
506 F.3d 170 (2007)
UNITED STATES of America, Appellee,
v.
David RUTKOSKE, Defendant-Appellant.
Docket No. 06-4067-cr.
United States Court of Appeals, Second Circuit.
Heard: August 27, 2007.
Decided: October 25, 2007.
*171 Marsha R. Taubenhaus, New York, N.Y., for Defendant-Appellant.
Chi T. Steve Kwok, Asst. U.S. Atty., New York, N.Y. (Michael J. Garcia, U.S. Atty., Diane Gujarati, Asst. U.S. Atty., New York, N.Y., on the brief), for Appellee.
Before: NEWMAN, WINTER and KATZMANN, Circuit Judges.
JON O. NEWMAN, Circuit Judge.
This appeal from a conviction for securities fraud primarily concerns the timeliness of an indictment and the calculation of the amount of loss for purposes of determining the sentence. Defendant-Appellant David Rutkoske appeals from a judgment of conviction for securities fraud and conspiracy to commit securities fraud entered on August 23, 2006, by the District Court for the Southern District of New York (Richard Conway Casey, District Judge) following a jury trial. Rutkoske contends that (1) the indictment and the superceding indictment were untimely, (2) the evidence was insufficient, (3) evidence of subsequent acts was improperly admitted, and (4) the sentence is unreasonable. We reject the challenges to the conviction but remand for resentencing.


*172 Background
The Defendant. At all relevant times, Rutkoske owned a brokerage firm, Lloyd Wade Securities ("Lloyd Wade"). Lloyd Wade, headquartered in Dallas, encompassed eight to ten offices across the country by 1999. Rutkoske worked out of the Dallas office. Lloyd Wade sold stock to retail customers and provided investment banking services to institutional clients. The indictment stems from the firm's involvement with NetBet, a start-up internet gaming company.
The Indictments. On December 11, 2003, the Government filed an initial indictment charging Rutkoske's co-defendants with participation in a securities fraud conspiracy in connection with Lloyd Wade's purchase and sale of NetBet stock. Rutkoske was not charged in this initial indictment.
On April 6, 2004, the grand jury returned a superceding indictment ("Indictment S1") adding Rutkoske as a defendant. The indictment charged Rutkoske with securities fraud, in violation of 15 U.S.C. §§ 78j (b), 78ff and 18 U.S.C. § 2, and conspiracy to commit securities fraud, commercial bribery, and wire fraud, in violation of 18 U.S.C. § 371. It charged that the conspiracy continued from December 1996 "to at least on or about April 9, 1999," rendering the indictment facially timely by just three days. Indictment S1 charged numerous overt acts in furtherance of the conspiracy; of these, only one was alleged to have occurred within the applicable five-year limitations period, "[o]n or about April 9, 1999."
After the filing of Indictment S1, Rutkoske repeatedly sought from the Government details of the alleged April 9, 1999, overt act in order to pin down the "on or about" phrasing to a precise date. At a hearing in July 2005, Rutkoske notified the District Court that he intended to move to dismiss Indictment S1 as untimely, and the Government stated that it was planning to file a superceding indictment.
A second superceding indictment ("Indictment S2"), charging Rutkoske alone, was returned on July 28, 2005. Indictment S2 charged Rutkoske with the same offenses as Indictment S1. It did not include the April 9 overt act, but instead alleged two other overt acts occurring on April 15 and 16, 1999, acts that would have been within Indictment S1's limitations period.
In September 2005, Rutkoske moved to dismiss Indictment S2 as untimely. At a hearing on the motion, defense counsel told the Court that the Government had realized in September that the April 9 overt act alleged in Indictment S1 had not occurred on that date, and contended that this concession rendered Indictment S1 untimely and unavailable for Indictment S2 to relate back to it.
The District Judge denied the motion. See United States v. Rutkoske, 394 F.Supp.2d 641 (S.D.N.Y.2005). Judge Casey concluded that Indictment S1, though containing "a latent defect," was validly pending at the time Indictment S2 was filed. See id. at 646. He also concluded that Indictment S2 did not materially broaden the charges against Rutkoske. See id. Therefore, he ruled, Indictment S2 related back to Indictment S1 for purposes of satisfying the statute of limitations. See id.
