The issue on this appeal is whether plaintiffs, suing for stock fraud, were on inquiry notice that started the running of a statute of limitations early enough to render their suit time-barred. This issue arises in the context of an insurance company that took increasingly large reserve charges and did not disclose its continuing failure to establish adequate reserves. Plaintiff-Appellant LC Capital Partners, LP (“LC Capital”) appeals from the February 7, 2002, judgment of the District Court for the Southern District of New York (Lawrence M. McKenna, District Judge), dismissing, for failure to state a timely claim, its class action against Frontier Insurance Group, Inc. (“Frontier”), its officers and directors, and its outside auditor, Ernst & Young, LLP (“E & Y”).1 We conclude that the suit is time-barred and therefore affirm.
Background
LC Capital, acting on behalf of itself, other named consolidated plaintiffs, and a putative class, is an investor that purchased securities issued by Frontier between August 5, 1997, and April 14, 2000 (“the Class Period”). Frontier is an insurance holding company that, through subsidiaries, conducts business as a specialty insurer and reinsurer. During the Class Period, Frontier’s shares were traded on the New York Stock Exchange.
Allegations of fraud. The Plaintiffs allege that during the Class Period, Frontier engaged in irresponsible and negligent insurance practices. The Plaintiffs focus on three areas of the Defendants’ conduct. First, the Plaintiffs allege that the Defendants implemented reserve policies with the deliberate purpose and systematic effect of under-reserving for claims. Second, the Plaintiffs allege that the Defendants’ information systems were grossly inadequate, such that reserves could not properly be recorded and claim histories necessary for responsible actuarial analysis were unavailable. Third, in order to cover the revenue shortfalls created by Frontier’s failure to reserve adequate sums and price policies correctly, the company engaged in a “pyramid scheme”: it rapidly expanded its business by acquiring other insurance companies, offered policies at predatory prices, and used the premium income thus generated to pay claims on existing policies. The Plaintiffs allege that the individual Defendants were aware that these policies were reckless, and that they ignored or fired employees and independent actuaries who raised concerns about these policies.
The Plaintiffs allege that the Defendants’ policies gradually eroded the financial health of Frontier. During the Class Period, Frontier took a series of reserve *151charges: $17.5 million in 1994, $40 million in 1997, $139 million in 1998, and $136 million in 1999. The price of its common stock decreased from the Class Period high of $35,227 to $0,875 a share.
The Plaintiffs allege that, in a series of financial reports, press releases, and other public statements issued throughout the Class Period, the Defendants made false and misleading statements and material omissions to conceal Frontier’s practices and their effects. Much of the language that the Plaintiffs take issue with is language that essentially says “all is well.” For instance, Frontier’s Form 10-Q for the quarter ended June 30, 1997, states, “The Company’s subsidiaries maintain liquid operating positions and follow investment guidelines that are intended to provide for an acceptable return on investment while preserving the Company’s capital, maintaining sufficient liquidity to meet their obligations and, as to the Company’s insurance subsidiaries, maintaining a sufficient margin of capital and surplus to ensure their unimpaired ability to write insurance and assume reinsurance.”
With respect to E & Y, the Plaintiffs allege that the accounting firm recklessly disregarded numerous warning signals to which it would have had special access as Frontier’s auditor. The Plaintiffs allege that E & Y’s opinions during the Class Period certifying Frontier’s financial statements were materially false and misleading and in violation of federal securities law.
Potential storm warnings. In 1994, Frontier took a $17.5 million restructuring charge, apparently the first time that Frontier was required to take a charge since its founding in 1986. The charge was attributed to aggressive expansion into Florida’s insurance market where the reserve models that the company had previously used turned out to be insufficient.
On February 17, 1998, Frontier announced it would take a $40 million charge and also announced a loss of $9.8 million for the fourth quarter of 1997. Frontier issued a press release describing this charge as a “reserve restructuring charge.” Harry W. Rhulen, Frontier’s CEO, stated that the charge was “attributable to the adoption of a more conservative reserving policy.”
