Blackstone Holdings III SC 13D/A Ellington Residential Mortgage REIT / Blackstone Holdings III ownership change

Exhibit 4

Form of Selling Shareholder Lock-up Agreement

June [    ], 2021

Ellington Residential Mortgage REIT

53 Forest Avenue

Old Greenwich, CT 06870

Morgan Stanley & Co. LLC

UBS Securities LLC

As Representatives of the Several Underwriters

c/o Morgan Stanley & Co. LLC

1585 Broadway

New York, New York 10036

c/o UBS Securities LLC

1285 Avenue of the Americas

New York, New York 10019

Ladies and Gentlemen:

As an inducement to the underwriters (the “Underwriters”) to execute the Underwriting Agreement (the “Underwriting Agreement”) relating to the proposed public offering (the “Public Offering”) of common stock, $0.01 par value per share (the “Securities”), of Ellington Residential Mortgage REIT, and any successor (by merger or otherwise) thereto (the “Company”), the undersigned hereby agrees that during the period specified in the following paragraph (the “Lock-Up Period”), the undersigned will not offer, sell, contract to sell, pledge or otherwise dispose of, directly or indirectly, any Securities or securities convertible into or exchangeable or exercisable for any Securities, enter into a transaction which would have the same effect, or enter into any swap, hedge or other arrangement that transfers, in whole or in part, any of the economic consequences of ownership of the Securities, whether any such aforementioned transaction is to be settled by delivery of the Securities or such other securities, in cash or otherwise, or publicly disclose the intention to make any such offer, sale, pledge or disposition, or to enter into any such transaction, swap, hedge or other arrangement, without, in each case, the prior

written consent of Morgan Stanley & Co. LLC (“Morgan Stanley”). In addition, the undersigned agrees that, without the prior written consent of Morgan Stanley, it will not, during the Lock-Up Period, make any demand for or exercise any right with respect to, the registration of any Securities or any security convertible into or exercisable or exchangeable for the Securities. Any Securities received upon exercise of options granted to the undersigned will also be subject to this Agreement. The restrictions described in this Agreement shall not apply to (i) the sale of the undersigned’s Securities pursuant to the Underwriting Agreement, as applicable or (ii) the establishment of a trading plan pursuant to Rule 10b5-1 under the Securities and Exchange Act of 1934, as amended (the “Exchange Act”), provided that (i) no transfer shall occur under such plan during the Lock-Up Period and (ii) to the extent a public announcement or filing under the Exchange Act, if any, is required of or voluntarily made by or on behalf of the undersigned or the Company regarding the establishment of such plan, such announcement or filing shall include a statement to the effect that no transfer of Securities may be made under such plan during the Lock-Up Period.

The Lock-Up Period will commence on the date of this Agreement and continue and include the date 30 days after the public offering date set forth on the final prospectus used to sell the Securities (the “Public Offering Date”) pursuant to the Underwriting Agreement, to which you are or expect to become parties.

Notwithstanding the foregoing, the undersigned may transfer the undersigned’s Securities (i) by will or intestacy, (ii) as a bona fide gift or gifts, including to charitable organizations, (iii) to any trust, partnership, limited liability company or other entity for the direct or indirect benefit of the undersigned or the immediate family of the undersigned (for purposes of this Agreement, “immediate family” shall mean any relationship by blood, current or former marriage or adoption, not more remote than first cousin), (iv) to any immediate family member or other dependent, (v) as a distribution to limited partners, members or stockholders of the undersigned, (vi) to the undersigned’s affiliates or to any investment fund or other entity controlled or managed by the undersigned, (vii) to a nominee or custodian of a person or entity to whom a disposition or transfer would be permissible under clauses (i) through (vi) above, (viii) pursuant to an order of a court or regulatory agency, (ix) from an executive officer to the Company or its parent entities upon death, disability or termination of employment, in each case, of such executive officer, (x) in connection with transactions by any person other than the Company relating to Securities acquired in open market transactions, (xi) pursuant to a bona fide third-party tender offer, merger, consolidation or other similar transaction in each case made to all holders of the Company’s Securities involving a Change of Control (as defined below), provided that in the event that such tender offer, merger, consolidation or other such transaction is not completed, the undersigned’s Securities shall remain subject to the provisions of this Agreement, (xii) to the Company (1) pursuant to the exercise, in each case on a “cashless” or “net exercise” basis, of any option to purchase Securities granted by the Company pursuant to any employee benefit plans or arrangements described in the general disclosure package included in the Underwriting Agreement (the “General Disclosure Package”) which are set to expire during the Lock-Up Period, where any Securities received