Pre-trial evidentiary ruling. Before trial, the Government moved to admit testimony about, and recordings of, conversations between Rutkoske and a co-conspirator as evidence of "other acts," admissible under Rule 404(b) of the Federal Rules of Evidence. See United States v. Rutkoske, No. 03 Cr. 1452, 2005 WL 3358596, at *1 (S.D.N.Y. Dec.8, 2005). Judge Casey *173 ruled that the proposed evidence, which suggested that Rutkoske had engaged in a similar market manipulation scheme after the events alleged in Indictment S2, was relevant and was being offered for the proper purpose of rebutting an "innocent participation" defense. See id. at *2. However, because it was unclear whether Rutkoske would present such a defense, Judge Casey concluded that he could not conduct the Rule 403 balancing analysis in advance of trial and therefore denied the motion without prejudice to renewal. See id. at *2-*3. The evidence was admitted at trial.
Trial. At the jury trial the Government presented the testimony of Rutkoske's alleged co-conspirators, some of Lloyd Wade's customers, and securities experts, and introduced documentary evidence showing Rutkoske's knowledge of undisclosed commissions earned by his brokers. In brief, the evidence permitted the jury to find the following. In 1997, Rutkoske permitted Manuel Bello, who had a history of stock manipulation, to head a new branch office in West Paterson, New Jersey. Bello introduced Rutkoske to the executive team at NetBet. Lloyd Wade's Head of Research and Investment Banking discouraged Rutkoske from doing business with NetBet, but Rutkoske entered an investment banking agreement with NetBet. The agreement contained a "lock-up" provision prohibiting significant shareholders from selling their shares and obliged NetBet to use its best efforts to ensure that all sales occurred through Lloyd Wade. Bello, with Rutkoske's knowledge, bought discounted blocks of NetBet stock from entities controlled by NetBet insiders.
Lloyd Wade began selling NetBet stock to its customers. When it wanted to sell NetBet stock at prices above the market price, Lloyd Wade would "take out" offers by buying stock from other firms making a market in the stock, thereby increasing the price. It was not difficult to increase the price of NetBet stock because it was thinly traded and Lloyd Wade controlled the vast majority of shares. Rutkoske sometimes instructed Bello to increase the price.
Brokers in the West Paterson office used "boiler room" tactics to sell NetBet stock. Cold callers posing as brokers called prospective customers and pretended that they had previously spoken. Brokers used high-pressure sales pitches to induce customers to buy NetBet stock. They sometimes lied about having visited NetBet's facilities and having met its management. One broker purchased NetBet stock for a client over the client's objection. Brokers avoided customers' phone calls when the customers wanted to sell NetBet stock, and one broker refused to comply with a client's instruction to sell the stock. Rutkoske visited the West Paterson office four or five times, and the brokers did not attempt to hide their tactics from him during all but the first of those visits.
Brokers selling NetBet stock received large commissions, which Rutkoske personally authorized. The commissions were not disclosed to clients; in fact, brokers often told their clients that they received no commission, and trade confirmations stated that there was no commission. Following an audit by the National Association of Securities Dealers ("NASD"), Lloyd Wade recharacterized the commissions as trading profits and created a new trading account to track the hidden commissions. Rutkoske knew that the firm was hiding commissions.
From January 1997 to April 1999, Lloyd Wade accounted for 72 percent of retail sales of NetBet stock; from July to December 1997, it accounted for 90 percent of the trading volume. Eventually, the price of NetBet shares plummeted. Investors lost more than $12 million.
*174 The District Judge allowed "other acts" evidence of conversations between Rutkoske and Bello about the stock of a company owned by Rutkoske, Paradise Tan. The conversations, which occurred four years after the charged conspiracy, revealed that Rutkoske desired to push up the stock price. For example, he stated, "I need a friendly market maker to help me set the market so I can cross some stock." Bello and Rutkoske discussed how to take out offers to increase the price and how to compensate brokers for their role in these efforts. Rutkoske told Bello to comply with the registration and solicitation regulations "so you don't draw attention," stating crudely, "[G]et [] me all my registrations and all that other shit, now I can go fuck around with the stock." The District Court gave the jury a limiting instruction at the time of the testimony and in the jury instructions.
The jury convicted Rutkoske on both counts.
