a hearing was being held.

The judge had agreed with Razmilovic’s position that a hearing was needed to determine the amount Razmilovic gained as a result of the frauds, and had rejected the position of the SEC that it was entitled, without the need for a hearing, to disgorgement of “every single dollar of Mr. Razmilovic’s compensation while he was at Symbol” (Conf. Tr. 9 (Razmilovic’s counsel characterizing the SEC’s position)).

And having agreed with Razmilovic that the equitable remedy of disgorgement should be granted only with respect to so much of Razmilo-vic’s gains as were causally related to the frauds, it was well within the court’s equitable powers and discretion to allow the SEC, prior to Razmilovic’s presentation of any defense, to reopen its case-in-chief to present evidence of causation.

We note that Razmilovic complains that he “moved in essence for a directed verdict [and ]the Court sua, sponte invited the SEC to reopen its remedies case to cure th[e] defect” (Coopersmith Decl. ¶ 4 (emphasis added); see id. ¶ 22 (Razmilovic made “a motion effectively for a directed verdict after a party has rested”)) — as if such a motion itself precluded any further presentation of evidence by the SEC.

But when a party moves for a “directed verdict” (known since 1991 as a “judgment as a matter of law”) in a jury trial, it must do so — with specificity as to the alleged evi-dentiary deficiency — before the case is submitted to the jury, see Fed.R.Civ.P. 50(a)(2); both the timing requirement and the specificity requirement are designed “to assure the responding party an opportunity to cure any deficiency in that party’s proof,” Piesco v. Koch, 12 F.3d 332, 340 (2d Cir.1993) (internal quotation marks omitted); see, e.g., Lore v. City of Syracuse, 670 F.3d 127, 152-53 (2d Cir.2012); 9B C. Wright & A.

Miller, Federal Practice and Procedure § 2533, at 494-507 (3d ed.1998). While the standards for assessing such motions under Rule 50 do not govern motions for judgment in a case tried to the court without a jury, it should be beyond cavil that the court, in a proceeding in which it will rule on proposed equitable remedies, has no less authority than it has in a case to be decided by a jury to allow a party to attempt to cure an alleged deficiency in its proof before the matter is submitted to the decisionmaker. In sum, we see no abuse of discretion in the district judge’s denial of Razmilovic’s recusal motion. 2.

The Merits Razmilovic contends that the district court erred in ordering him to disgorge any more than $4,870,849, arguing principally (

a) that the court should not have required disgorgement of any of his executive compensation from Symbol, and (

b) that, with respect to his stock transactions, the court should have, inter alia, excluded the evidence of the SEC’s expert O’Neal and should not have found that Razmilo-vic’s expert Martin was unqualified. We are unpersuaded. ’ “Once the district court has found federal securities law violations, it has broad equitable power to fashion appropriate remedies, including ordering that culpable defendants disgorge their profits.” SEC v. First Jersey Securities, Inc., 101 F.3d 1450, 1474 (2d Cir.1996) (“First Jersey”), cert. denied, 522 U.S. 812, 118 S.Ct. 57, 139 L.Ed.2d 21 (1997).

Disgorgement “is a method of forcing a defendant to give up the amount by which he was unjustly enriched.” SEC v. Commonwealth Chemical Securities, Inc., 574 F.2d 90, 102 (2d Cir.1978). Thus, in order to establish a proper disgorgement amount, “the party seeking disgorgement must distinguish between the legally and illegally derived profits,” CFTC v. British American Commodity Options Corp., 788 F.2d 92, 93 (2d Cir.), cert. denied, 479 U.S. 853, 107 S.Ct. 186, 93 L.Ed.2d 120 (1986), so that disgorgement is ordered only with respect to those that were illegally derived.

Nonetheless, because of the difficulty of determining with certainty the extent to which a defendant’s gains resulted from his frauds — especially profits from transactions in securities whose market price has been affected by the frauds — the court need not determine the amount of such gains with exactitude. “The amount of disgorgement ordered need only be a reasonable approximation of profits causally connected to the violation.” First Jersey, 101 F.3d at 1475 (internal quotation marks omitted); see also SEC v. Warde, 151 F.3d 42, 50 (2d Cir.1998) (“Warde ”); SEC v.

