Exhibit 4.1

DESCRIPTION OF SECURITIES

Title of Class of Security: Core Macro Portfolio - Class 0 Units, Class 2 Units, Class 3-A Units and Class 3-B Units

Dividend Rights

The Manager has sole discretion in determining what distributions of profits and income, if any, are made to investors. Due to the capital appreciation investment objective of the Fund and the fact that Units may be redeemed monthly, the Manager does not anticipate paying dividends or making distributions to investors.

Redemption Provisions

The Units are not subject to any minimum holding period. Members may redeem Units at their Net Asset Value as of each Valuation Day upon not less than three business days’ prior written notice to the Administrator, or upon such other notice and on such other dates as the Manager may permit in its sole and absolute discretion. The Manager may reject a partial redemption request, with respect to each Class of Units, for an amount less than $10,000 or that would result in an investor owning a total Net Asset Value of less than $10,000. The redemption proceeds normally will be remitted within 15 business days after the Valuation Day, without interest for the period from the Valuation Day to the payment date. Redemption payments will ordinarily be made in U.S. dollars, and will be remitted either by wire transfer to an account designated by the investor or by check posted at the investor’s risk (as specified by the investor in his written redemption notice). The Administrator will process redemption requests which are initially received by facsimile, but no part of the redemption proceeds will be paid to redeeming members until the Administrator has received the original redemption request signed by the redeeming member or by an authorized signatory of the redeeming member. Neither the Fund nor the Administrator shall be responsible for any mis-delivery or non-receipt of any facsimile. Facsimiles sent to the Administrator shall only be effective when actually received by the Administrator.

The Manager has the right to require the compulsory redemption of all Units held by a member for any reason in its discretion. Compulsory redemptions will be made at the Net Asset Value as of the Valuation Day next following the issuance of a notice of redemption to the member. The Manager may suspend the right of any member to redeem Units, as well as the issuance of additional Units, upon the occurrence of any of the following circumstances:

(1)

when any exchange, board of trade or organized inter-dealer market on which a significant portion of the assets of the Fund is regularly quoted or traded is closed (other than for holidays) or trading thereon has been restricted or suspended;

(2)

whenever, as a result of events, conditions or circumstances beyond the control or responsibility of the Fund, disposal of the assets of the Fund or other transactions in the ordinary course of the Fund’s business involving the sale, transfer, delivery or withdrawal of securities or Funds is not reasonably practicable without being detrimental to the interests of the Fund or the investors;

(3)

if it is not reasonably practicable to determine the Net Asset Value of the Units on an accurate and timely basis; or

(4)

if the Manager has adopted a resolution calling for the liquidation and dissolution of the Fund.

The Manager may withhold payment to any person whose Units have been tendered for redemption until after any suspension has been lifted. Notice of any suspension will be given to any investor who has tendered his Units for redemption and to whom full payment of the redemption proceeds has not yet been remitted. If a redemption request is not withdrawn by an investor following notification of a suspension, the redemption will be completed as of the next Valuation Day following the end of the suspension on the basis of the Net Asset Value as of such Valuation Day.

Voting Rights

Members have no voting rights with respect to any matters pertaining to the Fund, other than the right to vote on amendments to the Company Agreement approved by the Manager when such a vote is required by the Company Agreement or as otherwise provided under the terms of the Company Agreement or by law.

Liquidation Rights

The Company Agreement provides that the Fund shall remain in existence until the year 2050, except upon prior dissolution. Dissolution of the Fund may occur at the end of its term or earlier upon the election of the Manager to dissolve the Fund or the occurrence of the bankruptcy of the Manager or any event which results in the Manager (or a successor to its business) ceasing to be the Manager of the Fund or the date on which the Fund ceases to have more than one member. Upon the occurrence of any such event, the Manager (or a liquidator elected by a majority in interest of the members, if the Manager is unable to perform this function) is charged with winding up the affairs of the Fund and liquidating its assets. Upon the liquidation of the Fund, its assets are to be distributed: (i) first to satisfy the debts, liabilities and obligations of the entity (other than debts to members), including liquidation expenses, actual or anticipated; (ii) next to repay debts owing to the members; and (iii) finally to the members proportionately in accordance with the balances in their respective Capital Accounts. Assets may be distributed in kind on a pro rata basis if the Manager or liquidator determines that such a distribution would be in the interests of the members in facilitating an orderly liquidation.

Restrictions on Alienability

The Units are subject to restrictions on alienability. A member may not assign or pledge its Units in whole or in part, except by operation of law, nor substitute for itself as a member any other person, without the prior written consent of the Manager, which may be withheld in its sole and absolute discretion.

GRAHAM ALTERNATIVE INVESTMENT FUND II LLC 10-K