VITALIANO, District Judge:

We return to our consideration of this appeal with the benefit of answers provided by the Supreme Court of Connecticut in Arrowood Indem. Co. v. King, 304 Conn. 179, 39 A.3d 712 (2012) ("Arrowood IV"), reconsideration denied No. SC 18658 (Conn.Sup.Ct. May 2, 2012), in response to three questions we certified to it in Arrowood Indem. Co. v. King, 605 F.3d 62, 80 (2d Cir.2010) ("Arrowood III"). Familiarity with Arrowood III, which set forth the facts and procedural history of this case, is presumed. Some of those background details are recounted here, largely for the purpose of providing a contextual anchor for the Connecticut Supreme Court's answers to our certified questions.

Background

Defendants-Appellants Pendleton King, Daphne King and Pendleton King Jr. ("Junior") (collectively, the "Kings" or "Appellants") appeal from a judgment of the United States District Court for the District of Connecticut (Stefan R. Underhill, Judge). The district court held that none of three separate liability insurance policies owned by the Kings covered their alleged liability to a third-party child, Conor McEntee ("Conor"). Conor was injured when he fell from a skateboard while being towed by a rope attached to an all-terrain vehicle (the "ATV") owned by the Kings and operated by Junior. The accident occurred near the Kings' home on a portion of a private road located within the residential development managed by the Kings' homeowners association.

The three insurance policies in litigation are (1) a homeowner's liability policy issued by Royal Indemnity Company ("RIC"); (2) an umbrella liability policy issued by Royal Insurance Company of America ("RICA"); and (3) an excess liability policy issued by National Surety Corporation ("National").2 Each policy was procured through the Kings' insurance broker, New England Brokerage Corporation ("NEBC"). After investigating the accident, RIC and RICA (collectively, "Royal") filed a declaratory judgment action in the district court seeking to disclaim any duty under the homeowner's and umbrella policies to defend or indemnify the Kings for claims arising from the ATV accident. Soon after, the McEntees filed a tort complaint in Connecticut Superior Court, naming all three Kings as defendants. Among the causes of action pleaded in the McEntees' complaint were claims of negligent supervision of Junior and negligent entrustment of the ATV to him. Meanwhile, the Kings answered Royal's complaint and counterclaimed against Royal. They also filed a third-party complaint in which they named National and NEBC as third-party defendants. Lastly, NEBC, filed cross-claims against Royal.

In granting summary judgment, the district court found that the homeowner's policy did not cover the ATV accident because, in short, (1) the event location relevant to determining the availability of coverage was the accident site (not, e.g., the place where the ATV was entrusted to the minors) and (2) the accident site was not an "insured location" as provided in the homeowner's policy. Royal Indem. Co. v. King, 512 F.Supp.2d 117, 124-27 (D.Conn. 2007) ("Arrowood I"). Coverage was also properly disclaimed under the umbrella policy, the court found, because the Kings failed to list the ATV on a declarations page of that policy as required by the policy's terms. Id. at 133. The Kings fared no better below on their remaining claims.

In our initial consideration of Appellants' arguments, and with particular attention to those regarding whether coverage existed under the homeowner's policy, we observed that "Connecticut law is unsettled as to whether a negligent entrustment claim in this context should be deemed to arise where the subject vehicle was entrusted, where the vehicle was housed, or where the accident itself took place." Arrowood III, 605 F.3d at 69. We further noted that Connecticut law lacked binding precedent for determining whether an "insured location," as that term was used in the homeowner's policy, could cover the portion of the private road where the accident in this case occurred. Id. at 71.

Our first certified question sought guidance in addressing the issue of when and where the tort of negligent entrustment is deemed to accrue under Connecticut law. The second question sought guidance on the construction of the "insured location" language, an apparent term of art when used in insurance policies which had been construed in a plethora of ways by various American courts. See id. at 71-77. Our final certified question, directed at the Kings' delay in alerting their insurers of the accident, asked whether post-accident, friendly social interactions belying any litigation intent, such as had occurred between the Kings and the McEntees, could justify delaying notice to an insurer under Connecticut insurance law.

In answering our first two certified questions, the Connecticut Supreme Court (1) held that under the Kings' homeowner's policy a negligent entrustment claim brought under Connecticut law, regardless of the locus of the entrustment, arises at the site of the injury-causing accident and (2) determined that the portion of the private road where this accident happened was not an "insured location" within the terms of the policy as that language is properly construed under Connecticut insurance law. In answering our third question, the Connecticut Supreme Court held that social interactions unrelated to litigation do not justify delayed notice. The answer to the third certified question is rendered academic on this appeal by the Supreme Court of Connecticut's answers to the first two questions.3

Standard of Review and Applicable Law

A district court's summary disposition of claims is reviewed de novo. Papelino v. Albany Coll. of Pharmacy of Union Univ., 633 F.3d 81, 88 (2d Cir.2011). A district court's denial of a motion for leave to amend a pleading is reviewed de novo when based on rulings of law but is otherwise reviewed for an abuse of discretion. Id.