Patel, 61 F.3d 137, 139 (2d Cir.1995) (“Patel ”). Despite sophisticated econometric modeling, predicting stock market responses to alternative variables is ... at best speculative. Rules for calculating disgorgement must recognize that separating legal from illegal profits exactly may at times be a near-impossible task. SEC v. First City Financial Corp., 890 F.2d 1215, 1231 (D.C.Cir.1989) (“First City ”).

Given these difficulties, “[s]o long as the measure of disgorgement is reasonable, any risk of uncertainty should fall on the wrongdoer whose illegal conduct created that uncertainty.” Warde, 151 F.3d at 50 (internal quotation marks omitted); see, e.g., First Jersey, 101 F.3d at 1475; Patel, 61 F.3d at 140. Once the SEC has met the burden of establishing a reasonable approximation of the profits causally related to the fraud, the burden shifts to the defendant to show that his gains “were unaffected by his offenses.” SEC v.

Lorin, 76 F.3d 458, 462 (2d Cir.1996) (“Lorin”)-, see also Warde, 151 F.3d at 50 (after district court reached a “reasonable approximation of profits causally connected to the violation,” defendant “was entitled to prove that the district court’s measure [wa]s inaccurate” (internal quotation marks omitted)); First City, 890 F.2d at 1232 (after SEC provided a reasonable approximation of unjust enrichment, defendants “were then obliged clearly to demonstrate that the disgorgement figure was not a reasonable approximation”); SEC v. Platforms Wireless International Corp., 617 F.3d 1072, 1096 (9th Cir.2010) (same).

We review a district court’s disgorgement order, and its ancillary findings, for abuse of discretion. See, e.g., Warde, 151 F.3d at 49; First Jersey, 101 F.3d at 1475; Lorin, 76 F.3d at 462 (amount to be disgorged); Patel, 61 F.3d at 140 (causation). a. Razmilovic’s Executive Compensation With regard to Razmilovic’s executive compensation, the district court rejected the SEC’s contention that all of the salary and bonuses received by Razmilovic throughout his tenure at Symbol should be disgorged, finding that only so much of that compensation as resulted from the fraud should be disgorged.

Although Raz-milovic argues that the court made no sustainable finding as to causation, we disagree. The frauds at issue were principally accounting frauds that created the appearance that Symbol’s performance met the company’s prior optimistic financial predictions. The district court excluded from disgorgement most of Razmilovic’s base salary because, inter alia, under Razmilo-vic’s employment agreement, adjustments in his base salary were unrelated to Symbol’s performance.

However, noting that Symbol’s reported increase in earnings in 1999 “indisputably resulted from the fraud,” 822 F.Supp.2d at 255, and that Razmilovic was promoted from COO to CEO shortly thereafter, id. at 255-56, the court found it “reasonable to infer a causal connection between Razmilovic’s fraud and his promotion to CEO,” id. at 255. It thus ordered disgorgement of the difference between Razmilovic’s salary as COO and his higher salary as CEO.

The district court’s findings as to the sequence and timing of these events are not clearly erroneous, and we see no abuse of discretion in its ruling that Razmilovic should disgorge that difference. The court also noted that Symbol’s proxy materials stated that, while adjustments in an executive’s base salary were generally not tied to the company’s performance, the opposite was true of bonuses and stock options.

Those materials stated that “ ‘[Symbol] promotes a pay-for-performance philosophy,’ ” that “ ‘[o]verall compensation paid to senior executives should be tied to how well [Symbol] performs financially,’ ” and that “ ‘[u]nder the Executive Bonus Plan, each year [Symbol] establishes] corporate financial performance objectives ..., based on earnings per share.’ ” 822 F.Supp.2d at 243 (quoting Symbol’s 2000, 2001, and 2002 proxy statements).

