Directors' Deferred Compensation Plan of Hudson City Bancorp, Inc

Exhibit 10.31

Directors’ Deferred Compensation Plan

of

Hudson City Bancorp, Inc.

Adopted on January 18, 2005
Effective as of January 18, 2005
Amended and Restated as of December 31, 2008

TABLE OF CONTENTS

Directors’ Deferred Compensation Plan

of

Hudson City Bancorp, Inc.

Article I

Definitions

The following definitions shall apply for the purposes of this Plan unless a different meaning is clearly indicated by the context:

           Section 1.1 Acceleration Event means, with respect to a Participant, any of the events described in section 6.1 on the basis of which the Administrator may permit acceleration of the payment of the balance credited to the Participant’s Memorandum Account.

           Section 1.2 Administrator means any person, committee, corporation or organization appointed by the Committee to perform the responsibilities assigned to the Administrator hereunder.

           Section 1.3 Beneficiary means the person or persons designated by a Participant under section 6.3 of the Plan.

           Section 1.4 Board means the Board of Directors of the Company.

           Section 1.5 Code means the Internal Revenue Code of 1986 (including the corresponding provisions of any succeeding law).

           Section 1.6 Company means Hudson City Bancorp, Inc. or any successor thereto.

           Section 1.7 Change in Control Event means, with respect to a Participant: (a) a change in ownership of the Participant’s Service Recipient; (b) a change in effective control of the Participant’s Service Recipient; or (c) a change in the ownership of a substantial portion of the assets of the Participant’s Service Recipient. The existence of a Change in Control Event shall be determined by the Administrator in accordance with section 409A of the Code and the regulations thereunder.

           Section 1.8 Cash Compensation means the monetary compensation payable to a Non-Employee Director for service as a member of the board of directors of a Participating Company, including retainer payments and fees for attendance at board and committee meetings.

           Section 1.9 Committee means the Compensation Committee of the Board.

           Section 1.10 Compensation means, during any period, the compensation payable to a Non-Employee Director by any Participating Company that is reportable to the Internal Revenue Service as compensation for such period on Form 1099 in the absence of an election to defer receipt thereof under the terms of this Plan. Compensation shall include Cash

Compensation, Equity Compensation and Option-Related Compensation. Compensation shall not include amounts that become payable under this Plan.

           Section 1.11 Disability means, with respect to a Participant, any medically determinable physical or mental impairment which can be expected to result in death or to last for a continuous period of at least twelve (12) months and as a result of which either: (a) the Participant is unable to engage in any substantial gainful activity or (b) the Participant has been receiving income replacement benefits for a period of at least three (3) months under an accident and health plan covering employees of the Participant’s employer. The existence of a Disability shall be determined by the Administrator in accordance with section 409A and the regulations thereunder.

           Section 1.12 Effective Date means January 18, 2005.

           Section 1.13 Equity Compensation means, with respect to any Participant, that portion of the Participant’s Compensation, other than Option-Related Compensation and/or stock appreciation rights, that is paid to him in Shares or the amount of which is based upon the value, or increase in value, of a Share.

           Section 1.14 Fair Market Value means, with respect to a Share on a specified date:

          (a) the final reported sales price on the date in question (or if there is no reported sale on such date, on the last preceding date on which any reported sale occurred) as reported in the principal consolidated reporting system with respect to securities listed or admitted to trading on the principal United States securities exchange on which the Shares are listed or admitted to trading; or

          (b) if the Shares are not listed or admitted to trading on any such exchange, the closing bid quotation with respect to a Share on such date on the National Association of Securities Dealers Automated Quotations System, or, if no such quotation is provided, on another similar system, selected by the Committee, then in use; or

          (c) if sections 1.14(a) and (b) are not applicable, the fair market value of a Share as the Administrator may determine.

           Section 1.15 Investment Benchmark means a hypothetical investment classification in which a Participant’s Memorandum Account shall be deemed to be invested for purposes of crediting or charging earnings, losses, appreciation or depreciation with respect to the Participant’s Memorandum Account, in accordance with section 3.2.

           Section 1.16 ISO Share means a Share acquired upon exercise of an incentive stock option (within the meaning of section 422 of the Code).