Substantively, under Connecticut law, "`[a]n insurance policy is to be interpreted by the same general rules that govern the construction of any written contract.'" Conn. Med. Ins. Co. v. Kulikowski, 286 Conn. 1, 5, 942 A.2d 334, 338 (2008) (quoting Enviro Express, Inc. v. AIU Ins. Co., 279 Conn. 194, 199, 901 A.2d 666, 669 (2006)). Consistent with the general rules of contract construction, the intent of the parties, as expressed by the policy language, is determinative in construing even the most opaque-appearing policy provisions. Hartford Cas. Ins. Co. v. Litchfield Mut. Fire Ins. Co., 274 Conn. 457, 463, 876 A.2d 1139, 1143-44 (2005). "If the terms of the policy are clear and unambiguous, then the [contract] language... must be accorded its natural and ordinary meaning." Schilberg Integrated Metals Corp. v. Cont'l Cas. Co., 263 Conn. 245, 267, 819 A.2d 773, 789 (2003) (citations omitted). "In determining whether the terms of an insurance policy are clear and unambiguous, a court will not torture words to import ambiguity where the ordinary meaning leaves no room for ambiguity.... Similarly, any ambiguity in a contract must emanate from the language used in the contract rather than from one party's subjective perception of the terms." Conn. Med. Ins. Co., 286 Conn. at 6, 942 A.2d at 338 (citations, internal quotation marks, and brackets omitted).

Discussion

A. The Homeowner's Policy

The Connecticut Supreme Court's answers leave no doubt that the district court correctly found (1) that the only location relevant in determining whether the homeowner's policy provided the subject coverage was the site of the accident and (2) that the accident did not occur at an "insured location," as that language is construed under Connecticut law. Accordingly, the district court properly granted summary judgment to Royal, declaring that the foundational homeowner's policy did not cover the ATV accident that allegedly caused injury to Conor.

B. The Umbrella and Excess Policies

Appellants argue that the ruling of the district court which found that the umbrella policy did not provide coverage is erroneous for two main reasons. They first contend that the policy Royal claims was the policy in effect at the time of the accident was, at best, ambiguous with regard to any requirement that, in order to secure coverage for any ATV, the ATV be listed in the policy's declarations page. To support this conclusion, Appellants point out that the document identified as the declarations page (1) lacks blank lines on which to list ATVs and (2) includes language limiting its subject matter to "off" premises use of ATVs, which, they go on to assert, implies coverage of "on" premises use of ATVs even if the ATV is not listed in the declarations. But, even such tortured linguistic deconstruction cannot escape the obvious reality that there is no ambiguity in the policy language itself. The umbrella policy specifically recites that the policy does not cover liabilities arising from the use of an ATV unless the ATV is "described as being covered in the declarations." (Appellants' Appendix at 1653.) It draws no distinction between "on" and "off" premises ATV use. The two quibbles identified by the Kings in the formatting and wording of the separate declarations page come nowhere near the showing that would be required to render the policy language ambiguous. Given the policy's plain language, the Kings' failure to list the ATV in the declarations was fatal to coverage under the umbrella policy.

Appellants' second wave of attack sidesteps their failure to list the ATV on the declarations page. They advance an earlier and different version of the umbrella policy, which, they press, was the policy actually in effect at the time of the accident and, which, they say, did not require a declarations page listing of the ATV. Specifically, Appellants argue the older version of the policy was not updated in accordance with Conn. Gen. Stat/ § 38a-323 and, therefore, any change, such as requiring the ATV to be listed, was ineffective as matter of law. After a complete review, we reject this argument for substantially the same reasons stated in the district court's thorough and carefully reasoned opinion. See Arrowood I, 512 F.Supp.2d at 128-29; id. at 132 (holding that the policy change was valid (1) because it neither (a) constituted a "nonrenewal" or "conditional nonrenewal" under Conn. Gen.Stat. § 38a-323, nor (b) triggered that section's notice requirements, and (2) because a post-amendment regulatory agency interpretation requiring notice had no retroactive effect).

Additionally, beyond determining the dispute regarding the umbrella policy, the district court's finding that there was no coverage under the extant umbrella policy had a broader, adverse reach for Appellants. Since it was uncontested that the excess liability policy "followed form" with the umbrella policy, any potential liability excluded from coverage under the umbrella policy was automatically excluded from coverage under the excess liability policy as well. Consequently, the district court correctly granted National summary judgment on the coverage claims brought against it. See id. at 132-33.

C. Appellants' Counterclaims Against Royal

The Kings pleaded two non-contract counterclaims, one pursuant to the Connecticut Unfair Trade Practices Act ("CUTPA"), Conn. Gen.Stat. §§ 42-110a et seq., and another sounding in bad faith. Both were predicated entirely on allegations that Royal's investigation of the accident was unreasonable because it concluded that the accident's situs was not a covered location. (See Appellants' Appendix at 172-73.) The counterclaims did not allege that Royal's investigation was unreasonable in any other way. Appellants' core argument on this point, of course, is now foreclosed by the Connecticut Supreme Court's answers to our certified questions. Royal's investigatory conclusion was more than reasonable — it was correct. Appellants' CUTPA and bad faith counterclaims fail as a matter of law. Because Appellants limited their counterclaims, we, like the district court, decline to consider whether, or under what other circumstances, a claimant could state a valid CUTPA or bad faith cause of action when the insurer correctly determined the contested coverage was unavailable under the policy as written.