The district court found that “there is evidence in the record as [a] whole, including Martin’s expert report, supporting the SEC’s claim that Razmilo-vic’s performance bonuses were causally connected to his fraud,” noting that “[Raz-milovic’s] own expert admitted in her report that Symbol’s restated earnings would not have met the target earnings amounts for performance-related bonuses in either year that he received those bonuses.” 822 F.Supp.2d at 257 (emphasis added). Thus, the court reasonably ruled that Razmilovic should disgorge the performance bonuses he received during his fraudulent conduct.

Nor do we see any abuse of discretion in the district court’s ruling that Razmilovic should disgorge the bonus he received in connection with Symbol’s acquisition of Telxon Corporation in a stock-for-stock merger. The court noted that the complaint — whose factual allegations are deemed true by reason of Razmilovic’s default — alleged that the entire transaction “had been improperly recorded and fraudulently used to ‘prop up’ Symbol’s earnings.” Id. at 258.

The court also reasonably ruled that Razmilovic should disgorge his $5 million severance payment, see 822 F.Supp.2d at 258-59, which he received at least in part for “ ‘relinquishing] his right to all outstanding stock options whether vested or unvested as of [February 14, 2002], with the exception of 236,250 shares granted to Razmilovic on October 19, 1998,’ ” id. at 247 (quoting the severance agreement).

In sum, the district court carefully sought to distinguish compensation Razmi-lovic received from Symbol that was not dependent on the company’s performance — and thus was not disgorgeable— from his various bonuses and stock option awards that were dependent on that performance and from the increased salary resulting from his promotion to CEO shortly after the fraudulently manipulated financial reports “improved” Symbol’s performance. We see no abuse of discretion in the court’s order that Razmilovic should disgorge those sums, which totaled $7,883,647.84. b. Razmilovic’s Stock Transactions As indicated in

Part I.B. above, the parties’ experts presented competing views as to the amount by which the frauds in which Razmilovic participated had inflated the market price of Symbol’s shares. The SEC’s expert, O’Neal, focused on three sharp declines in the market price of Symbol’s shares: (1) a drop of 30 percent following a July 16, 2001 announcement by Symbol that its quarterly earnings were below expectations, (2) a drop of 17 percent following a February 13, 2002 News-day

article revealing, inter alia, that Symbol had received an SEC inquiry and had commissioned an independent review of its sales practices, and (3) a drop of 29 percent following announcements by Symbol after the close of trading on February 14, 2002, that it was lowering earnings guidance for future quarters and that Razmilo-vic had retired that day — a retirement that investors could view as significantly abrupt, given the announcement of an SEC inquiry the day before. O’Neal opined that prior to the first of these events, the frauds had inflated Symbol’s share price by $11.54.

Martin, Razmilovic’s expert, opined that the amount by which the frauds had inflated Symbol’s share price was only $3.42. Her analysis focused on the price change following the Newsday report of the SEC inquiry and on price changes following 10 other events not mentioned by O’Neal; and she concluded that most of the declines in Symbol’s share price were attributable to industry trends.

Martin disregarded both the 30 percent price decline that followed the July 16, 2001 announcement that Symbol would not meet prior expectations for quarterly earnings and the 29 percent decline that followed the similar February 14, 2002 announcement of lower earnings guidance, which was accompanied by the announcement of Razmi-lovic’s sudden retirement.

Razmilovic contends the district court’s conclusion that the Symbol share price was inflated by $11.54 was erroneous, arguing first that the court should have excluded the opinion of O’Neal on the ground that O’Neal confined his price fluctuation analysis to the time period that the SEC instructed him to consider, and second that the court should not have viewed Martin as less qualified than O’Neal to opine on the inflation question. We disagree. In a

section of its opinion entitled “Weight Afforded Expert Reports,” the district court explained as follows: Although I accept Razmilovic’s contention that the proper measure of disgorgement in this case is the amount by which the value of Symbol’s stock was inflated as a result of the fraud, I nonetheless reject his expert’s calculation of the value of that inflation. ....

Both parties’ experts utilized an “event study” methodology, which, inter alia, examines the effect of an event on a corporation’s stock price by looking for “abnormal returns during those event periods, usually days, when a stock moves differently than predicted based upon market and industry factors” and determines whether those abnormal returns are related to the alleged fraud. In re Xerox Corp. Securities Litigation, 746 F.Supp.2d 402, 408 (D.Conn.2010). It is undisputed that such methodology is a generally accepted method of calculating the inflation in a stock’s price in cases involving securities fraud....