On December 16, 1998, Frontier announced that it would take a $139 million charge, which would result in a “loss for the year.” Frontier described this charge as a “reserve strengthening charge.” Rhulen stated that “with these charges, we have ‘paid the bill’ for past over emphasis on growth.”
On December 18, 1998, A.M. Best Company placed the ratings of Frontier “under review with negative implications.” On December 21, 1998, National Underwriter published an article discussing Frontier’s reserve problems. The article quoted Rhulen’s statement that Frontier had “paid the bill.” The article also quoted Patrick Kenney, a Frontier executive vice-president, as stating, “[T]he issue is now behind us.”
On December 28,1998, Frontier issued a press release in which it downplayed the most recent reserve charge, stating that the charge resulted from problems that arose from an office that was since closed, and that Frontier “has strengthened its control and oversight of its operations .... [and] adopted a more conservative reserving philosophy.”
On February 10, 1999, Frontier issued another press release in which it announced losses for the fourth quarter of 1998 and a loss of $50 million for the full year 1998. The article' included a quote from Rhulen downplaying the negative implication of these numbers: “While finan*152cial results were negatively impacted in 1998, it was a year of many accomplishments. We ... put many of our past problems behind us and start 1999 well positioned to achieve our financial goals.”
On March 31, 1999, in a letter to shareholders Rhulen made comments implying that past problems were resolved and that “Midden beneath the financial impact of the reserve strengthening ... was a significant amount of profitable growth which augers well for 1999 and the future.” A press release issued on May 5, 1999, expressed positive sentiment about the “direction in which the company is heading.”
On June 28,1999, National Underwriter published an article in which Rhulen discussed Frontier’s problems in 1998, attributing them largely to Frontier’s decision to enter the insurance market for physician malpractice insurance in Florida and elsewhere. The article reported that Rhulen acknowledged that “[without the actuarial capacity to monitor developments, ‘we wrote this for three or four years before we knew we had a problem.’ ” Suzanne Sclafane, “Two Firms Take Different Restructuring Paths,” at *4, available at 1999 WL 8859677 (Jun. 28, 1999) (quoting Harry Rhulen). The article also reported Rhulen as observing that the problems in Florida, Ohio, and elsewhere had amounted to “ ‘a fairly disastrous set of events.’ ” Id.
On August 4, 1999, Frontier issued a press release announcing its unaudited financial results for the second quarter of 1999 and also making positive statements about the company’s business model. On August 16,1999, Frontier filed its 1999 10-Q in which it made various statements to the effect that it was setting reserves in a careful and reasonable manner.
On November 15, 1999, Frontier announced it would take a $136 million reserve charge and also announced a $175.8 million loss for the third quarter of 1999. On November 22, 1999, in its Form 10-Q, Frontier reported that capital and surplus had fallen below risk-based capital requirements and that as of September 30, 1999, Frontier was in violation of debt covenants with lenders.
On December 17, 1999, Frontier announced that it was suspending the company’s quarterly common stock dividend. On February 1, 2000, Business Wire reported that Standard & Poor’s had lowered its rating on Frontier to “BBB + ” from “A-.” Rhulen responded, “We are positive about our position in the competitive environment.” On February 17, 2000, Frontier issued a press release announcing a 71-person staff reduction.
On February 23, 2000, Frontier announced a loss of $44.7 million for the fourth quarter of 1999 and a loss of $187.8 million for the full year 1999.
On March 17, 2000, A.M. Best Company announced that it had downgraded Frontier to a “B” and stated:
The companies’ weakened financial condition is the result of aggressive growth and significant under-pricing predominantly in medical malpractice as well as under-reserving. This resulted in sizable back-to-back reserve strengthening in 1998 and 1999, largely related to physician medical malpractice.
Frontier issued a statement in response that “Frontier is continuing to take the necessary steps to strengthen our financial position .... ”
On April 14, 2000, the last day of the Class Period, Frontier issued a press release indicating that there was “substantial doubt about the Company’s ability to continue as a going concern” and revising the net loss for the fourth quarter of 1999 to $90.2 million.