D. The Claims Against NEBC

The negligence claim stated by the Kings, as would likely be suspected, rested solely on NEBC's alleged failure to procure umbrella and excess policies that "followed form" to the homeowner's policy. (Appellants' Appendix at 134-35.) In light of the now affirmed finding that the homeowner's policy did not cover the accident, no damages could possibly flow from any failure by NEBC to see to it that the other policies were congruent in coverage with the homeowner's policy. Appellants' contention that they alleged negligence broader than a failure to ensure the umbrella and excess policies followed form with the homeowner's policy has no support in the pleadings and is, correspondingly, rejected. Appellants' citation to their presentation of this same argument to the district court during a teleconference (Appellants' Opening Brief at 33) adds nothing. Claims are to be supported by pleaded facts, see, e.g., Ashcroft v. Iqbal, 556 U.S. 662, 677-78, 129 S.Ct. 1937, 1949, 173 L.Ed.2d 868 (2009), not by discussion or argument.

Appellants fare no better in their attempt to salvage their breach of contract and breach of fiduciary duty claims, which, they contend, were dismissed on April 27, 2005 "with leave to amend following discovery." (Appellants' Opening Brief at 33.) Unharmoniously, Appellants also state these same claims were dismissed sua sponte by the district court on October 31, 2007. (Id. at 34.) The record is at odds with both contentions, revealing that the district court dismissed those claims upon NEBC's motion on April 27, 2005, with 30 days leave to replead the contract claim and four months leave to replead the breach of fiduciary duty claim. (Motion Hearing Transcript, April 27, 2005, at 19-20.) Appellants made no attempt, the record further reveals, to timely replead either claim.4 Instead, more than two years after dismissal, at a teleconference held after the district court's Arrowood I summary judgment decision, Appellants tried to move forward on their breach of contract claim. See generally Royal Indem. Co. v. King, 532 F.Supp.2d 404, 408-09 & n. 5 (D.Conn.2008) ("Arrowood II"). But, as observed above — and as noted 18 at the 2007 conference with the district court — both claims originally pled against NEBC had been dismissed over two years earlier. (Id.) Dispositively, moreover, that 2005 dismissal is not challenged in Appellants' opening brief. Accordingly, that dismissal presents no preserved issue for review. See JP Morgan Chase Bank v. Altos Hornos de Mex., S.A. de C.V., 412 F.3d 418, 428 (2d Cir.2005) ("[A]rguments not made in an appellant's opening brief are waived....").

E. The Denial of Further Leave to Amend

Lastly, Appellants take exception to the district court's denial of their motion to amend the pleading of their CUTPA and bad faith claims against Royal and their negligence claim against NEBC. (Appellants' Opening Brief at 36.). The district court dismissed these claims soon after granting summary judgment, finding they were not viable in light of that decision. See generally Arrowood II, 532 F.Supp.2d at 410-16 (denying reconsideration). The Kings' motion to amend these dismissed CUTPA and bad faith claims was made on November 19, 2007 as an adjunct to their motion for reconsideration of the decision dismissing them. Id. at 416-17 ("The Kings have moved, in the alternative, to amend their complaint to add new facts and legal theories to support their rejected claims.... The Kings have not submitted a proposed amended third-party complaint or proposed second amended counterclaims.... It is clear from their briefing, however, that the Kings seek leave to allege an entirely new factual and legal basis for their CUTPA/CUIPA and bad faith claims against Royal, and their negligence claim against NEBC."). This late-stage motion to amend, however, was made long after the April 30, 2005 deadline that the district court had set on April 20, 2005 for the filing of motions to amend.5 (See Dist. Ct. Elec. Docket Entry Nos. 54-55.) Appellants point to nothing that explains their failure to either meet or move timely to extend that deadline. Nor do they explain why they could not have moved to amend these claims at some point long before November 19, 2007, when they sought to do so. Knowing all along that dispositive motions were pending that could, and ultimately did, end their case as pleaded, Appellants sat idly. Either by strategy or happenstance, Appellants did not act until after the summary judgment motions had been decided adversely to them. Then, with the legal mine field mapped in the district court's decision, Appellants sought leave to steer a new course hoping to snatch away the victors' success. Denial of additional time to amend in those circumstances was hardly an abuse of the discretion accorded the district court by the letter and spirit of Rule 15 of the Federal Rules of Civil Procedure. Whether based on Rule 15 alone or in tandem with the "good cause" requirement of Rule 16, we cannot say on this record that the district court abused its discretion in denying Appellants' motion. See Aetna Cas. & Sur. Co. v. Aniero Concrete Co., Inc., 404 F.3d 566, 603 (2d Cir.2005) (discussing Rule 15); Grochowski v. Phoenix Constr., 318 F.3d 80, 86 (2d Cir.2003) (discussing Rule 16).

Conclusion

For the foregoing reasons, we AFFIRM the judgment of the district court. We thank the Supreme Court of Connecticut for its assistance.