Exhibit 10.31

INVESTMENT MANAGEMENT AGREEMENT – FIXED INCOME

THIS AGREEMENT, dated as of the 26 day of June, 2003, by and between Asset Allocation & Management Company, L.L.C, an Delaware limited liability company having its principal place of business at Thirty North LaSalle Street, 35th Floor, Chicago, Illinois, 60602 (herein “AAM”), and Max Re Ltd., having its principal place of business at Max Re House, 2 Front Street, Hamilton, HM 11 Bermuda (herein “Client”).

In consideration of the promises set forth in this Agreement, AAM and Client agree as follows:

Subject to the terms and conditions set forth herein, Client hereby designates and appoints AAM as investment adviser for the management of securities with regard to the cash and securities listed in Exhibit A, which is attached hereto, and such other cash and securities (other than those identified as Unmanaged Assets, as defined below) as shall be subsequently contained in Client’s account by reason of purchases, sales, exchanges, withdrawals, additions or otherwise. Assets placed in the Client’s account by the Client that are not managed by AAM are either separately identified on Schedule A or shall be identified subsequently (“Unmanaged Assets”). AAM shall include Unmanaged Assets in its periodic reports to the Client, but will exclude their value in calculating AAM’s advisory fees.

AAM shall have full authority and discretion to supervise the management of said cash and securities (other than Unmanaged Assets), including, without limitation, authority and discretion to select, purchase and sell securities and to determine timing and means of execution for such selection, sales or purchases, in accordance with the investment guidelines set forth on Exhibit B hereto (the “Investment Guidelines”). The Client may modify the Investment Guidelines from time to time; provided, that, any such modification shall be effective only upon the provision of notice of such modification by the Client in accordance with the notice provisions herein.

For its investment advisory services, AAM shall be compensated based on a percentage of the value, as determined below, of all assets in the Client’s account (excluding Unmanaged Assets) as of the last trading day of each calendar month. The applicable percentages for calculating the advisory fee are set forth on the schedule of fees attached hereto. Upon sixty (60) days prior written notice to Client, AAM may amend or change the schedule of compensation.

AAM will value all of the securities in the portfolio on a monthly basis utilizing reputable industry standard pricing services or direct dealer quotes. Where the market value of any security is not readily available from standard pricing sources, AAM will price the security through multiple direct dealer quotes.

Advisory fees will be payable quarterly in arrears within thirty (30) days after receipt of AAM’s invoice by the Client. Any advisory fee payable for less than a full calendar quarter shall be pro-rated. Upon any termination of this Agreement other than at the end of a calendar quarter, the advisory fee shall be calculated as of the termination date.

This Agreement shall be effective as of the date of this Agreement and shall continue in effect until terminated by either party upon thirty (30) days prior written notice.

In the event of termination of this Agreement, this Agreement, except for Section 4 (Limitation of Liability), Section 12 (Confidentiality), Section 14 (Arbitration), and this Section 3 (Term of Agreement), shall immediately become void and have no further force or effect. Section 9 (Confidentiality) shall survive for a one year period following the termination date. Termination of this Agreement will not affect the Client’s obligation to pay advisory fees in accordance with Section 2 (Advisory Fees) through the date of termination.

Upon termination of this Agreement and upon specific written request, AAM shall within twenty (20) business days return to the Client all books and records of the Client, and all other information relating to the Client’s account then in the possession of AAM, except for any software or other intellectual property that is proprietary to, or owned or licensed by, AAM or any of its affiliates, which shall remain the property of AAM.

AAM shall be liable to and indemnify the Client to the extent any loss, liability, or damage results from the negligence or bad faith of AAM, violation of applicable law by AAM or the reckless disregard by AAM of its obligations and duties under this Agreement.

Except as set forth in the immediately preceding paragraph of this Section 4 (Limitation of Liability), neither AAM nor any of its employees, stockholders, members, managers, or any officers, or directors shall be liable hereunder for any action performed or omitted to be performed or for any errors or judgments in connection with AAM’s services rendered under this Agreement. The federal securities laws impose liabilities under certain circumstances on persons who act in good faith, and therefore, nothing herein shall in any way constitute a waiver or limitation of any rights which Client may have under any federal securities laws.

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Where AAM places orders for the execution of transactions, AAM may select such brokers and dealers for execution on such markets and at such process or commission rates as AAM determines in its good faith judgment to be in the best interests of Client. AAM may take into consideration in the selection of such brokers and dealers not only the available prices and rates of brokerage commissions, but also other relevant factors (such as, without limitation, execution capabilities and the value of its ongoing relationship with such brokers and dealers) without having to demonstrate that such factors are of a direct benefit to Client.

Under no circumstances shall AAM act as custodian for or hold Client’s cash and securities. AAM may issue instructions to the client’s custodian as may be appropriate in connection with the settlement of transactions initiated by AAM hereunder.

AAM shall manage the Client’s account in accordance with the Investment Guidelines; provided, however, that AAM will not be responsible for giving the Client investment advice or taking any other action with respect to Unmanaged Assets.