           Section 1.17 Memorandum Account means, with respect to a Participant, a bookkeeping account maintained by the Company to which is credited the amount of the Participant’s deferred Compensation, together with any earnings and appreciation thereon, and

against which are charged any losses, depreciation or distributions thereof, pursuant to Article III.

           Section 1.18 Memorandum Subaccount means, with respect to a Participant, a portion of the Participant’s Memorandum Account that is separately accounted for by the Company due to the application of unique provisions relating to the applicable distribution schedule or Investment Benchmark(s).

           Section 1.19 Non-Employee Director means a voting member of the board of directors of a Participating Company who is not an officer or employee of any Participating Company.

           Section 1.20 Option-Related Compensation means, with respect to an option to purchase Shares that is exercised by paying the entire exercise price therefor by actual or constructive delivery of Previously Acquired Shares, a number of Shares equal to the excess of (a) the total number of Shares as to which the option is exercised, over (b) the number of Shares actually or constructively delivered in payment of the exercise price.

           Section 1.21 Participant means a Non-Employee Director or former Non-Employee Director who has a Memorandum Account under the Plan.

           Section 1.22 Participating Company means the Company, Hudson City Savings Bank, and any other company which, with the prior approval of the Board, may adopt this Plan.

           Section 1.23 Phantom Share a unit of value that, at any relevant date, corresponds to the Fair Market Value of a Share.

           Section 1.24 Plan means the Directors’ Deferred Compensation Plan of Hudson City Bancorp, Inc.

           Section 1.25 Previously Acquired Share means, with respect to a Participant on any date: (a) a Share (other than an ISO Share) that was acquired by the Participant more than six (6) months prior to such date and has been held by the Participant continuously since such acquisition and (b) an ISO Share that was acquired by the Participant upon the exercise, at least one year prior to such date, of an incentive stock option (within the meaning of section 422 of the Code) that was granted to him at least two (2) years prior to such date and has been held by the Participant continuously since such acquisition.

           Section 1.26 Share means a share of Common Stock, par value $.01 per share, of the Company.

           Section 1.27 Service Recipient means with respect to a Participant on any date: (a) the corporation for which the Participant is performing services on such date; (b) all corporations that are liable to the Participant for the benefits due to him under the Plan; (c) a corporation that is a majority shareholder of a corporation described in section 1.27(a) or (b); or (d) any corporation in a chain of corporations each of which is a majority shareholder of another corporation in the chain, ending in a corporation described in section 1.27 (a) or (b).

           Section 1.28 Unforeseeable Emergency means, with respect to a Participant, a severe financial hardship to the Participant resulting from an illness or accident of the Participant, the Participant’s spouse or a dependent (within the meaning of section 152(e) of the Code) of the Participant, loss of the Participant’s property due to casualty, or other similar extraordinary and unforeseeable circumstances arising as a result of events beyond the control of the Participant. The existence of an Unforeseeable Emergency shall be determined by the Administrator in accordance with section 409A of the Code and the regulations hereunder.

Article II

Participation

           Section 2.1 Election to Participate.

          Any Non-Employee Director may elect to become a Participant in the Plan by submitting to the Administrator a written election, on a form prescribed by the Administrator, to defer the receipt of all or any portion of his Compensation; provided, however, that no Non-Employee Director shall be permitted to defer receipt of Compensation that is required to be withheld and remitted to any federal, state or local taxing authority pursuant to any requirement for the collection of tax at the source or that is required to fund any contribution or premium payment or co-payment required of the Non-Employee Director as a condition of participation in any employee benefit plan maintained by the Company or any other Participating Company at the time the election is made. A Non-Employee Director who elects to become a Participant may make separate deferral elections with respect to Cash Compensation, Equity Compensation and Option-Related Compensation. The Administrator may deny participation to any Non-Employee Director whose initial election to become a Participant does not contemplate the deferral of a minimum of $2,000 on an annualized basis.

           Section 2.2 Election to Defer Cash Compensation.