Sentencing. The Presentence Report ("PSR") calculated a total offense level of 31, which comprised a base offense level of 6, see U.S.S.G. § 2F1.1(a) (1998); a 15-level enhancement for loss of more than $10 million, see id. § 2F1.1 (b)(1)(P); and other enhancements for a scheme to defraud more than one victim, use of mass marketing, a leadership role in an activity involving at least five participants, and abuse of a position of trust.[1] A total offense level of 31 and a Criminal History Category of I yielded a Guidelines range of 108 to 135 months' imprisonment.
Rutkoske objected to the PSR's loss calculation, which had been based on the trial testimony of an NASD expert, which we discuss further below. The District Court rejected Rutkoske's objections, accepted the testimony of the witness, and estimated the loss to be $12,057,928. Judge Casey imposed a sentence of 108 months' imprisonment and required restitution in the amount of $12,057,928.

Discussion
I. Timeliness of the Indictments
Rutkoske contends that both indictments were untimely. The statute of limitations governing securities fraud and conspiracy is five years. See 18 U.S.C. § 3282(a) (indictment must be "found" within five years after offense committed)[2]. When conspiracy requires proof of an overt act, as in this case, the statute of limitations is satisfied if the Government proves that the conspiracy operated within the five-year period preceding the date of the indictment and that a conspirator *175 knowingly committed an overt act in furtherance of the conspiracy within that same period. See United States v. Salmonese, 352 F.3d 608, 614 (2d Cir.2003). It is well-established that the Government may satisfy this test "`by proof of an overt act not explicitly listed in the indictment, as long as a defendant has had fair and adequate notice of the charge for which he is being tried, and he is not unduly prejudiced by the asserted variance in the proof.'" Id. at 620 (quoting United States v. Frank, 156 F.3d 332, 339 (2d Cir.1998)).
This Court's seminal opinion in United States v. Grady, 544 F.2d 598 (2d Cir. 1976), governs the timeliness of a superceding indictment filed after the expiration of the statute of limitations. In Grady, the original indictment properly alleged overt acts in furtherance of a conspiracy taking place within the five-year statute of limitations. See id. at 601. A superceding indictment was filed after the limitations period had run. See id. The Court noted that the bringing of the original indictment tolled the statute of limitations "as to the charges contained in that indictment." Id. It then held:
Since the statute stops running with the bringing of the first indictment, a superseding indictment brought at any time while the first indictment is still validly pending, if and only if it does not broaden the charges made in the first indictment, cannot be barred by the statute of limitations.
Id. at 601-02 (footnote omitted). Subsequent cases applying Grady have stated that a superceding indictment relates back to "a pending timely indictment" so long as the superceding indictment does not "materially broaden or substantially amend the original charges." Salmonese, 352 F.3d at 622 (emphasis added); accord United States v. Ben Zvi, 242 F.3d 89, 98 (2d Cir.2001).
Thus, Grady and its progeny impose a two-part test for relation back of a superceding indictment: the original indictment must be validly pending, and the superceding indictment must not materially broaden or substantially amend the charges. Rutkoske contends that the indictments fail both prongs of this test.
Whether Indictment S1 was validly pending. Rutkoske first contends that Indictment S1 was not validly pending because it was untimely. The premise of this argument, not previously considered in this Circuit, is that an indictment that is facially valid only because of one alleged overt act within the limitations period should not be considered to have been validly pending under Grady when the Government concedes that the overt act did not occur within the limitations period.
There can be no doubt that Indictment S1 was facially timely when returned. It alleged a conspiracy that extended into the limitations period and an overt act occurring within that period, unlike the initial indictment in Ben Zvi, 242 F.3d at 97, which alleged no overt acts within the limitations period. Furthermore, had the Government proceeded to trial on Indictment S1 and failed to prove that the alleged April 9 overt act occurred within the limitations period, it could nonetheless have satisfied the statute of limitations by proving another overt act within the limitations period, even though the other act was not alleged in the indictment. See Salmonese, 352 F.3d at 620; Frank, 156 F.3d at 339. Since failure to prove the April 9 overt act at trial would not have rendered Indictment S1 dismissable as long as a timely act, although uncharged, was proved, it is arguable that the Government's concession in advance of trial should not matter, regardless of when the concession was made. See United States v. Smith, 197 F.3d 225, 228-29 (6th Cir. *176 1999) ("[A]n original indictment remains pending until it is dismissed or until double jeopardy or due process would prohibit prosecution under it."). Whether or not that would be so, we see no basis to deem Indictment S1 untimely on the facts of this case where the concession did not occur until after the return of Indictment S2. On the day Indictment S2 was returned, Indictment S1 was facially timely and validly pending. Nothing in the record suggests that the Government deliberately withheld its concession concerning the April 9 overt act until after return of Indictment S2.
