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                                                                     EXHIBIT 4.1

                           APEX MORTGAGE CAPITAL, INC.
                      865 SOUTH FIGUEROA STREET, SUITE 1800
                          LOS ANGELES, CALIFORNIA 90017

July 15, 2003

The Bank of New York
101 Barclay Street
New York, New York 10286
Attn: Mr. Steve Jones

     Re:  First Amendment to Shareholder Rights Agreement

Mr. Jones:

     Reference is made to that certain Shareholder Rights Agreement dated as of
July 19, 1999 (the "Rights Agreement"), by and between Apex Mortgage Capital,
Inc., a Maryland corporation (the "Company") and The Bank of New York, a New
York corporation (the "Rights Agent"). Capitalized terms used in this First
Amendment to Shareholder Rights Agreement (this "First Amendment") and not
otherwise defined herein shall have the meanings set forth in the Rights
Agreement.

     Pursuant to Section 27 of the Rights Agreement, the Company hereby directs
that Section 1(p) of the Rights Agreement shall be deleted in its entirety and
replaced by the following:

          "(p) "Exempt Persons" shall mean (i) The TCW Group, Inc. and its
     Affiliates (the "TCW Affiliates"), and (ii) American Home Mortgage
     Holdings, Inc. ("AHM"), AHM New Holdco, Inc. ("New Holdco"), and their
     respective Affiliates (the "AHM Affiliates"); provided, however, that (A)
     the TCW Affiliates shall cease to be Exempt Persons beginning on the 91st
     day following the date on which the TCW Investment Management Company
     ceases to serve as the manager of the Company's assets; and (B) the AHM
     Affiliates shall cease to be Exempt Persons beginning on the date on which
     that certain Agreement and Plan of Merger dated as of July 12, 2003, by and
     among AHM, New Holdco and the Company, shall have been terminated in
     accordance with its terms."

     The undersigned, on behalf of the Company, hereby certifies that this First
Amendment is in compliance with the terms of Section 27 of the Rights Agreement.
Except as amended in this First Amendment, the Rights Agreement shall remain in
full force and effect and unmodified.

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The Bank of New York, July 15, 2003 - Page 2

     By your counter-signature below, you hereby confirm that this First
Amendment is in compliance with the terms of Section 27 of the Rights Agreement
and agree to amend the Rights Agreement as described herein.

                                             APEX MORTGAGE CAPITAL, INC.

                                             By: /s/ Philip S. Barach
                                                --------------------------------
                                             Name: Philip S. Barach
                                                  ------------------------------
                                             Its: CEO
                                                 -------------------------------

Agreed to and acknowledged as of
July 15, 2003 by:

THE BANK OF NEW YORK

By: /s/ Edward Damons
   -------------------------------
Name:   Edward Damons
     -----------------------------
Its:    Vice-President
    ------------------------------

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