Exhibit 99.1

March 1, 2009

The Board of Directors

IPC Holdings, Ltd.

American International Building

29 Pembroke Road

Pembroke, HM 08, Bermuda

Members of the Board of Directors:

You have requested our opinion as to the fairness, from a financial point of view, to IPC Holdings, Ltd. (the “Company”) of the Exchange Ratio (as defined below) in the proposed amalgamation (the “Transaction”) of a wholly-owned subsidiary of the Company with Max Capital Group Ltd. (the “Merger Partner”). Pursuant to the Agreement and Plan of Amalgamation (the “Agreement”), among the Company, IPC Limited, a wholly-owned subsidiary of the Company (the “Amalgamation Sub”) and the Merger Partner, the Merger Partner will be amalgamated (the “Amalgamation”) with the Amalgamation Sub whereupon the amalgamated company will be a wholly-owned subsidiary of the Company. Pursuant to the Amalgamation, each outstanding common share, par value $1.00 per share, of the Merger Partner (the “Merger Partner Common Shares”), other than Merger Partner Common Shares owned by the Company and its subsidiaries and Dissenting Shares (as defined in the Agreement), will be converted into the right to receive 0.6429 (the “Exchange Ratio”) common shares, par value $0.01 per share, of the Company (the “Company Common Shares”).

In arriving at our opinion, we have (i) reviewed a draft dated February 28, 2009 of the Agreement; (ii) reviewed certain publicly available business and financial information concerning the Merger Partner and the Company and the industries in which they operate; (iii) compared the financial and operating performance of the Merger Partner and the Company with publicly available information concerning certain other companies we deemed relevant and reviewed the current and historical market prices of the Merger Partner Common Shares and the Company Common Shares and certain publicly traded securities of such other companies; (iv) reviewed certain financial analyses and forecasts provided by the management of the Company and/or the Merger Partner, or prepared as directed by the management of the Company, including (a) certain internal financial analyses and forecasts prepared by the management of the Company relating to the Company’s business, (b) certain internal financial analyses and forecasts prepared by the management of the Merger Partner relating to the Merger Partner’s business as adjusted as directed by the management of the Company to account for certain assumptions developed jointly by the managements of the Company and the Merger Partner (the “Merger Partner Case 1 Projections”), (c) an alternative set of financial analyses and forecasts for the Merger Partner (the “Merger Partner Case 2 Projections”) based on the Merger Partner Case 1 Projections as adjusted as directed by the management of the Company to account for certain alternative loss ratio estimates (the “Alternative Loss Ratios”) developed by an independent consulting firm retained by the Company (the “Company Consultants”), (d) certain internal financial analyses and forecasts prepared jointly by the managements of the Company and the Merger Partner, or as directed by the management of the Company, relating to the combined business of the Company and the Merger Partner following the Transaction (such combined business following the Transaction, the “Combined Business”; and such financial analyses and forecasts, the “Combined Business Case 1 Projections”) and (e) an alternative set of financial analyses and forecasts for the Combined Business based on the Combined Business Case 1 Projections as adjusted as directed by the management of the Company to account for the Alternative Loss Ratios (the “Combined Business Case 2 Projections”); and (v) performed such other financial studies and analyses and considered such other information as we deemed appropriate for the purposes of this opinion.

In addition, we have held discussions with certain members of the management of the Merger Partner and the Company with respect to certain aspects of the Transaction, and the past and current business operations of the Merger Partner and the Company, the financial condition and future prospects and operations of the Merger Partner and the Company, the effects of the Transaction on the financial condition and future prospects of the Company, the Combined Business and certain other matters we believed necessary or appropriate to our inquiry.