Whether Indictment S2 impermissibly broadened the charges. Rutkoske next argues that even if Indictment S1 was validly pending, Indictment S2 impermissibly broadened the scope of the conspiracy. A superceding indictment containing additional overt acts relates back to a previous indictment when the additional overt acts "simply flesh out or provide more detail about the originally charged crime without materially broadening or amending it." Salmonese, 352 F.3d at 622. Indictment S2 alleged two new overt acts extending the scope of the conspiracy by one week. This one-week extension cannot be characterized as a material broadening of the charges against Rutkoske. Cf. United States v. Ratcliff, 245 F.3d 1246, 1253-54 (11th Cir.2001) (holding that a superceding indictment could not relate back when it expanded the conspiracy by twelve years and ten conspirators). Rutkoske contends that the one-week extension of the conspiracy was critically important because its purpose was to save the indictment from dismissal. This contention simply restates Rutkoske's first argument that Indictment S1 was not validly pending when Indictment S2 was returned.
Since Indictment S2 did not materially broaden the scope of the conspiracy charge, it related back to Indictment S1 and was therefore timely.
II. Sufficiency of the Evidence
At trial, the Government based the conspiracy and securities fraud charges on theories of both failure to disclose brokers' profits and material misrepresentations. Rutkoske argues that the evidence was insufficient to establish that Lloyd Wade's brokers had a duty to disclose their profits to their customers. We need not consider this argument because, whether or not the omission theory was proved, the evidence was sufficient to support the misrepresentation theory, and the Supreme Court has held that a verdict should be affirmed when two theories of an offense are submitted to the jury and the evidence supports one theory but not the other. See Griffin v. United States, 502 U.S. 46, 56-60, 112 S.Ct. 466, 116 L.Ed.2d 371 (1991); see also United States v. Vasquez, 85 F.3d 59, 60-61 (2d Cir.1996). In such cases, courts assume that the verdict is based on the valid theory. See, e.g., United States v. Skelly, 442 F.3d 94, 99 n. 4 (2d Cir. 2006); see also United States v. Washington, 861 F.2d 350, 352 (2d Cir.1988) ("[W]here an impermissible basis of conviction arises from an insufficiency of evidence and a valid basis remains on an alternative theory, a defendant must request the trial judge not to submit the invalid basis to the jury or else the objection will be deemed waived.").
III. The Admission of the Paradise Tan Evidence
Rutkoske's final challenge to his conviction concerns the "other acts" evidence of his conversations with Bello about Paradise Tan. Rule 404(b) of the Federal Rules of Evidence permits the introduction of evidence of other acts for the purpose of proving a defendant's knowledge. Evidence *177 may be introduced under Rule 404(b) if (1) it is introduced for a proper purpose, (2) it is relevant to the charged offense, (3) its prejudicial effect does not substantially outweigh its probative value, and (4) it is admitted with a limiting instruction if requested. See Huddleston v. United States, 485 U.S. 681, 691-92, 108 S.Ct. 1496, 99 L.Ed.2d 771 (1988); see also United States v. Edwards, 342 F.3d 168, 176 (2d Cir.2003). Rutkoske implicitly concedes that the Paradise Tan evidence was introduced for the permissible purpose of proving his knowledge, and he does not challenge the District Court's limiting instruction. His arguments are thus confined to the second and third elements of Huddleston.
Relevancy determinations are reviewed for abuse of discretion, and the district court is accorded "wide latitude." United States v. Ramirez, 894 F.2d 565, 569 (2d Cir.1990). Relevancy "`exists only as a relation between an item of evidence and a matter properly provable in the case.'" Id. (quoting Huddleston, 485 U.S. at 689, 108 S.Ct. 1496 (internal quotation marks omitted)). Rutkoske's defense at trial was that he neither knew nor approved of the fraud in the West Paterson office. The Paradise Tan evidence is relevant if it tends to make the existence of Rutkoske's knowledge more probable than it would be without the evidence. See Fed.R.Evid. 401.
