Exhibit 9

PURCHASE AGREEMENT, dated as of April 23, 2018 (the “Agreement”), by and between AXA Equitable Holdings, Inc., a Delaware corporation (formerly known as AXA America Holdings, Inc., “Buyer”), and Coliseum Reinsurance Company, a Delaware insurance company (“Seller”).

WHEREAS, Seller and Buyer are both indirect subsidiaries of AXA S.A., a société anonyme organized under the laws of France (“AXA”);

WHEREAS, in furtherance of an internal reorganization of AXA and certain of its subsidiaries, Seller desires to sell to Buyer, and Buyer desires to purchase from Seller, 8,160,000 units of Limited Partnership Interests in AllianceBernstein L.P., a Delaware limited partnership (“AllianceBernstein”), owned beneficially and of record by Seller (the “Units”).

NOW, THEREFORE, for good and valuable consideration, the receipt and sufficiency of which are hereby acknowledged, the parties hereto agree as follows:

Section 1.01. Purchase and Sale of Units. Pursuant to the terms of this Agreement, on the Transfer Date (as defined below), Seller shall sell the Units to Buyer, and Buyer shall purchase the Units from Seller.

Section 1.02. Purchase Price. The aggregate purchase price for the Units to be purchased by Buyer shall be $216,566,400 (the “Purchase Price”). The Purchase Price shall be paid to Seller on April 23, 2018 or on such other date as shall be agreed to by the parties (such date being the “Transfer Date”). On the Transfer Date:

(a) Buyer shall deliver to Seller (or as Seller may direct) the Purchase Price in immediately available funds by wire transfer to an account designated by Seller, by notice to Buyer.

(b) Seller shall irrevocably transfer the Units to Buyer by submitting Seller’s certificate including the Units, accompanied by a stock power executed by Seller with medallion signature guarantee, to AllianceBernstein’s transfer agent, which shall issue a certificate indicating that Buyer is the registered owner of the Units.

Section 1.03. Further Assurances. Each of Buyer and Seller hereby agrees to execute and deliver such documents, certificates, agreements and other writings as may be reasonably necessary or desirable in order to consummate or implement expeditiously the transactions contemplated by this Agreement.

Section 2.01. Corporate Existence. Seller is an insurance company duly incorporated and validly existing and in good standing under the laws of Delaware.

Section 2.02. Corporate Authorization. The execution, delivery and performance by Seller of this Agreement and the consummation by Seller of the transactions contemplated hereby are within Seller’s corporate powers and have been duly authorized by all necessary corporate action by or on behalf of Seller. This Agreement constitutes a valid and binding agreement of Seller.

Section 2.03. Governmental Authorization. The execution, delivery and performance by Seller of this Agreement and the consummation by Seller of the transactions contemplated hereby require no action by or in respect of, or filing with, any governmental body, agency or official other than as have been obtained or made or as Seller will timely make.

Section 2.04. Noncontravention. The execution, delivery and performance by Seller of this Agreement and the consummation by Seller of the transactions contemplated hereby do not and will not (i) violate any organizational documents of Seller, (ii) violate any applicable law, rule, regulation, judgment, injunction, order or decree, or (iii) require any consent or other action, except consents or other actions pursuant to the Amended and Restated Agreement of Limited Partnership of AllianceBernstein, dated as of October 29, 1999 (the “AllianceBernstein Limited Partnership Agreement”), by any person under, constitute a default under, or give rise to any right of termination, cancellation or acceleration of any right or obligation of Seller or to a loss of any benefit to which Seller is entitled under, any provision of any agreement or other instrument binding upon Seller.

Section 2.05. Ownership of Units. Seller is the sole legal and beneficial owner of the Units, free and clear of any lien and any other limitation or restriction, except such restrictions as may apply generally to all outstanding AllianceBernstein units of Limited Partnership Interests, and on the Transfer Date Seller will transfer and deliver to Buyer valid title to the Units free and clear of any lien and any other limitation or restriction, except such restrictions as may apply

generally to all outstanding AllianceBernstein units of Limited Partnership Interests or that may result directly or indirectly from Buyer’s affiliation with AXA SA. Seller received the Units either in the Exchange (as defined in the AllianceBernstein Limited Partnership Agreement) or in a transfer that was approved by AllianceBernstein Corporation, the general partner of AllianceBernstein.