*153Prior litigation. On November 9, 1994, following the announcement of the first reserve charge, a securities class action was filed against Frontier in the Eastern District of New York (“Frontier I ”). This action alleged that Frontier fraudulently concealed and misrepresented its knowledge of, among other things, the fact that Frontier’s reserves for losses in relation to policies it had issued in Florida were “grossly inadequate” and that Frontier was “insufficiently staffed to properly evaluate the exposure presented by claims in Florida.”
In 1997, the District Court in Frontier I granted certification to a class composed of individuals who had purchased Frontier stock between February 10, 1994, and November 8, 1994. On February 17, 2000, the plaintiff class moved to amend the class period to extend through November 15, 1999. The basis on which this extension was sought was Frontier’s November 15, 1999, disclosure that it would take a $136 million reserve charge for the third quarter of 1999. The Frontier I plaintiffs contended that this demonstrated a “continuing pattern and practice of fraud and deceit by defendants relating back at least five years.”
The motion was referred to Magistrate Judge Poliak, who issued a Report and Recommendation dated November 13, 2000. She determined that, at least as early as December 21, 1998, when the National Underwriter article indicated that the November 1998 $139 million reserve charge applied to losses incurred from 1995 to 1998, investors were on inquiry notice as to claims arising during the period for which leave to amend was sought. Among other grounds for recommending denial of the motion to amend, Magistrate Judge Poliak stated that the amended claim would be futile because leave to amend was sought more than one year after the plaintiffs were on inquiry notice. Judge Nickerson approved the Report and Recommendation and denied the plaintiffs’ motion to amend in Frontier I.
The pending class action. Beginning on July 19, 2000, several class action complaints were filed in the Southern District of New York against Frontier and the individual defendants. The actions were consolidated on November 16, 2000. On February 5, 2001, a corrected consolidated amended class action complaint was filed, which for the first time named E & Y as a defendant.2
The Defendants moved to dismiss. On February 6, 2002, judgment was entered dismissing the complaint- as time-barred. The District Court expressly followed the finding of Frontier I that the Frontier shareholders were on inquiry notice as to possible fraud as of December 1998, after Frontier took its second reserve charge in a year, and its third in four years. The Court found that these reserve charges “dealt directly with Frontier’s reserve levels,” and therefore were highly relevant to the claim of inadequate reserve levels on which the Plaintiffs’ case relies. The Court also ruled that the existence of Frontier I, being litigated in the Eastern District of New York, should have “alerted plaintiffs to possible fraud.” The Court determined that the Plaintiffs were on notice as to potential fraud by E & Y at the *154same time they were on notice as to Frontier. For this reason, the Court did not reach the issue of whether the amendment bringing E & Y into the lawsuit should relate back to the filing of the original complaint for statute of limitations purposes because, even if it did, the Plaintiffs’ claims were barred as of the earlier date.
Discussion
Section 10(b) of the Securities Exchange Act of 1934 provides that “[n]o action shall be maintained to enforce any liability created under this section, unless brought within one year after the discovery of the facts constituting the violation and within three years after such violation.” 15 U.S.C. § 78i(e) (2000); see Lampf, Pleva, Lipkind, Prupis & Petigrow v. Gilbertson, 501 U.S. 350, 364 & n. 9, 111 S.Ct. 2773, 115 L.Ed.2d 321 (1991). The one-year limitations period applicable to discovery of the violation begins to run after the plaintiff “obtains actual knowledge of the facts giving rise to the action or notice of the facts, which in the exercise of reasonable diligence, would have led to actual knowledge.” Kahn v. Kohlberg, Kravis, Roberts & Co., 970 F.2d 1030, 1042 (2d Cir.1992) (emphasis added). The emphasized words have been referred to as “constructive or inquiry notice.” Menowitz v. Brown, 991 F.2d 36, 41-42 (2d Cir.1993). As we have explained, “[W]hen the circumstances would suggest to an investor of ordinary intelligence the probability that she has been defrauded, a duty of inquiry arises.” Dodds v. Cigna Securities, Inc., 12 F.3d 346, 350 (2d Cir.1993). “Such circumstances are often analogized to ‘storm warnings.’ ” Id. (quoting Cook v. Avien, Inc., 573 F.2d 685, 697 (1st Cir.1978)).