At reasonable times and upon reasonable notice, AAM shall provide access to all books, records, accounts, facilities, and personnel that relate specifically to the performance of its obligations to the Client under this Agreement to the internal and independent auditors and regulators of the Client.

Within six (6) days following the end of each month, AAM shall send to the Client monthly written reports showing the identity, cost and current market value of the assets in the Client’s account and each transaction made for the Client’s account during the period covered by the report.

At the close of each business day, AAM shall provide to the Client an electronic trade blotter detailing the transaction that occurred during such business day, in a form reasonably agreed by the parties.

AAM, a limited liability company, shall notify Client of any substantial change subsequent to the date of this Agreement in the ownership of the limited liability company. Such notification shall be made in accordance with the notice provisions herein.

This Agreement and the rights and obligations hereunder shall not be subject to assignment by AAM except with the written consent of Client.

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Each party hereto represents that (a) the execution of and performance contemplated under this Agreement do not and will not violate or abridge any obligation or duty of such party, (b) this Agreement has been authorized by appropriate action and when executed and delivered will be binding upon such party in accordance with its terms, and (c) it will deliver to the other party such evidence of such authority as such other party may reasonably require, either by way of a certified resolution or otherwise.

AAM represents, warrant and covenants to the Client that (i) it is, and will remain during the term of this Agreement, a registered investment adviser under the Investment Advisers Act of 1940, as amended; and (ii) it currently has, and agrees that it will maintain, the skilled personnel, computer hardware and software, and other facilities necessary to prepare the reports and perform the services required by this Agreement.

The names and specimen signatures of each individual who is authorized to give directions to AAM on the Client’s behalf under this Agreement are set forth on Exhibit C, as may be amended from time to time by the Client in accordance with the notice provisions herein. Directions received by AAM from the Client must be signed by at least one such person. If AAM receives directions from the Client that are not signed by a person that AAM reasonably believes is authorized to do so, the Client shall not be required to comply with such directions until it verifies that the directions are properly authorized by the Client.

Without the express prior written consent of AAM, Client shall not directly or indirectly employ or solicit for employment any employee of AAM, or its affiliates, during the term of this Agreement and for a period of 12 months after termination of the Agreement; provided, however, that the foregoing provision will not prevent the Client from employing any such person if such person contacts the Client on his or her own initiative in response to a published general solicitation not specifically targeted at such person.

From time to time in the course of the performance of this Agreement, the Client and AAM will be providing each other with certain financial, strategic and other information. Except as required by law, regulation, stock exchange rule or legal process and except as otherwise permitted by this Agreement, all such information of a non-public nature that is obtained by one party pursuant to this Agreement shall be held in confidence by such party and may not be disclosed to any other person without the prior written consent of the other party.

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All notices and other communications required or permitted to be given pursuant to this Agreement shall be in writing and shall be considered as properly given or made if (i) sent by overnight delivery by a nationally recognized air courier service, or (ii) mailed by registered or certified mail, return receipt requested, and if addressed to the respective address listed below:

All notices will be deemed effective upon receipt. Any party may change its address for the receipt of notices by providing notice, in the manner provided in this Section 13, to each other party.

In the event of any dispute, controversy or claim which relates to, arises out of, or is connected with this Agreement (including, without limitation, the creation, validity, interpretation, breach or termination of this Agreement), each party shall designate an officer whose task it will be to meet and in good faith resolve the matter amicably. Any such matter which has not been mutually resolved by the parties shall, on the written demand be either party to the other party, be determined and settled in Hamilton, Bermuda by a panel of three arbitrators in accordance with the Commercial Arbitration Rules of the American Arbitration Association. The award entered by the arbitrators shall be final and binding on both parties. Such award shall specify the factual and legal basis for the award, shall not include any multiple, punitive or exemplary damages, and shall remain confidential. The cost of the arbitration shall be borne equally by the Client and AAM; each party shall bear its own expenses (including counsel fees) incurred in connection with the arbitration

This Agreement contains the full agreement between AAM and the Client and supersedes any and all agreements, oral or written, which may have been heretofore entered into between AAM and the Client.

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No amendment to this Agreement will be effective unless in writing and signed by each of the parties and no waiver of compliance with any provision or condition, and no consent provided for in this Agreement, shall be effective unless in a writing duly executed by the party sought to be charged with such waiver or consent; provided, however, that the Client may amend Exhibits A, B and C by providing notice to AAM in accordance with Section 13 herein.

This Agreement shall be construed and enforced in accordance with the laws of the State of New York, without reference to the choice of law rules thereof.

In the event that any provision or condition in this Agreement shall be invalid, illegal, or unenforceable under applicable law of mandatory application, the validity, legality, and enforceability of that provision or condition in other instances and of the remaining provisions and conditions shall not in any way be affected thereby.

Section headings are for convenience of reference only and shall not affect the construction of this Agreement.

This Agreement may be executed in two or more counterparts, each of which when executed shall be deemed to be an original and all of which together shall be deemed to be one and the same instrument.

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IN WITNESS WHEREOF, the parties have executed this Agreement on the day, month, and year above written.

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