Exhibit 8.4

Hogan Lovells US LLP Columbia Square 555 Thirteenth Street, NW Washington, DC 20004 T +1 202 637 5600 F +1 202 637 5910 www.hoganlovells.com

May 31, 2018

Annaly Capital Management, Inc.

1211 Avenue of the Americas

New York, New York 10036

Re: MTGE Investment Corp.

Ladies and Gentlemen:

We have acted as special tax counsel to MTGE Investment Corp., a Maryland corporation (the “Company”), in connection with the transactions contemplated by the Agreement and Plan of Merger dated as of May 2, 2018 (the “Merger Agreement”), by and among the Company, Annaly Capital Management, Inc., a Maryland corporation (“Parent”), and Mountain Merger Sub Corporation, a Maryland corporation and a wholly-owned subsidiary of Parent (“Purchaser”), with respect to the proposed exchange offer and subsequent merger of the Company with and into Purchaser, with Purchaser surviving the merger, and certain other transactions. Pursuant to Section 7.11(b) of the Merger Agreement, this opinion letter is being delivered to you and is to be filed as an exhibit to the Registration Statement on Form S-4 (Registration No. 333-224968) initially filed by Parent with the Securities and Exchange Commission on May 16, 2018, as amended through the date hereof (together with the documents incorporated by reference therein, the “Registration Statement”) under the Securities Act of 1933, as amended, including the prospectus (the “Prospectus”) included therein. Capitalized terms used herein which are defined in the Merger Agreement shall have the meanings set forth in the Merger Agreement, unless otherwise defined herein.

Bases for Opinion

The opinion set forth in this letter is based on relevant current provisions of the U.S. Internal Revenue Code of 1986, as amended (the “Code”), the Treasury Regulations promulgated thereunder (including proposed and temporary Treasury Regulations), and interpretations of the foregoing as expressed in court decisions, applicable legislative history, and the administrative rulings and practices of the U.S. Internal Revenue Service (the “IRS”), including its practices and policies in issuing private letter rulings, which are not binding on the IRS except with respect to a taxpayer that receives such a ruling, all as of the date hereof. These provisions and interpretations are subject to change by the IRS, Congress and the courts (as applicable), which may or may not be retroactive in effect and which might result in material modifications of our opinion. Our opinion does not foreclose the possibility of a contrary determination by the IRS or a court of competent

Hogan Lovells US LLP is a limited liability partnership registered in the District of Columbia. “Hogan Lovells” is an international legal practice that includes Hogan Lovells US LLP and Hogan Lovells International LLP, with offices in:   Alicante   Amsterdam   Baltimore   Beijing   Berlin   Brussels   Caracas   Colorado Springs   Denver   Dubai   Dusseldorf   Frankfurt   Hamburg   Hanoi   Ho Chi Minh City Hong Kong   Houston   London   Los Angeles   Madrid   Miami   Milan   Moscow   Munich   New York   Northern   Virginia   Paris   Philadelphia   Prague   Rome   San Francisco   Shanghai   Silicon Valley Singapore   Tokyo   Ulaanbaatar   Warsaw   Washington DC   Associated offices:   Budapest   Jakarta   Jeddah   Riyadh   Zagreb.   For more information see www.hoganlovells.com

Annaly Capital Management, Inc.

May 31, 2018

Page 2

jurisdiction, or of a contrary position taken by the IRS or the United States Treasury Department in regulations or rulings issued in the future. In this regard, an opinion of counsel with respect to an issue represents counsel’s best professional judgment with respect to the outcome on the merits with respect to such issue, if such issue were to be litigated, but an opinion is not binding on the IRS or the courts, and is not a guarantee that the IRS will not assert a contrary position with respect to such issue or that a court will not sustain such a position asserted by the IRS.

In rendering the following opinion, we have examined such statutes, regulations, records, agreements, certificates and other documents as we have considered necessary or appropriate as a basis for the opinion, including but not limited to (1) the Registration Statement, (2) the Merger Agreement, and (3) certain organizational documents of the Company and certain of its subsidiaries (those documents referred to in clauses (1) through (3), the “Reviewed Documents”).

The opinion set forth in this letter is premised on, among other things, the written representations of the Company contained in a letter to us dated as of the date hereof (the “Management Representation Letter”). Although we have discussed the Management Representation Letter with the signatories thereto, for purposes of rendering our opinion, we have not made an independent investigation or audit of the facts set forth in the Reviewed Documents and the Management Representation Letter. We consequently have relied upon the representations and statements of the Company and Parent as described in the Reviewed Documents and the Management Representation Letter, and assumed that the information presented in such documents or otherwise furnished to us is accurate and complete in all material respects. In particular, we note that the Company has engaged in transactions in connection with which we have not provided legal advice and may not have reviewed. Moreover, we note that we did not represent the Company as special tax counsel prior to April 19, 2018.