The duty of inquiry results in the imputation of knowledge of a fraud in two different ways, depending on whether the investor undertakes some inquiry. If the investor makes no inquiry once the duty arises, knowledge will be imputed as of the date the duty arose. Id.; Armstrong v. McAlpin, 699 F.2d 79, 88 (2d Cir.1983). However, if the investor makes some inquiry once the duty arises, we will impute knowledge of what an investor “in the exercise of reasonable diligence, should have discovered” concerning the fraud, Rothman v. Gregor, 220 F.3d 81, 98 (2d Cir.2000), and in such cases the limitations period begins to run from the date such inquiry should have revealed the fraud, id.
In the pending case, the District Court ruled that a duty of inquiry arose at least as early as December 1998 and that the complaint was time-barred because it was not filed until July 19, 2000. The Plaintiffs contended in the District Court, and on appeal, that the earliest date on which they could have become aware of the alleged fraud was April 14, 2000, when Frontier’s Form 10-K announced that there was “substantial doubt about Frontier’s ability to continue as a going concern,” Brief for Appellant at 37, 42, a date within one year prior to filing the complaint. Because the Plaintiffs make no claim that they undertook any inquiry in December 1998 or at any time between then and April 2000, whether the complaint is time-barred depends on whether a duty of inquiry arose at least by December 1998.3
*155We agree with the District Court that the “storm warnings” evident on the face of the detailed complaint and in related publicly available documents gave rise to a duty of inquiry no later than December 1998. The principal warnings were the three substantial reserve charges taken within a brief period of time: $17.5 million in 1994, $40 million in 1997, and $139 million in 1998. Many companies take one-time charges to reflect unanticipated developments without creating any suspicion of impropriety, see Siebert v. Nives, 871 F.Supp. 110, 114-16 (D.Conn.1994), but a series of three charges in substantial and increasing amounts for the same purpose within four years should alert any reasonable investor that something is seriously wrong. Also contributing to a duty of inquiry was the National Underwriter article discussing Frontier’s reserve problems and the 1994 Eastern District litigation in Frontier I. We note that Judge Nickerson denied a motion to amend the complaint in Frontier I on the ground that the plaintiffs in that suit were on notice of Frontier’s pattern of fraud after the December 1998 reserve charge. As Judge McKenna noted in the pending case, all of these warnings “relate[ ] to the misrepresentations later alleged, because the focus of the alleged fraud in this action is the inadequacy of reserve levels attributable to inadequate internal controls.”
The Plaintiffs contended in the District Court and on appeal that, even if storm warnings were present, they were dissipated by the reassuring statements of Frontier’s management. Major reliance is placed on Rhulen’s December 1998 statement that with the third reserve charge, Frontier had “paid the bill” and Kenney’s statement in the same month that the reserve problem “is now behind us.”
There are occasions when, despite the presence of some ominous indicators, investors may not be considered to have been placed on inquiry notice because the warning signs are accompanied by reliable words of comfort from management. See, e.g., Milman v. Box Hill Systems Corp., 72 F.Supp.2d 220, 229 (S.D.N.Y.1999) (“[Cjourts have been reluctant to find that public disclosures provided inquiry notice where those disclosures were tempered with positive statements.”); Siebert, 871 F.Supp. at 115 (disclosure of FDIC investigation did not trigger inquiry notice where company simultaneously announced that it had revised its policies to meet investigators’ concerns). Such statements are among the factors that must be considered when evaluating whether “the circumstances would suggest to an investor of ordinary intelligence the probability that she has been defrauded.” Dodds, 12 F.3d at 350. However, reassuring statements will prevent the emergence of a duty to inquire or dissipate such a duty only if an investor of ordinary intelligence would reasonably rely on the statements to allay the investor’s concern. See Farr v. Shearson Lehman Hutton, Inc., 755 F.Supp. 1219, 1228 (S.D.N.Y.1991) (“[Statements of cautious optimism, reiterations of the goal of providing income to investors, and explanations for past poor performance do not rise to the level ... necessary to excuse a reasonable investor from the duty of inquiry.”) (footnote omitted). Whether reassuring statements justify reasonable reliance that apparent storm warnings have dissipated will depend in large part on how significant the company’s disclosed problems are, how likely they are of a recurring nature, and how substantial are the “reassuring” steps announced to avoid their recurrence.