Where the experts’ opinions diverge, however, is in their selection of the variables to use in their analysis and the weight to be accorded to such variables. For the reasons set forth below, I find O’Neal’s opinion to be entitled to greater weight than Martin’s. Martin’s opinions, and particularly her calculations of the amount by which the value of Symbol shares were inflated during the fraud period and the amount Razmilovic is liable to disgorge, are entitled to little or no weight because, inter alia, in addition to her omission of two (2) statistically relevant dates,[ ] (

a) she is not qualified to testify as to the amount Razmilovic is liable to disgorge from his stock transactions insofar as she testified during her deposition that she has no prior experience with disgorgement cases involving the exercise of stock options and that she did not literally know how the [stock exercise] transaction occurred] in this case ...; (

b) she did not base her opinion upon economic literature ... and used an earnings response model unsupported by accepted econometric principles; and (

c) she did not follow her own procedures in this case, e.g., she compared the performance of Symbol stock against only one (1) index, as opposed to two (2) or more.... In sum, although Martin properly utilized an event study methodology, she did not apply that methodology reliably to the facts of this case. To the contrary, O’Neal’s opinions are based upon a reliable foundation.

In his report, O’Neal, inter alia, adequately explains how he identified the statistically relevant dates he utilized in his event study and how he utilized those events to determine the effect that the pervasive fraud scheme had on the value of Symbol’s stock during the fraud period. 822 F.Supp.2d at 261-63 (other internal quotation marks omitted) (emphases added). We see no basis for reversal in these observations and evaluations. Assessments of relevance are committed to the sound discretion of the district court, see, e.g., George v.

Celotex Corp., 914 F.2d 26, 28 (2d Cir.1990), and it was entirely reasonable for the court to discount Martin’s opinion on inflation on the basis that she disregarded two events (followed, respectively, by 30 percent and 29 percent price drops) that the court considered relevant and significant. Further, perceived gaps, inconsistencies, or errors in the reasoning leading to an expert’s opinion are matters that properly go to-the weight of the evidence; and the weight of the evidence is a matter to be argued to the trier of fact, not a basis for reversal on appeal, see, e.g., Anderson v.

Bessemer City, 470 U.S. 564, 573-74, 105 S.Ct. 1504, 84 L.Ed.2d 518 (1985); Schwartz v. Capital Liquidators, Inc., 984 F.2d 53, 54 (2d Cir.1993). Although the court’s reliance on a clearly erroneous finding of fact would constitute an abuse of discretion, we see no such findings here, for the factfinder’s choice between competing views of the facts or events cannot be clearly erroneous. See Anderson, 470 U.S. at 574, 105 S.Ct. 1504.

Given the district court’s permissible assessments of the relevance of the various events and the opinions of the experts, we see no basis for disturbing its finding that Razmilovic’s fraud inflated the Symbol share price by a total of $11.54. Razmilovic does not challenge the court’s mathematical applications of the $11.54 figure in its determination of the amounts that Razmilovic should disgorge with respect to his collar transactions and his exercises of stock options, see 822 F.Supp.2d at 267-74, although he does contend that none of his profits from those transactions should be disgorged.

These contentions are meritless as well. The district court’s order that Razmilovic disgorge his profits from the collar transactions was based on the finding that the transactions themselves were fraudulent because Razmilovic falsely represented to the other party that he was not in possession of material nonpublic information. Further, had it not been for the fraud, the market price of Symbol stock at the time Razmilovic entered into the collar transactions would have been lower, and it was not clear error for the court to infer that the strike price of the put options too would have been set lower.

To the extent that there is any uncertainty as to whether a lower strike price would have been below Symbol’s market price at the time the option period expired, the burden of that uncertainty must be borne by Razmilovic, whose fraud caused the distortion of the market prices. Razmilovic’s argument with respect to his stock options—that he should not have been required to disgorge “paper” profits, i.e., profits from price increases of shares he did not sell—finds no support even from his own expert, as Razmilovic used the fraudulently appreciated value of those shares to fund his exercise of the stock options.