In this regard, we have assumed with your consent the following:

(1)        that (A) all of the representations and statements as to factual matters set forth in the Reviewed Documents and the Management Representation Letter are true, correct and complete as of the date hereof, (B) any representation or statement in the Reviewed Documents and the Management Representation Letter made as a belief or made “to the knowledge of” or similarly qualified is true, correct and complete as of the date hereof, without such qualification, (C) each agreement described in the Reviewed Documents is valid and binding in accordance with its terms, and (D) each of the obligations of the Company and its subsidiaries, as described in the Reviewed Documents, has been or will be performed or satisfied in accordance with its terms;

(2)        the genuineness of all signatures, the proper execution of all documents, the authenticity of all documents submitted to us as originals, the conformity to originals of documents submitted to us as copies, and the authenticity of the originals from which any copies were made;

(3)        that any documents as to which we have reviewed only a form were or will be duly executed without material changes from the form reviewed by us;

(4)        that the Merger Agreement is valid and binding in accordance with its terms;

(5)         that the Offer and the Merger will be consummated in accordance with the Merger Agreement (including satisfaction of all pre-closing covenants and conditions to the obligations of the parties without amendment, waiver, or breach thereof);

(6)        that the Offer and the Merger, taken together, will qualify as a “reorganization” within the meaning of Section 368(a) of the Code;

Annaly Capital Management, Inc.

May 31, 2018

Page 3

(7)        that Parent will timely file a U.S. federal income tax return on Form 1120-REIT for the Company for its taxable year that ends on the Effective Time;

(8)        that Parent will comply with the requirements of Code Section 857(f)(1) and Treas. Reg. Sections 1.857-8 and 1.857-9 (related to records to be maintained concerning stock ownership and information required to be requested from shareholders as specified in applicable Treasury Regulations) with respect to the Company for its taxable year that ends on the Effective Time; and

(9)        that, from and after the date of this letter, the Company and Parent each will utilize all appropriate “savings provisions” (including the provisions of Sections 856(c)(6), 856(c)(7), and 856(g) of the Code, and the provision included in Section 856(c)(4) of the Code (flush language) allowing for the disposal of assets within 30 days after the close of a calendar quarter, and all available deficiency dividend procedures) available to the Company and/or Parent under the Code in order to correct any violations of the applicable real estate investment trust (“REIT”) qualification requirements of Sections 856 and 857 of the Code to the full extent the remedies under such provisions are available.

Any material variation or difference in the facts from those set forth in the documents that we have reviewed and upon which we have relied (including, in particular, the Registration Statement, the Prospectus, and the Management Representation Letter) may adversely affect the conclusions stated herein.

Opinion

Based upon, and subject to the assumptions and qualifications set forth herein, including, without limitation, the discussion in the next three paragraphs below, we are of the opinion that, commencing with the Company’s taxable year that ended on December 31, 2011 and through and including the taxable year that ends on the Effective Time, the Company has been organized and has operated in conformity with the requirements for qualification and taxation as a REIT under the Code.

The Company’s qualification and taxation as a REIT under the Code depends upon the ability of the Company to meet on an ongoing basis (through actual quarterly and annual operating results, distribution levels, diversity of share ownership and otherwise) the various qualification tests imposed under the Code, and upon the Company and/or Parent utilizing any and all appropriate “savings provisions” (including the provisions of Sections 856(c)(6), 856(c)(7), and 856(g) of the Code and the provision included in Section 856(c)(4) of the Code (flush language) allowing for the disposal of assets within 30 days after the close of a calendar quarter, and all available deficiency dividend procedures) available to the Company and/or Parent under the Code to correct violations of specified REIT qualification requirements of Sections 856 and 857 of the Code. Our opinion set forth above does not foreclose the possibility that the Company and/or Parent may have to utilize one or more of these “savings provisions” in the future, which could require the Company and/or Parent to pay an excise or penalty tax (which could be significant in amount) in order to maintain the Company’s REIT qualification. We have not undertaken to review the Company’s and Parent’s compliance with these requirements on a continuing basis. Accordingly, no assurance can be given that the actual results of the Company’s operations, the sources of its income, the nature of its assets, the level of its distributions to shareholders and the diversity of its share ownership for any given taxable year will satisfy the requirements under the Code for qualification and taxation as a REIT.

Annaly Capital Management, Inc.

May 31, 2018

Page 4

This opinion letter addresses only the specific U.S. federal income tax matters set forth above and does not address any other U.S. federal, state, local or foreign legal or tax issues.

This opinion letter has been prepared for your use in connection with the filing of the Registration Statement and speaks as of the date hereof. We assume no obligation by reason of this opinion letter or otherwise to advise you or any other person of any changes in our opinion subsequent to the delivery of this opinion letter. We hereby consent to the filing of this opinion letter as an exhibit to the Registration Statement. In giving this consent, we do not thereby admit that we are an “expert” within the meaning of the Securities Act of 1933, as amended.

Very truly yours,

/s/ HOGAN LOVELLS US LLP

HOGAN LOVELLS US LLP