APOLLO RESIDENTIAL MORTGAGE, INC. PRIVATE PLACEMENT PURCHASE AGREEMENT

Exhibit 10.10

APOLLO RESIDENTIAL MORTGAGE, INC.

PRIVATE PLACEMENT PURCHASE AGREEMENT

PRIVATE PLACEMENT PURCHASE AGREEMENT (this “Agreement”) made as of this 27^th day of July, 2011, by and between Apollo Residential Mortgage, Inc., a Maryland corporation (the “Company”), and Keith Rosenbloom (the “Purchaser”).

WHEREAS, the Purchaser has a substantive, pre-existing relationship with the Company;

WHEREAS, the Company has filed a registration statement on Form S-11 (File No. 333-172980) (the “Registration Statement”) under the Securities Act of 1933, as amended (the “Securities Act”) with the Securities and Exchange Commission (the “SEC”) in connection with a proposed initial public offering (the “IPO”) of 10,000,000 shares of the Company’s common stock, par value $0.01 per share (the “Common Stock”); and

WHEREAS, concurrent with the consummation of the IPO, the Company desires to issue and sell, and the Purchaser desires to purchase, upon the terms and conditions set forth in this Agreement, 5,000 shares of Common Stock (the “Private Placement Shares” and each, a “Private Placement Share”).

NOW, THEREFORE, for and in consideration of the premises and the mutual covenants hereinafter set forth, the parties hereto do hereby agree as follows:

1. Sale and Purchase of Private Placement Shares. Subject to and concurrent with the consummation of the IPO, the Company shall issue and sell to the Purchaser and the Purchaser shall purchase from the Company, at a purchase price per Private Placement Share equal to the public offering price per share of Common Stock sold in the IPO, the Private Placement Shares.

2. Closing. The closing of the purchase and sale of the Private Placement Shares hereunder, including payment for and delivery of the Private Placement Shares, will take place at the offices of the Company or the Company’s legal counsel concurrently with, and shall be subject to, the completion of the IPO.

3. Representations and Warranties of the Company. In connection with the issuance and sale of the Private Placement Shares, the Company hereby represents and warrants to the Purchaser the following:

3.1 The Company is a corporation duly formed, validly existing and in good standing under the laws of the State of Maryland and the Company has all necessary corporate power and authority to enter into this Agreement and to consummate the transactions contemplated hereby.

3.2 All corporate action necessary to be taken by the Company to authorize the execution, delivery and performance of this Agreement and all other agreements and instruments delivered by the Company in connection with the transactions contemplated hereby has been duly and validly taken and this Agreement has been duly executed and delivered by the Company. This Agreement constitutes the valid, binding and enforceable obligation of the Company, enforceable in accordance with its terms, except as enforceability may be limited by applicable bankruptcy, insolvency, reorganization, moratorium, fraudulent transfer or similar laws of general application now or hereafter in

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effect affecting the rights and remedies of creditors and by general principles of equity (regardless of whether enforcement is sought in a proceeding at law or in equity). The issuance and sale by the Company of the Private Placement Shares does not conflict with any material contract by which the Company or its property or assets is bound, or any federal or state laws or regulations or decree, ruling or judgment of any United States or state court applicable to the Company or its property or assets.

3.3 Upon issuance in accordance with, and payment pursuant to, the terms hereof, the Purchaser will have good title to the Private Placement Shares free and clear of all liens, claims and encumbrances of any kind, other than transfer restrictions hereunder and under other agreements contemplated hereby.

3.4 The Company has a substantive, pre-existing relationship with the Purchaser and was directly contacted by the Purchaser or its agents outside of the IPO effort. The Company (i) did not identify or contact the Purchaser through the marketing of the IPO and (ii) was not independently contacted by the Purchaser as a result of the general solicitation by means of the Registration Statement.

4. Representations and Warranties of the Purchaser. The Purchaser hereby represents and warrants to the Company that:

4.1 The Purchaser is an “accredited investor” as that term is defined in Rule 501 of Regulation D promulgated under the Securities Act. The Purchaser has accurately completed the Accredited Investor Questionnaire attached hereto as Exhibit A indicating the basis for such Purchaser’s accredited investor status.

4.2 The Private Placement Shares are being acquired for the Purchaser’s own account, only for investment purposes and not with a view to, or for resale in connection with, any public distribution or public offering thereof within the meaning of the Securities Act.

4.3 The Purchaser has all necessary power and authority to enter into this Agreement and to consummate the transactions contemplated hereby.

4.4 All action necessary to be taken by the Purchaser to authorize the execution, delivery and performance of this Agreement and all other agreements and instruments delivered by the Purchaser in connection with the transactions contemplated hereby has been duly and validly taken and this Agreement has been duly executed and delivered by the Purchaser. This Agreement constitutes the valid, binding and enforceable obligation of the Purchaser, enforceable in accordance with its terms, except as enforceability may be limited by applicable bankruptcy, insolvency, reorganization, moratorium, fraudulent transfer or similar laws of general application now or hereafter in effect affecting the rights and remedies of creditors and by general principles of equity (regardless of whether enforcement is sought in a proceeding at law or in equity). The purchase by the Purchaser of the Private Placement Shares does not conflict with the organizational documents of the Purchaser or with any material contract by which the Purchaser or its property or assets is bound, or any laws or regulations or decree, ruling or judgment of any court applicable to the Purchaser or its property or assets.

4.5 The Purchaser understands and acknowledges that (i) the offering of the Private Placement Shares pursuant to this Agreement will not be registered under the

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Securities Act on the grounds that the offering and sale of the Private Placement Shares is exempt from registration under the Securities Act pursuant to Rule 506 of Regulation D thereof and exempt from registration pursuant to applicable state securities or blue sky laws and, therefore, the Private Placement Shares will be characterized as “restricted securities” under the Securities Act and such laws and may not be sold unless the Private Placement Shares are subsequently registered under the Securities Act and qualified under state law or unless an exemption from such registration and such qualification is available.