The district court noted that Razmilovic’s expert concedes that the profits Razmilovic earned on the shares of Symbol stock that he “swapped” during his exercise of stock options to pay the options price and withholding taxes should be included in any disgorgement calculation “since they would not have been earned absent the alleged earnings misstatement and associated stock price inflation.” (Martin Rpt., at 8; see Martin Deck, at 8) (“Once the correct inflation is calculated, ... it has to be applied to Mr. Razmilovic’s four exercises of employee stock options....”) 822 F.Supp.2d at 259.

In sum, we reject all of Razmilovic’s challenges to the district court’s requirement that he disgorge a total of $33,869,975.20 in unlawful profits from his stock transactions. Including the $7,883,647.84 in executive compensation gained from his fraud, we affirm the court’s order that Razmilovic disgorge a total of $41,753,623.04. C. Prejudgment Interest and the Civil Penalty In connection with a disgorgement award, the district court has discretion to require the defendant to pay prejudgment interest for the period during which he had the use of his unlawful gains. See, e.g., First Jersey, 101 F.3d at 1477.

In addition, the 1933 and 1934 Acts give the court discretion to order a defendant who has violated those statutes to pay civil penalties. Razmilovic challenges the amounts of the district court’s awards of prejudgment interest and penalties on several grounds. He challenges both on the basis that they were calculated with reference to the amount he is ordered to disgorge and argues that each should be lower because the disgorgement amount should be lower; these challenges fail because we uphold the disgorgement order. 1.

Prejudgment Interest Razmilovic’s other challenge to the order that he pay $27,260,953.99 in prejudgment interest may have somewhat greater merit. The district court ruled that Raz-milovic was “liable to pay prejudgment interest on the entire amount of his ill-gotten gains for the entire period from the time of his unlawful gains to the entry of judgment.” 822 F.Supp.2d at 278; see id. n. 72 (setting various starting dates — the earliest being February 1,- 2002 — for interest calculations with respect to different components of the $41,753,623.04 disgorgement amount).

Razmilovic contended that he should not be liable for prejudgment interest because the United States government had caused some $17.4 million of his funds in Swiss bank accounts to be frozen in 2004, and he had been denied access to those funds since that time.

The district court rejected that contention, stating (1) that there was “no evidence ... that all of [Razmilovic’s] assets have been frozen by the government since 2004,” (2) that there was no evidence that Razmilovic had attempted to access the frozen funds to pay living expenses, and (3) that the total disgorgement ordered was well in excess of the total amount of frozen funds. Id. at 278 (emphasis in original).

Although the district court’s third rationale justifies an award of prejudgment interest on at least the amount by which the disgorgement sum exceeds the frozen $17.4 million, the remainder of the court’s reasoning appears flawed. And there is uncertainty with respect to the frozen funds that neither side has addressed on appeal or, apparently, in the district court.

Since “[t]he primary purpose of disgorgement as a remedy for violation of the securities laws is to deprive violators of their ill-gotten gains, thereby effectuating the deterrence objectives of those laws,” First Jersey, 101 F.3d at 1474; see also SEC v. Palmisano, 135 F.3d 860, 865 (2d Cir.) (“Palmisano ”) (“ ‘deterrence may serve civil as well as criminal goals’ ” (quoting Hudson v.

United States, 522 U.S. 93, 105, 118 S.Ct. 488, 139 L.Ed.2d 450 (1997) (other internal quotation marks omitted))), cert. denied, 525 U.S. 1023, 119 S.Ct. 555, 142 L.Ed.2d 462 (1998), it is within the discretion of a court to award prejudgment interest on the disgorgement amount for the period during which a defendant had the use of his illegal profits, see, e.g., First Jersey, 101 F.3d at 1474-77.

However, where, as here, the defendant has had some or all of his assets frozen at the behest of the government in connection with the enforcement action, an award of prejudgment interest relating to those funds would be inappropriate with respect to the period covered by the freeze order, for the defendant has already, for that period, been denied the use of those assets.