by the undersigned upon any such exercise will be subject to the terms of this Agreement, or (2) for the purpose of satisfying any withholding taxes (including estimated taxes) due as a result of the exercise of any option to purchase Securities or the vesting of any restricted stock awards granted by the Company pursuant to employee benefit plans or arrangements described in the General Disclosure Package which are set to expire or automatically vest during the Lock-Up Period, in each case on a “cashless” or “net exercise” basis, where any Securities received by the undersigned upon any such exercise or vesting will be subject to the terms of this Agreement, [(xiii) in connection with the pledge, hypothecation or other granting of a security interest in the Securities or securities convertible into or exchangeable for Securities to one or more lending institutions as collateral or security for any loan, advance or extension of credit and any transfer upon foreclosure upon such Securities or such securities, provided, that the undersigned or the Company, as the case may be, shall provide Morgan Stanley prior written notice informing them of any public filing, report or announcement with respect to such pledge, hypothecation or other grant of a security interest,]¹; provided that:

(1) in the case of each transfer or distribution pursuant to clauses (ii) through (vii) and (ix) above, (a) each donee, trustee, distributee or transferee, as the case may be, agrees to be bound in writing by the restrictions set forth herein; and (b) any such transfer or distribution shall not involve a disposition for value, other than with respect to any such transfer or distribution for which the transferor or distributor receives (x) equity interests of such transferee or (y) such transferee’s interests in the transferor; and

(2) in the case of each transfer or distribution pursuant to clauses (ii) through (vii), if any public reports or filings (including filings under Section 16(a) of the Exchange Act) reporting a reduction in beneficial ownership of Securities shall be required or shall be voluntarily made during the Lock-Up Period or any extension thereof (a) the undersigned shall provide Morgan Stanley prior written notice informing them of such report or filing and (b) such report or filing shall disclose that such donee, trustee, distributee or transferee, as the case may be, agrees to be bound in writing by the restrictions set forth herein; and

(3) in the case of clauses (x) and (xii), no public reports or filings (including filings under Section 16(a) of the Exchange Act reporting a reduction in beneficial ownership of Securities shall be required or shall be voluntarily made during the Lock-Up Period or any extension thereof; and

(4) for purposes of clause (xi), “Change of Control” shall mean the transfer (whether by tender offer, merger, consolidation or other similar transaction), in one transaction or a series of related transactions, to a person or group of affiliated persons (other than an Underwriter pursuant to the Offering), of the Company’s voting securities if, after such transfer, such person or group of affiliated persons would hold more than 50% of the outstanding voting securities of the Company (or the surviving entity).

¹  NTD: To be included for lockups delivered by entities only.

[Notwithstanding the foregoing, clauses (1)(a) and 2(b) above shall not apply with respect to any transfer of Securities to charitable organization transferees or recipients (including any direct or indirect member or partner of the undersigned that receives such Securities pursuant to a distribution in-kind to such member or partner and is subject to restrictions requiring such Securities to be transferred only to charitable organizations pursuant to clause (ii) above) in an aggregate amount, together with any such transfers pursuant to any substantially similar lock-up agreement with Morgan Stanley, not to exceed 1.0% of the outstanding Securities.]²

The undersigned acknowledges and agrees that the Underwriters have not provided any recommendation or investment advice nor have the Underwriters solicited any action from the undersigned with respect to the Public Offering of the Securities and the undersigned has consulted their own legal, accounting, financial, regulatory and tax advisors to the extent deemed appropriate. The undersigned further acknowledges and agrees that, although the Underwriters may provide certain Regulation Best Interest and Form CRS disclosures or other related documentation to you in connection with the Public Offering, the Underwriters are not making a recommendation to you to participate in the Public Offering or sell any Securities at the price determined in the Public Offering, and nothing set forth in such disclosures or documentation is intended to suggest that any Underwriter is making such a recommendation.

Whether or not the Public Offering actually occurs depends on a number of factors, including market conditions. Any Public Offering will only be made pursuant to an Underwriting Agreement, the terms of which are subject to negotiation between the Company and the Underwriters.

In furtherance of the foregoing, the Company and its transfer agent and registrar are hereby authorized to decline to make any transfer of Securities if such transfer would constitute a violation or breach of this Agreement.

This Agreement shall be binding on the undersigned and the successors, heirs, personal representatives and assigns of the undersigned. This Agreement shall lapse and become null and void if the Public Offering Date shall not have occurred on or before June 30, 2021. This Agreement shall be governed by, and construed in accordance with, the laws of the State of New York.

²  NTD: To be included for lockups delivered by entities only.

Very truly yours,

(Name)

(Address)