Exhibit 23.2

CONSENT OF INDEPENDENT REGISTERED PUBLIC ACCOUNTING FIRM

We consent to the incorporation by reference in this Registration Statement on Form S-8 of our report dated April 22, 2011 relating to the balance sheet of Apollo Residential Mortgage, Inc., appearing in the Registration Statement on Form S-11 (No. 333-172980) of Apollo Residential Mortgage Inc.

/s/ Deloitte & Touche LLP

New York, New York

July 27, 2011