In such a case, after a final order of disgorgement, the funds previously frozen would presumably be turned over to the government in complete or partial satisfaction of the disgorgement order, along with any interest that has accrued on them during the freeze period.

In that circumstance, the remedial purpose of prejudgment interest would already have been served with respect to the period of the freeze; to require the defendant to pay prejudgment interest on the entire disgorgement amount including the earlier frozen amount would, for the freeze period, deprive him twice of interest on the portion of the disgorgement award that is satisfied by the frozen assets. Cf.

Palmisano, 135 F.3d at 863 (noting the SEC’s concession that a defendant should not be required to disgorge amounts that he paid as restitution to his victims as ordered in his criminal case, because a “[defendant is only required to give back the proceeds of his securities fraud once” (internal quotation marks omitted)).

The first and second facts cited by the district court, ie., that Razmilovic apparently has assets other than those that were frozen and that he has had no need to use the frozen assets for his living expenses, did not take into account either the fact that Razmilovic has been denied the right to use the assets that were frozen or the fact that the disgorgement order was not designed to strip Razmilovic of “all” of his assets. “The [disgorgement] remedy consists of factfinding by a district court to determine the amount of money acquired through wrongdoing ... and an order compelling the wrongdoer to pay that amount plus interest to the court....

Because the remedy is remedial rather than punitive, the court may not order disgorgement above this amount.” SEC v. Cavanagh, 445 F.3d 105, 116 & n. 25 (2d Cir.2006). The very purpose of the trial in this case was to allow the court to distinguish Razmilovic’s fraudulent gains from those that did not result from his frauds, and to order. disgorgement of only the former. The question remains, however, whether Razmilovic’s frozen funds can or will be used in satisfaction of his disgorgement obligation.

The SEC does not dispute that an order freezing $17,379,735 of Razmilovic’s assets in two Swiss bank accounts was obtained on or about July 2, 2004. However, the freeze was sought not by the SEC in connection with this enforcement action but by the Justice Department in connection with the criminal prosecution.

The Justice Department explained to the Swiss authorities that Raz-milovic had been indicted for various fraud and conspiracy offenses in a 25-count indictment, that the funds in those accounts were “believed to be proceeds of fraud,” that “each conspiracy and substantive securities fraud count carries a maximum fine of $5,000,000,” and that the indictment seeks the “forfeiture ” of “approximately $63 million.” (Letter from Mary Ellen Warlow, United States Department of Justice, to Raphael Mauro, Swiss Federal Office of Justice dated July 1, 2004, at 1-2 (emphases added).) The Justice Department’s letter stated that the freeze was needed “to prevent the dissipation of substantial criminal proceeds which are subject to forfeiture under United States law.” Id. at 3 (emphasis added).

Thus, Razmilo-vic’s potential monetary liability in criminal fines and forfeiture in the criminal case far exceeds the value of his frozen assets. Since Congress has the power to impose both. criminal and civil sanctions for the same conduct, a defendant may be required in a criminal proceeding to pay a fine and forfeiture and be required in a civil enforcement proceeding to disgorge his unlawful gains. See, e.g., Palmisano, 135 F.3d at 865-66.

If Razmilovic’s frozen $17,379,735 is to remain frozen in connection with still-pending criminal charges against Razmilovic, Razmilovic would be obligated to pay the entire $41,753,623.04 disgorgement amount ordered in this civil enforcement, action; and given the non-punitive, remedial purpose of disgorgement, it would be within the district court’s discretion to order him to pay prejudgment interest on that entire amount.

If, however, Razmilovic’s frozen funds are to be used in partial satisfaction of his disgorgement obligation, we would conclude that Razmilovic should not be required to pay prejudgment interest on such funds as were frozen, for the period during which they were frozen. On remand, the government will be required to decide whether to apply the frozen $17.4 million to the judgment in the present case and forgo prejudgment interest on it, or to persist in demanding prejudgment interest on the entire forfeiture amount.