Section 2.06. Legal Opinion. Seller has received a legal opinion from Proskauer Rose LLP confirming that the sale of the Units by Seller to Buyer (the “Sale”) will not cause AllianceBernstein to be classified as a publicly traded partnership within the meaning of Section 7704(a) of the Internal Revenue Code of 1986, as amended.

Section 3.01. Corporate Existence. Buyer is a corporation duly incorporated and validly existing and in good standing under the laws of Delaware.

Section 3.02. Corporate Authorization. The execution, delivery and performance by Buyer of this Agreement and the consummation by Buyer of the transactions contemplated hereby are within Buyer’s corporate powers and have been duly authorized by all necessary corporate action by or on behalf of Buyer. This Agreement constitutes a valid and binding agreement of Buyer.

Section 3.03. Governmental Authorization. The execution, delivery and performance by Buyer of this Agreement and the consummation by Buyer of the transactions contemplated hereby require no action by or in respect of, or filing with, any governmental body, agency or official other than as have been obtained or made or as will be timely made.

Section 3.04. Noncontravention. The execution, delivery and performance by Buyer of this Agreement and the consummation of the transactions contemplated hereby do not and will not (i) violate the organizational documents of Buyer, (ii) violate any applicable law, rule, regulation, judgment, injunction, order or decree, or (iii) require any consent or other action, except consents or other actions pursuant to the AllianceBernstein Limited Partnership Agreement, by any person under, constitute a default under, or give rise to any right of termination, cancellation or acceleration of any right or obligation of Buyer or to a loss of any benefit to which Buyer is entitled under, any provision of any agreement or other instrument binding upon Buyer.

Section 4.01. Termination. This Agreement may be terminated at any time prior to the Transfer Date by the mutual written consent of Buyer and Seller.

Section 4.02. Amendments and Waivers. This Agreement may be amended and the observance of any provision hereof may be waived (either generally or in a particular instance and either retroactively or prospectively) only with the written consent of Seller and Buyer.

Section 4.03. Non-Survival of Representations, Warranties and Covenants. None of the representations, warranties, covenants and agreements contained herein or made in writing by Buyer or by Seller in this Agreement shall survive the Transfer Date, except for (a) those covenants and agreements, and the rights arising out of any breach of such covenants and agreements, contained herein that by their terms apply or are to be performed in whole or in part after the Transfer Date and (b) Sections 4.03- 4.14 of this Agreement.

Section 4.04. Assignability. Neither this Agreement nor any right, remedy, obligation or liability arising hereunder or by reason hereof shall be assignable by any of Buyer or Seller without the prior written consent of the other party.

Section 4.05. Waiver of Jury Trial. THE PARTIES HERETO IRREVOCABLY WAIVE ANY AND ALL RIGHT TO TRIAL BY JURY WITH RESPECT TO ANY LEGAL PROCEEDING ARISING OUT OF THE TRANSACTIONS CONTEMPLATED BY THIS AGREEMENT.

Section 4.06. Submission to Jurisdiction. With respect to any suit, action or proceeding relating to this Agreement (“Proceedings”), each of the parties hereto (a) consents to submit itself to the personal jurisdiction of the courts of the State of New York or, if under applicable law exclusive jurisdiction over such matter is vested in the federal courts, any court of the United States located in the State of New York, in the event any dispute arises out of this Agreement or any of the transactions contemplated by this Agreement, (b) agrees that it shall not attempt to deny or defeat such personal jurisdiction by motion or other request for leave from any such court, (iii) agrees that it shall not bring any action relating to this Agreement or any of the transactions contemplated by this Agreement in any court other than the courts of the State of New York or, if under applicable law exclusive jurisdiction over such matter is vested in the federal courts, any court of the United States located in the State of New York, and (iv) consents to service being made through the notice procedures set forth in Section 4.11.

Section 4.07. Expenses. Except as otherwise provided herein, all costs, fees and expenses incurred in connection with this Agreement and the transactions contemplated hereby, whether or not consummated, shall be paid by the party incurring such cost, fee or expense.

Section 4.08. Governing Law. This Agreement and the rights and duties hereunder of the parties hereto shall be governed by and construed and interpreted in accordance with the laws of the State of New York, without giving effect to the principles or rules of conflicts of law thereof to the extent such principles or rules are not mandatorily applicable by statute and would require or permit the application of the laws of another jurisdiction.

Section 4.09. Section and Other Headings. The section and other headings contained in this Agreement are for reference purposes only and shall not affect the meaning or interpretation of this Agreement.