In giving our opinion, we have relied upon and assumed the accuracy and completeness of all information that was publicly available or was furnished to or discussed with us by the Merger Partner or the Company or otherwise reviewed by or for us, and we have not independently verified (nor have we assumed responsibility or liability for independently verifying) any such information or its accuracy or completeness. We have not conducted any valuation or appraisal of any assets or liabilities, nor have we evaluated the solvency of the Merger Partner or the Company under any state, federal or other laws relating to bankruptcy, insolvency or similar matters. We have not been provided with any valuation or appraisal of any assets or liabilities on which we were permitted to or did rely. In relying on financial analyses and forecasts provided to us or prepared as directed by management of the Company or derived from any of the foregoing, we have assumed that they have been reasonably prepared based on assumptions reflecting the best currently available estimates and judgments by management as to the expected future results of operations and financial condition of the Company, the Merger Partner and the Combined Business, except that with respect to the Alternative Loss Ratios we have assumed that they have been reasonably prepared by the Company Consultants based on their market knowledge, their operational assessments of the Merger Partner, and reasonableness tests based upon industry benchmarks of estimated losses by line of business for historical years. We note that the management of the Company directed us to perform our analysis (i) with respect to the Merger Partner, based on both the Merger Partner Case 1 Projections and the Merger Partner Case 2 Projections and (ii) with respect to the Combined Business, based on both the Combined Business Case 1 Projections and the Combined Business Case 2 Projections. We express no view as to any analyses or forecasts referred to herein or the assumptions on which they were based, including the Alternative Loss Ratios. We have also assumed that the Transaction and the other transactions contemplated by the Agreement will qualify as a tax-free reorganization for United States federal income tax purposes, have the purchase accounting consequences described in discussions with, and materials furnished to us by, representatives of the Merger Partner and the Company, and will be consummated as described in the Agreement, and that the definitive Agreement will not differ in any material respects from the draft thereof furnished to us. We have also assumed that the representations and warranties made by the Company and the Merger Partner in the Agreement and the related agreements are and will be true and correct in all ways material to our analysis. We are not legal, regulatory, actuarial or tax experts and have relied on the assessments made by advisors to the Company with respect to such issues. We have further assumed that all material governmental, regulatory or other consents and approvals necessary for the consummation of the Transaction will be obtained without any adverse effect on the Merger Partner or the Company or on the contemplated benefits of the Transaction.

Our opinion is necessarily based on economic, market and other conditions as in effect on, and the information made available to us as of, the date hereof. It should be understood that subsequent developments may affect this opinion and that we do not have any obligation to update, revise, or reaffirm this opinion. Our opinion is limited to the fairness, from a financial point of view, to the Company of the Exchange Ratio in the proposed Transaction and we express no opinion as to the fairness of the Transaction to the holders of any class of securities, creditors or other constituencies of the Company or as to the underlying decision by the Company to engage in the Transaction. Furthermore, we express no opinion with respect to the amount or nature of any compensation to any officers, directors, or employees of any party to the Transaction, or any class of such persons relative to the Exchange Ratio in the Transaction or with respect to the fairness of any such compensation. We are expressing no opinion herein as to the price at which the Merger Partner Common Shares or the Company Common Shares will trade at any future time.

We have acted as financial advisor to the Company with respect to the proposed Transaction and will receive a fee from the Company for our services, a substantial portion of which will become payable only if the proposed Transaction is consummated. In addition, the Company has agreed to indemnify us for certain liabilities

arising out of our engagement. During the two years preceding the date of this letter, we and our affiliates have had commercial or investment banking relationships with the Company for which we and such affiliates have received customary compensation. Such services during such period have included an engagement to act as financial advisor to the Company in connection with its analysis and consideration of various potential strategic alternatives. That engagement resulted in our engagement to act as the Company’s financial advisor in connection with the Transaction. In addition, our commercial banking affiliate is a lender under the outstanding $500,000,000 senior credit facilities of the Company (the “Company Credit Facility”), for which it receives customary compensation or other financial benefits. It is anticipated that the Company Credit Facility will be amended in connection with the Transaction and that such amendment will result in the payment of customary compensation to our affiliate and in certain of the terms under the Company Credit Facility being amended to be more favorable to the lenders thereunder. In the ordinary course of our businesses, we and our affiliates may actively trade the debt and equity securities of the Company or the Merger Partner for our own account or for the accounts of customers and, accordingly, we may at any time hold long or short positions in such securities.

On the basis of and subject to the foregoing, it is our opinion as of the date hereof that the Exchange Ratio in the proposed Transaction is fair, from a financial point of view, to the Company.

The issuance of this opinion has been approved by a fairness opinion committee of J.P. Morgan Securities Inc. This letter is provided to the Board of Directors of the Company in connection with and for the purposes of its evaluation of the Transaction. This opinion does not constitute a recommendation to any shareholder of the Company as to how such shareholder should vote with respect to the Transaction or any other matter. This opinion may not be disclosed, referred to, or communicated (in whole or in part) to any third party for any purpose whatsoever except with our prior written approval. This opinion may be reproduced in full in any proxy or information statement mailed to shareholders of the Company but may not otherwise be disclosed publicly in any manner without our prior written approval.

Very truly yours,

/s/    J.P. MORGAN SECURITIES INC.