Here, all three factors point against the reasonableness of reliance on Frontier’s reassurances. Under-reserving is obviously a serious problem for an insurance com*156pany. The prospect that the problem would recur was heightened when three substantial reserve charges were taken within four years, indicating the likelihood of either a fundamental defect in the company’s reserve methodology or the company’s refusal to face reality. The “reassuring” statements by management were mere expressions of hope, devoid of any specific steps taken to avoid under-reserving in the future. In these circumstances, the claimed reassurances are unavailing. See In re JWP Inc. Securities Litigation, 928 F.Supp. 1239, 1250 (S.D.N.Y.1996). The complaint was properly held to be time-barred as to Frontier and the individual defendants.
The District Court’s ruling that the time-bar applied to the claims against E & Y filed on February 5, 2001, requires brief additional comments. The Appellant contended in the District Court that the corrected complaint relates back to the original complaint, but has not renewed that contention on appeal. The standards for relating back a complaint that changes the identity of a defendant have not been met. See Fed.R.Civ.P. 15(c)(3); Cornwell v. Robinson, 23 F.3d 694 (2d Cir.1994). The Appellant does contend, albeit in a footnote, see Brief for Appellant at 63 n. 5, that the corrected complaint should relate back to October 12, 2000, the date of a joint stipulation between the Plaintiffs and the Defendants in the original class actions. That stipulation, which was filed November 16, 2000, consolidated the class actions and set a schedule for the filing of an amended complaint.
The Appellant makes the extravagant claim that the stipulation date renders their complaint timely because the stipulation placed no restrictions on the naming of new defendants. What is required, however, is notice to a proposed defendant, see Rothman, 220 F.3d at 96, and the stipulation made no mention of E & Y, which did not receive notice until the filing of the corrected complaint on February 5, 2001. All of the storm warnings existing by December 1998 very likely render the claims against E & Y time-barred, as the District Court ruled, and, in any event, Frontier’s fourth reserve charge — $136 million in 1999 — enhanced the duty of inquiry. The District Court correctly ruled that the corrected complaint, filed February 5, 2001, was time-barred as to E & Y.
We recognize that whether a plaintiff had sufficient facts to place it on inquiry notice is “often inappropriate for resolution on a motion to dismiss under Rule 12(b)(6).” Marks v. CDW Computer Centers, Inc., 122 F.3d 363, 367 (7th Cir.1997). However, as we have observed, “Where ... the facts needed for determination of when a reasonable investor of ordinary intelligence would have been aware of the existence of fraud can be gleaned from the complaint and papers ... integral to the complaint, resolution of the issue on a motion to dismiss is appropriate,” Dodds, 12 F.3d at 352 n. 3, and we have done so in “a vast number of cases,” id.; see In re Ultrafem Inc. Securities Litigation, 91 F.Supp.2d 678, 692 (S.D.N.Y.2000) (“Dismissal is appropriate when the facts from which knowledge may be imputed are clear from the pleadings and the public disclosures themselves.”); Salinger v. Projectavision, Inc., 934 F.Supp. 1402, 1408-09 (S.D.N.Y.1996). Once the facts on the face of the complaint and related documents give rise to a duty of inquiry, it is appropriate to require a plaintiff, resisting a motion to dismiss on limitations grounds, at least to allege that inquiry was made. In this case, as we have noted, the Appellant concedes that it made no inquiry until April 2000, more than a year after the duty of inquiry arose.
*157We agree with the District Court that the circumstances here were sufficiently clear on the face of the complaint and related documents as to make the time-bar ruling appropriate on a motion to dismiss.
Conclusion
The judgment of the District Court is affirmed.