Section 4.10. Counterparts. This Agreement may be executed in any number of counterparts and by electronic means, each of which when so executed and delivered shall be deemed to be an original and all of which together shall be deemed to be one and the same agreement.

Section 4.11. Notices. All notices, requests, claims, demands and other communications hereunder shall be in writing and shall be given, and shall be deemed to have been duly given as follows, (a) if delivered in person, upon receipt, (b) if delivered by electronic mail, when delivered and, immediately after transmission, receipt of which has been confirmed by telephone or electronic mail by the sender, (c) if delivered by registered or certified mail (postage prepaid, return receipt requested), upon receipt to the respective parties at the following addresses (or at such other address for a party as shall be specified by like notice):

Any of the parties hereto may designate another addressee or change its address for notices and other communications hereunder by a notice given to the other applicable parties in the manner provided for in this Section 4.11.

Section 4.12. Binding Effect. The provisions of this Agreement shall be binding upon and accrue to the benefit of the parties hereto and their respective heirs, legal representatives, successors and assigns.

Section 4.13. Severability. If any term or provision of this Agreement is invalid, illegal or unenforceable in any jurisdiction, such invalidity, illegality or unenforceability shall not affect any other term or provision of this Agreement or invalidate or render unenforceable such term or provision in any other jurisdiction.

Section 4.14. Entire Agreement. This Agreement represents the entire understanding of the parties hereto with respect to the matters contemplated hereby and supersedes any and all prior negotiations, agreements, and understandings, whether oral or written heretofore made.

IN WITNESS WHEREOF, the parties hereto have duly executed this Agreement by their authorized representatives as of the date first above written.


SELLER:

COLISEUM REINSURANCE COMPANY

By:		/s/ Thomas J. Taylor
		Name: Thomas J. Taylor
		Title: President & CEO


BUYER:

AXA EQUITABLE HOLDINGS, INC.

By:		/s/ Robin M. Raju
		Name: Robin Raju
		Title: Senior Vice President and Treasurer

Pursuant to Section 12.03(a) and Section 12.03(c) of the Amended and Restated Agreement of Limited Partnership of AllianceBernstein L.P., dated as of October 29, 1999 and as amended on February 24, 2006 (“Agreement”), the General Partner and AXA Equitable Life Insurance Company hereby respectively approve the transfer of 8,160,000 Units of Limited Partnership Interests in AllianceBernstein L.P. by Coliseum Reinsurance Company to AXA Equitable Holdings, Inc. Terms defined in the Agreement are used herein as so defined.


ALLIANCEBERNSTEIN CORPORATION

By:		/s/ David Lesser
		Name: David Lesser
		Title: Corporate Secretary

[Signature Page – Written Approval Pursuant to Section 12.03(a) and Section 12.03(c)]


AXA EQUITABLE LIFE INSURANCE COMPANY

By:		/s/ Robin M. Raju
		Name: Robin Raju
		Title: Managing Director

[Signature Page – Written Approval Pursuant to Section 12.03(a) and Section 12.03(c)]

AXA Equitable Holdings, Inc. (EIN: 90-0226248), in its capacity as Substituted Limited Partner in respect of 8,160,000 Limited Partnership Interests previously owned by Coliseum Reinsurance Company, hereby accepts all of the terms and provisions of the Amended and Restated Agreement of Limited Partnership of AllianceBernstein L.P., dated as of October 29, 1999 and as amended on February 24, 2006 (“Agreement”), including the grant of the powers of attorney provided for in the Agreement, and represents that the transfer of such Limited Partnership Interests was made in accordance with all applicable laws and regulations. Terms defined in the Agreement are used herein as so defined.


AXA EQUITABLE HOLDINGS, INC.

By:		/s/ Robin M. Raju
		Name: Robin Raju
		Title: Senior Vice President and Treasurer

Pursuant to Section 12.03(a) of the Amended and Restated Agreement of Limited Partnership of AllianceBernstein L.P., dated as of October 29, 1999 and as amended on February 24, 2006 (“Agreement”), Coliseum Reinsurance Company, as a Limited Partner that wishes to transfer its Limited Partnership Interests, hereby certifies that it received its entire Limited Partnership Interests either in the Exchange or in a transfer that was approved by the General Partner pursuant to Section 12.03 of the Agreement. Terms defined in the Agreement are used herein as so defined.


COLISEUM REINSURANCE COMPANY

By:		/s/ Thomas J. Taylor
		Name: Thomas J. Taylor
		Title: President & CEO