Rutkoske presents two arguments pertaining to relevancy. He first argues that he did not discuss improper stock manipulation with Bello; he explains that the conversations "led to a host of competing inferences, none of which was rendered any more likely than the others." However, as the District Court observed, the Paradise Tan and NetBet schemes both "display an effort to manipulate a `thinly-traded' stock by buying out offers below a predetermined target price and . . . required the cooperation of brokers and market-makers, lured by the promise of personal financial gain, to carry out the stock manipulation." Rutkoske, 2005 WL 3358596, at *2. Rutkoske's demonstrated understanding of how the Paradise Tan scheme would work showed that he was "conversant in the language of stock manipulation," id., making it more likely that he understood the role of excessive commissions and "taking out" offers in the NetBet scheme.
Rutkoske primarily contends that the Paradise Tan evidence is irrelevant because the conversations occurred four years after the alleged NetBet scheme. As the District Court recognized, see id. at *2 n. 1, this Court has refused to erect a per se bar to evidence of "other acts" occurring after the charged offense. See United States v. Germosen, 139 F.3d 120, 128 (2d Cir.1998) (allowing evidence of a similar scheme perpetrated shortly after the charged offenses to show intent); Ramirez, 894 F.2d at 569 (allowing evidence of narcotics involvement nine months after the charged offense to show knowledge). The courts of appeals mostly agree that the admission of subsequent acts under Rule 404(b) is governed by the same four-part test as prior acts, though some courts have recognized that the temporal relationship between the acts may have some bearing on the evidence's probative value. See, e.g., United States v. Anifowoshe, 307 F.3d 643, 647 (7th Cir.2002) ("The timing of the act is only relevant inasmuch as it affects considerations inherent in that test."); United States v. Latney, 108 F.3d 1446, 1449 (D.C.Cir.1997) (declining to adopt a special rule for subsequent acts but observing that "the strength of the evidence is a different matter than its relevancy").[3]
*178 In light of the similarity between the NetBet and Paradise Tan schemes, the District Court did not exceed its discretion in determining that the Paradise Tan conversations were relevant, notwithstanding the fact that they took place four years after the charged conspiracy. Moreover, the District Court conscientiously reviewed the Rule 403 factors and concluded that, if Rutkoske argued a lack of knowledge at trial, which he did, the probative value of the other acts evidence would "greatly increase [], such that the balance under Rule 403 would shift considerably in favor of admissibility." Rutkoske, 2005 WL 3358596, at *2.
IV. The Reasonableness of the Sentence
Rutkoske contends that his sentence was unreasonable because (1) the District Judge did not properly determine the amount of the shareholders' loss, a key component of selecting the appropriate Guidelines sentencing range, and (2) the District Judge accorded that range a presumption of reasonableness.
The loss calculation. Despite the Supreme Court's decision in United States v. Booker, 543 U.S. 220, 125 S.Ct. 738, 160 L.Ed.2d 621 (2005), rendering the Guidelines advisory, a sentencing court remains obliged to determine the appropriate Guidelines range and then decide whether to impose a sentence within that range. See United States v. Crosby, 397 F.3d 103, 113 (2d Cir.2005). For offenses like Rutkoske's, a key component of the Guidelines calculation is the amount of loss caused by the wrongful conduct. See U.S.S.G. § 2F1.1(b)(1). The District Judge determined the loss to be $12,057,928 and used that amount to increase Rutkoske's Guidelines range by 15 levels, the enhancement prescribed for a loss of more than $10 million, see id. § 2F1.1(b)(1)(P). This increase added 87 months to the minimum sentencing range. The Judge also ordered restitution for the same amount.
The Guidelines state that "[t]he court need only make a reasonable estimate of the loss, given the available information." Id. § 2F1.1 cmt. n. 9. Nevertheless, a court of appeals must "determine [] whether the trial court's method of calculating the amount of loss was legally acceptable." United States v. Olis, 429 F.3d 540, 545 (5th Cir.2005). Judge Casey's method in this case, following the Government's expert witness, was to take the losses sustained by Lloyd Wade customers in NetBet stock as a result of their purchases and sales between January 1997 and July 29, 1999, and, as to unsold shares, use the difference between purchase price and value on July 29, 1999. That date was the last date for which the parties had "blue sheets," reporting forms for market makers. That date had no particular relevance to the offense conduct, and in fact was three months after the end of the charged conspiracy. This method implicitly attributed the total amount of the decline in the value of NetBet shares to Rutkoske's offense conduct.