          An election to defer Cash Compensation shall specify the amount or percentage of each payment of Cash Compensation to be deferred, shall be made on or before the last day of any calendar year and shall be effective for the calendar year following the calendar year in which such election is made and all subsequent calendar years unless status as a Non-Employee Director ceases or a change in the rate of deferral is elected pursuant to section 2.5 ; provided, however, that an initial election to defer Cash Compensation made by a Non-Employee Director and filed with the Administrator during the thirty (30) day period immediately following the later of the Effective Date of the Plan or the date the Non-Employee Director first becomes eligible to participate in the Plan shall take effect with the first payment of Compensation that relates to a period of service that begins after such election is made, or such later date as the Non-Employee Director shall specify in his election.

           Section 2.3 Election to Defer Equity Compensation.

          An election to defer Equity Compensation shall specify the amount or percentage of each payment of Equity Compensation that is to be deferred, shall be made on or before the first day of the calendar year in which such Equity Compensation will be awarded and prior to the first day of the period of service for which such Equity Compensation is earned, and shall be

effective for all subsequent calendar years and service periods, unless status as a Non-Employee Director ceases or a change in the rate of deferral is elected pursuant to section 2.5; provided, however, that an initial election to defer Equity Compensation made by a Non-Employee Director and filed with the Administrator during the thirty (30) day period immediately following the later of the Effective Date or the date the Non-Employee Director first becomes eligible to participate in the Plan shall take effect with the first award of Equity Compensation that relates to a period of service that begins after such election is made, or such later date as the Non-Employee Director shall specify in his election. Acceptance of an election to defer Equity Compensation shall not be held or construed as a guarantee that any conditions precedent to the payment thereof (including but not limited to continued employment) will be met or the amount to be deferred will in fact be earned. In the event the dollar amount of Equity Compensation actually paid is less than the dollar amount for which a deferral election has been made, the election shall be deemed effective to defer the maximum permissible amount.

           Section 2.4 Election to Defer Option-Related Compensation and/or Compensation Related to Stock Appreciation Rights.

          No person shall elect to defer Option-Related Compensation, or compensation related to the exercise or settlement of stock appreciation rights, until such time as the Plan is amended to provide for such elections.

           Section 2.5 Changes in Participation.

          (a) An election by a Participant pursuant to section 2.2 shall continue in effect until termination of status as a Participant; provided, however, that the Participant may, by written election filed with the Administrator, increase or decrease the portion of his Cash Compensation to be deferred, or discontinue such deferral altogether. Such election shall be effective with respect to Cash Compensation payable for services rendered after the end of the calendar year in which such election is filed with the Administrator; provided, however , that if an election provides for the decrease or discontinuance of the Participant’s deferral of Cash Compensation and is made on account of Disability or an Unforeseeable Emergency or an Acceleration Event, such election shall, to the extent permitted under section 409A of the Code, be effective with respect to Cash Compensation payable after the filing of such election.

          (b) An election by a Participant pursuant to section 2.3 or 2.4 shall continue in effect until termination of status as a Participant; provided, however , that the Participant may, by written election filed with the Administrator, increase or decrease the portion of his Equity Compensation to be deferred, or discontinue such deferral altogether. Such election shall be effective with respect to Equity Compensation awarded after the calendar year in which, and on account of a period of service that begins after, such election is filed with the Administrator; provided, however , that if an election provides for the decrease or discontinuance of the Participant’s deferral of Equity Compensation and is made on account of Disability or an Unforeseeable Emergency or an Acceleration Event, such election shall be effective with respect to Equity Compensation, payable after the filing of such election.

          (c) In the event that a Participant ceases to be a Non-Employee Director or in the event that a Non-Employee Director ceases to defer receipt of his Compensation, the balance in his Memorandum Account shall continue to be adjusted in accordance with Article III. A

Non-Employee Director who has filed a written election to cease deferring receipt of any portion of his Compensation may thereafter again file an election to defer receipt of his Compensation in the manner described in sections 2.2 through 2.5.

           Section 2.6 Revocability of 2005 Elections.

          Notwithstanding anything in the Plan to the contrary, every election under the Plan to defer Compensation earned and payable in 2005 shall, to the maximum extent permitted and subject to the terms and conditions set forth in Internal Revenue Service Notice 2005-1, be revocable at any time during 2005. Such a revocation shall be effected by written notice given to and actually received by the Administrator on or before December 31, 2005 and shall result in the distribution of the entire balance credited to the Memorandum Account of the person revoking the election and in the inclusion of the entire amount distributed in gross income for federal income tax purposes in the 2005 taxable year.