4.6 The Purchaser has a substantive, pre-existing relationship with the Company and was directly contacted by the Company or the Company’s agents outside of the IPO effort. The Purchaser (i) was not identified or contacted through the marketing of the IPO and (ii) did not independently contact the Company as a result of the general solicitation by means of the Registration Statement.

4.7 The Purchaser (i) has such knowledge and experience in financial and business matters as to be capable of evaluating the merits and risks of the Purchaser’s prospective investment in the Private Placement Shares; (ii) has the ability to bear the economic risks of the Purchaser’s prospective investment; and (iii) has not been offered the Private Placement Shares by any form of advertisement, article, notice, or other communication published in any newspaper, magazine, or similar medium; or broadcast over television or radio; or any seminar or meeting whose attendees have been invited by any such medium.

5. Restriction on Sale of Private Placement Shares. Until 12 months from the date of this Agreement, the Purchaser will not, without the prior written consent of the Company, directly or indirectly, sell, offer, dispose of, hedge or enter into any transaction that is designed to, or might reasonably be expected to result in the disposition of, any Private Placement Shares. Notwithstanding the foregoing, the Purchaser may transfer Private Placement Shares: (1) to an immediate family member; (2) to one or more trusts of which the sole beneficiaries thereof are the Purchaser and/or the Purchaser’s immediate family members; (3) for estate planning purposes; and (4) as a bona fide gift or gifts; provided, however, that in the case of any transfer, it shall be a pre-condition to such transfer that the transferee or donee has agreed in writing with the Company to be bound by the terms of this Agreement.

6. Registration Rights Agreements. As a further inducement for the Purchaser to purchase the Private Placement Shares, at the time of the completion of the IPO, the Company and the Purchaser shall enter into a registration rights agreement, substantially in the form of Exhibit B hereto, pursuant to which the Company will grant certain registration rights to the Purchaser relating to the Private Placement Shares.

7. Successors and Assigns. Except as otherwise expressly provided herein, all covenants and agreements contained in this Agreement by or on behalf of any of the parties hereto shall bind and inure to the benefit of the respective successors of the parties hereto whether so expressed or not. Notwithstanding the foregoing or anything to the contrary herein, the parties may not assign this Agreement or their obligations hereunder.

8. Amendments. This Agreement may not be amended, modified or waived, in whole or in part, except by an agreement in writing signed by each of the parties hereto.

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9. Counterparts; Facsimile. This Agreement may be executed in any number of counterparts, each of which when so executed shall be deemed to be an original and all of which taken together shall constitute one and the same instrument. This Agreement or any counterpart may be executed via facsimile transmission, and any such executed facsimile copy shall be treated as an original.

10. Governing Law. This Agreement shall for all purposes be deemed to be made under and shall be construed in accordance with the laws of the State of New York. The parties hereby agree that any action, proceeding or claim against it arising out of or relating in any way to this Agreement shall be brought and enforced in the courts of the State of New York or the United States District Court for the Southern District of New York, and irrevocably submit to such jurisdiction, which jurisdiction shall be exclusive. The parties hereby waive any objection to such exclusive jurisdiction and agree not to plead or claim that such courts represent an inconvenient forum.

11. Third Party Beneficiaries. This Agreement is intended for the benefit of the parties hereto and their respective permitted successors and assigns, and is not for the benefit of, nor may any provision hereof be enforced by, any other person.

12. Legends. Each certificate, if any, representing the Private Placement Shares shall be endorsed with the following legend or a substantially similar legend:

“The securities represented by this certificate have not been registered under the Securities Act of 1933, as amended, and are “restricted securities” as defined in Rule 144 promulgated under the Securities Act. The securities may not be sold or offered for sale or otherwise distributed except (i) in conjunction with an effective registration statement for the shares under the Securities Act of 1933, as amended, or (ii) pursuant to an opinion of counsel, satisfactory to the company, that such registration or compliance is not required as to said sale, offer, or distribution. The securities represented by this certificate are subject to the terms and conditions of the Private Placement Purchase Agreement, dated as of July 27, 2011, by and between Apollo Residential Mortgage, Inc. and the Purchasers named therein.”

13. Severability. In case any provision of this Agreement shall be found by a court of law to be invalid, illegal, or unenforceable, the validity, legality, and enforceability of the remaining provisions of this Agreement shall not in any way be affected or impaired thereby.

14. Entire Agreement. This Agreement and the other documents delivered pursuant hereto constitute the full and entire understanding and agreement between the parties with regard to the subjects hereof and thereof and they supersede, merge, and render void every other prior written and/or oral understanding or agreement among or between the parties hereto.

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IN WITNESS WHEREOF, the parties hereto have executed this Agreement as of the date first written above.

(Signatures Continue on Next Page)

EXHIBIT A

ACCREDITED INVESTOR QUESTIONNAIRE

ACCREDITED INVESTOR STATUS FOR INDIVIDUALS (Please check the applicable subparagraphs):

1. ¨ A director or executive officer of the Company.

2. ¨ A natural person and have a net worth, either alone or with my spouse, at the time of purchase of the Shares that exceeds $1,000,000.

3. ¨ A natural person and had income in excess of $200,000 in each of the two most recent years and reasonably expect to have income in excess of $200,000 during the current year, or joint income with my spouse in excess of $300,000 in each of the two most recent years and reasonably expect to have joint income in excess of $300,000 during the current year.

Ex. A-1

EXHIBIT B

FORM OF REGISTRATION RIGHTS AGREEMENT

Ex. B-1