We recently considered the calculation of loss in a criminal stock fraud case in *179 United States v. Ebbers, 458 F.3d 110 (2d Cir.2006). In Ebbers, we acknowledged the complexities inherent in calculating the loss amount but emphasized that "[t]he loss must be the result of the fraud." Id. at 128. Many factors may cause a decline in share price between the time of the fraud and the revelation of the fraud. See id. In such cases, "[l]osses from causes other than the fraud must be excluded from the loss calculation." Id. In Ebbers, however, the total loss was so massive that the loss enhancement would have remained the same had the district court taken into account other causes of the price decline, and remand was therefore unnecessary. See id.
The Fifth Circuit, in a case cited approvingly in Ebbers, 458 F.3d at 128, looked to principles governing recovery of damages in civil securities fraud cases for guidance in calculating the loss amount for a Guidelines enhancement. See Olis, 429 F.3d at 546. Applying the teaching of the Supreme Court in Dura Pharmaceuticals, Inc. v. Broudo, 544 U.S. 336, 125 S.Ct. 1627, 161 L.Ed.2d 577 (2005), the Fifth Circuit stated that "there is no loss attributable to a misrepresentation unless and until the truth is subsequently revealed and the price of the stock accordingly declines" and that the portion of a price decline caused by other factors must be excluded from the loss calculation. See Olis, 429 F.3d at 546; see also United States v. Zolp, 479 F.3d 715, 719 (9th Cir.2007) ("[T]he court must disentangle the underlying value of the stock, inflation of that value due to the fraud, and either inflation or deflation of that value due to unrelated causes.").
Dura Pharmaceuticals, on which the Fifth Circuit relied, provides useful guidance. There, the Supreme Court rejected the Ninth Circuit's "inflated purchase price" theory of loss causation, which held that plaintiffs in a civil stock fraud case could establish loss causation simply by showing that the purchase price was inflated because of the defendants' misrepresentation. See 544 U.S. at 340, 125 S.Ct. 1627. In rejecting this theory, the Court observed that although an artificially inflated price might cause an investor's loss when the investor sells his shares "after the truth makes its way into the market-place," id. at 342, 125 S.Ct. 1627, other factors, such as changed economic conditions, might also contribute to a stock's decline in price, see id. at 343, 125 S.Ct. 1627, and a plaintiff must prove that the misrepresentation proximately caused the economic loss, see id. at 346, 125 S.Ct. 1627.
The Government contends that the principles set forth in Dura Pharmaceuticals, a civil case, should not apply to loss calculation in a criminal case. The dicta in Ebbers strongly undermines that position. Moreover, we see no reason why considerations relevant to loss causation in a civil fraud case should not apply, at least as strongly, to a sentencing regime in which the amount of loss caused by a fraud is a critical determinant of the length of a defendant's sentence.
Determining the extent to which a defendant's fraud, as distinguished from market or other forces, caused shareholders' losses inevitably cannot be an exact science. See Ebbers, 458 F.3d at 127 ("no easy task"). The Guidelines' allowance of a "reasonable estimate" of loss remains pertinent. And cases might arise where share price drops so quickly and so extensively immediately upon disclosure of a fraud that the difference between pre- and post-disclosure share prices is a reasonable estimate of loss caused by the fraud. Even there, however, a coincidentally precipitous decline in shares of comparable companies would merit consideration. For *180 example, a fraud disclosed just as the dot-com bubble burst might cause most, but not necessarily all, of the decline in previously high-flying technology stocks. Normally, expert opinion and some consideration of the market in general and relevant segments in particular will enable a sentencing judge to approximate the extent of loss caused by a defendant's fraud.
The Government contends that it satisfied whatever obligations Dura Pharmaceuticals, Ebbers, and Olis impose by showing that NetBet shares traded in a "thin" market and that "the scheme unraveled, and the price of NetBet stock plummeted." However, a "thin" market does not preclude the effect of market forces, although it may minimize them,[4] and the Government's expert linked the low share price of his calculation to an arbitrary date representing the end of available blue sheet data, rather than the date of disclosure of the fraud. The Government provides no record citation to any particular date to support its generalized claim that the scheme "unraveled."
The District Court's basic failure at least to approximate the amount of the loss caused by the fraud without even considering other factors relevant to a decline in NetBet share price requires a remand to redetermine the amount of the loss, both for purposes of the sentence and restitution.