Article III

Accounting for Deferred Amounts

           Section 3.1 In General.

          The Administrator shall maintain a separate Memorandum Account for each Participant and may establish within such Memorandum Account two or more Memorandum Subaccounts as may be necessary or appropriate to properly administer the Plan, including, but not limited to:

     (a) A separate Memorandum Subaccount for each portion of a Participant’s Memorandum Account to which a unique distribution schedule is applicable;

     (b) A separate Memorandum Subaccount for that portion of a Participant’s Memorandum Account that is attributable to Equity Compensation or Option-Related Compensation that has been deferred; and

     (c) A separate Memorandum Subaccount for that portion of a Participant’s Memorandum Account that is required to be adjusted for earnings and losses on the basis of an Investment Benchmark that is different from the Investment Benchmark(s) applicable to other portions of the Memorandum Account.

Credits, charges, and other adjustments to each Participant’s Memorandum Account and any Memorandum Subaccounts shall be made in accordance with this Article III. Neither the Company nor any Participating Company shall fund its liability for the balances credited to a Memorandum Account or Memorandum Subaccount, but each shall reflect its liability for such balances on its books.

           Section 3.2 Adjustments to Memorandum Accounts.

          (a) Each Participant’s Memorandum Account and applicable Memorandum Subaccount(s) shall be credited with amounts of Compensation deferred by the Participant as of the date on which such Compensation would have been paid to the Participant in the absence of a deferral election. For purposes of this section 3.2(a):

     (i) Equity Compensation consisting of Shares or other property which would be taxable for federal income tax purposes pursuant to section 83 of the Code that is being deferred shall be credited as of the date on which such Shares or other property become vested or, if later, the date on which such Shares or other property are contractually required to be transferred to the Participant; and

     (ii) Option-Related Compensation that is being deferred shall be credited as of the earliest date on which all actions have been taken and conditions satisfied to effectively exercise the related options;

all as determined by the Administrator, whose determination shall be conclusive and binding in the absence of manifest error.

          (b) Each Participant’s Memorandum Account shall be adjusted to reflect the amount of earnings, losses, appreciation or depreciation, as appropriate that would result if the balances credited to the Participant’s Memorandum Account, were actually invested in Investment Benchmarks according to the following guidelines:

     (i) That portion of a Participant’s Memorandum Account that is attributable to the deferral of Option-Related Compensation shall at all times be deemed to be invested in Phantom Shares. The number of Phantom Shares credited in connection with each deferral of Option-Related Compensation shall be equal to the number of Shares corresponding to the Option-Related Compensation that is being deferred. Additional Phantom Shares shall be credited to account for any stock dividends to holders of record of Shares in an amount equal to the product of (A) the number of Shares issued as a stock dividend to the holder of record of one Share, multiplied by (B) the number of Phantom Units credited to the Participant’s Memorandum Account as of the record date for the stock dividend. Additional Phantom Shares shall be credited to account for cash dividends paid to holders of record of Shares in an amount equal to the quotient of (A) the cash dividend per Share multiplied by the number of Phantom Shares credited to the Participant’s Memorandum Account as of the record date for the cash dividend, divided by (B) the Fair Market Value of a Share on the payment date for the cash dividend.

     (ii) That portion of a Participant’s Memorandum Account that is attributable to the deferral of Equity Compensation shall be deemed to be invested in Phantom Shares for so long as the Administrator may require.

     (iii) Any portion of the Participant’s Memorandum Account that is not subject to section 3.2(b)(i) or (ii) shall be deemed to be invested in such

Investment Benchmarks as the Participant, by notice given in such form and manner and subject to such terms, conditions and procedures as the Administrator may prescribe, shall designate from time to time. If one of the Investment Benchmarks is Phantom Shares, such terms, conditions and procedures shall be designed to prevent the occurrence of non-exempt short-swing transactions described in section 16 of the Securities Exchange Act of 1934, as amended, to assure compliance with the Company’s securities trading policy and applicable federal and state securities laws, and unless otherwise determined by the Administrator, to permit the Company to account for its liability with respect to such portion of the Memorandum Account on the basis of EITF 94-6 or corresponding guidance in subsequent accounting standards.

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