But for the reasons stated above, a judgment granting prejudgment interest on the entire forfeiture amount would preclude the application of the $17.4 million to this civil judgment. 2. The Civil Penalty Razmilovic’s remaining challenges to the $22,876,811.52 civil penalty imposed on him are (

a) that the amount is disproportionate to the civil penalties imposed on other defendants in this case, and (

b) that it is $2 million higher than the penalty amount stated in the court’s opinion. Only the latter contention has merit. Both the 1933 and 1934 Acts authorize three tiers of monetary penalties for statutory violations. See 15 U.S.C. § 77t(d); 15 U.S.C. § 78u(d)(3).

Under each statute, a first-tier penalty may be imposed for any violation; a second-tier penalty may be imposed if the violation “involved fraud, deceit, manipulation, or deliberate or reckless disregard of a regulatory requirement”; a third-tier penalty may be imposed when, in addition to meeting the requirements of the second tier, the “violation directly or indirectly resulted in substantial losses or created a significant risk of substantial losses to other persons,” 15 U.S.C. §§ 77t(d)(2)(A)-(C); 15 U.S.C. §§ 78u(d)(3)(B)(i)-(iii).

Each tier provides that, for each violation, the amount of penalty “shall not exceed the greater of” a specified monetary amount or the defendant’s “gross amount of pecuniary gain”; the amounts specified for an individual defendant for the first, second, and third tiers, respectively, are $5,000, $50,000, and $100,000. 15 U.S.C. § 77t(d)(2) (emphasis added); 15 U.S.C. § 78u(d)(3)(B) (same). Since the amount of Razmilovic’s disgorge-able gain was $41,753,623.04, the maximum civil penalty the court was allowed to impose on him was $41,753,623.04.

Beyond setting maximum penalties, the statutes leave “the actual amount of the penalty ... up to the discretion of the district court.” SEC v. Kern, 425 F.3d 143, 153 (2d Cir.2005). We thus review an award of penalties under the statutes for abuse of discretion. See id. at 153-54. The district court determined that the appropriate penalty for Razmilovic was one-half the authorized maximum.

In reaching this decision, it stated: Razmilovic was a direct participant in a pervasive fraud scheme, spanning over three (3) years and involving fraud, deceit, manipulation and deliberate, or at least, reckless disregard of regulatory requirements, which either resulted in substantial losses to Symbol investors or, at the very least, created a risk of substantial losses to Symbol investors. Yet instead of responding to the charges against him, Razmilovic fled the country, continues to refuse to admit any wrongdoing, and has never expressed any remorse for his conduct....

In light of, inter alia, the seriousness and pervasiveness of the fraud scheme, the significant role played by Razmilovic in the scheme, the extent of the benefits Raz-milovic received from his violations of the securities laws and his lack of remorse, a third tier penalty is appropriate. 822 F.Supp.2d at 280-81 (emphasis added). The court concluded that a penalty of $20,876,811.52, equal to one-half the amount of Razmilovic’s fraud-enabled pecuniary gains, was appropriate “to serve the punitive and deterrent purposes of the civil penalty statutes.” Id. at 282.

We conclude that the penalty of $20,876,811.52 was within the bounds of the district court’s discretion. We reject Razmilovic’s proportionality challenge because we see no other similarly situated codefendant. The judgment, however, which was prepared by the SEC, stated the amount of the civil fíne as $22,876,811.52, or $2 million greater than the amount ordered in the district court’s opinion. Nothing in the record justified this increase; the SEC states that the discrepancy was an inadvertent clerical error (see SEC brief on appeal at 4 n.2).

The judgment thus must be corrected to order that Razmilovic pay a civil penalty of $20,876,811.52. CONCLUSION We have considered all of Razmilovic’s contentions on this appeal, and except as indicated above, have found them to be without merit. The judgment of the district court is vacated to the extent that it orders Razmilovic (

a) to pay prejudgment interest in the amount of $27,260,953.99, and (

b) to pay a civil penalty in the amount of $22,876,811.52 instead of $20,876,811.52, and in all other respects is affirmed. The matter is remanded for further proceedings in accordance with the foregoing to determine the appropriate amount of prejudgment interest Razmilovic is to pay and for correction of the penalty amount to $20,876,811.52.