The claimed presumption concerning the Guidelines range. Rutkoske also contends that the District Judge improperly accorded the applicable Guidelines range a presumption of reasonableness. This claim raises an issue similar to the issue of whether a court of appeals should accord a presumption of reasonableness to a sentence that is within the applicable Guidelines range.[5] However, the claims are not identical. The appellate review issue concerns the use of a presumption in assessing the reasonableness of a particular sentence selected from within the applicable range. Rutkoske's claim is that the District Judge presumed that he should use the applicable range to define the limits of his sentence rather than use his post-Booker discretion to impose a non-Guidelines sentence. Rutkoske's claim is also similar to the claim that a sentencing judge erred in imposing a sentence within the applicable Guidelines range rather than exercising discretion to make a departure below the range.[6]
We need not resolve the presumption issue that Rutkoske endeavors to present because Judge Casey accorded no presumption to the applicable sentencing range. He merely stated that "the federal sentencing guidelines have been developed to take into consideration the other factors of Title 18 United States Code 3553(a)." This statement was entirely consistent with this Court's post-Booker observation *181 that the Guidelines "are the only integration of the multiple factors" in 18 U.S.C. § 3553(a). United States v. Rattoballi, 452 F.3d 127, 133 (2d Cir.2006) (internal quotation marks omitted). And the District Judge explicitly recognized that the Guidelines are not binding.

Conclusion
The conviction is affirmed; the case is remanded for resentencing.
NOTES
[1]  All references to the Guidelines are to the 1998 version.
[2]  The Supreme Court has used different words to describe a grand jury's action with respect to an indictment. See, e.g., Whitfield v. United States, 543 U.S. 209, 211, 125 S.Ct. 687, 160 L.Ed.2d 611 (2005) (indictment "returned"); United States v. Mauro, 436 U.S. 340, 346, 98 S.Ct. 1834, 56 L.Ed.2d 329 (1978) (indictment "filed"); United States v. Guest, 383 U.S. 745, 760, 86 S.Ct. 1170, 16 L.Ed.2d 239 (1966) (indictment "brought"). A leading case in this Circuit, United States v. Grady, 544 F.2d 598 (2d Cir.1976), discussed below, managed to use all three verbs on the same page. See id. at 601.

The Tenth Circuit has ruled that an indictment "is `found' under 18 U.S.C. § 3282 when the grand jury votes to indict the defendant and the foreperson subscribes the indictment as a true bill." United States v. Thompson, 287 F.3d 1244, 1251 (10th Cir.2002). Normally, the voting by the grand jury, the subscribing by the foreman, the return in open court, see Fed.R.Crim.P. 6(f), and the filing in a clerk's office all occur on the same date.
In the pending appeal, any gap in this sequence of events that might have occurred is without significance.
[3]  Rutkoske cites a Third Circuit case stating that "[t]he logic of showing prior intent or knowledge by proof of subsequent activity escapes us," United States v. Boyd, 595 F.2d 120, 126 (3d Cir.1978), but the Third Circuit arguably has retreated from that position, see United States v. Echeverri, 854 F.2d 638, 645 (3d Cir.1988) ("We do not dispute that there may be cases in which evidence of subsequent wrongful acts may properly be admitted under Rule 404(b)."). Citing Boyd, the Sixth Circuit has said that "rarely will an event that occurred subsequent to the charged crime be probative of motive, knowledge, or intent." United States v. Cowart, 90 F.3d 154, 158 (6th Cir.1996).
[4]  The record does not suggest that the District Court understood Lloyd Wade to have "promoted worthless stock in worthless companies," which would justify attributing the entire loss amount to Rutkoske's fraud. See Olis, 429 F.3d at 546.
[5]  On this appellate review issue, the Supreme Court has ruled that a court of appeals "may apply a presumption of reasonableness to a district court sentence that reflects a proper application of the Sentencing Guidelines," Rita v. United States, ___ U.S. ___, 127 S.Ct. 2456, 2462, 168 L.Ed.2d 203 (2007) (emphasis added), while recognizing that several circuits reject such a presumption, see id. This Circuit has declined to apply such a presumption. See United States v. Fernandez, 443 F.3d 19, 27 (2d Cir.2006).
[6]  We regularly reject that claim in the absence of any indication that the sentencing judge was unaware of departure authority. See, e.g., United States v. Valdez, 426 F.3d 178, 184 (2d Cir.2005); United States v. Galvez-Falconi, 174 F.3d 255, 257 (2d Cir.1999).
