<PAGE>
                                                                    EXHIBIT 10.2

LAW OFFICES OF GEORGE DONALDSON                          [STAMP]
GEORGE DONALDSON (79971)
DANIEL B. HARRIS (117230)
456 Montgomery Street, Suite 1250
San Francisco, CA 94104
Telephone:  415/394-8500

Settlement Counsel and
Attorneys for Plaintiffs


                          UNITED STATES DISTRICT COURT

                    FOR THE NORTHERN DISTRICT OF CALIFORNIA

JACK OLIVE, JONATHAN NOBLE,                  )   Case No. C 89 4331 MHP
M.D., JOHN P. PEDJOE AND                     )   DERIVATIVE ACTION
ALLSOP, INC. PROFIT SHARING                  )
PLAN & TRUST, on behalf of                   )
themselves and all                           )   AMENDMENT TO THE SECOND
others similarly situated and                )   AMENDMENT TO THE MODIFICATION
derivatively on behalf of                    )   OF STIPULATION OF SETTLEMENT
NATIONAL INCOME REALTY TRUST,                )
a California business trust,                 )
CONTINENTAL MORTGAGE AND EQUITY              )
TRUST, a California business                 )
trust, TRANSCONTINENTAL REALTY               )
INVESTORS, a California                      )
business trust, and INCOME                   )
OPPORTUNITY REALTY TRUST, a                  )
California                                   )
business trust,                              )
                                             )
                                Plaintiffs,  )
                                             )
         vs.                                 )
                                             )
GENE E. PHILLIPS; WILLIAM S.                 )
FRIEDMAN; RICHARD N. LAPP;                   )
MICHAEL E. SMITH; WILLIE K.                  )
DAVIS; RAYMOND V. J. SCHRAG;                 )
RANDALL K. GONZALEZ; JAMES W.                )
HAMMOND JR.; NATIONAL REALTY                 )
ADVISORS, INC., a Texas                      )
corporation; NATIONAL REALTY,                )
L.P.,                                        )
                                             )
                                             )
           -- caption continues --           )
---------------------------------------------



AMENDMENT TO THE SECOND AMENDMENT TO THE MODIFICATION OF STIPULATION OF
SETTLEMENT
<PAGE>



a Delaware limited partnership;         )
AMERICAN REALTY TRUST, INC., a          )
Georgia corporation; NATIONAL           )
OPERATING L.P., a Delaware              )
limited partnership;                    )
                                        )
                      Defendants,       )
                                        )
          -and-                         )
                                        )
                                        )
NATIONAL INCOME REALTY TRUST, a         )
California business trust;              )
CONTINENTAL MORTGAGE AND EQUITY         )
TRUST, a California business            )
trust; TRANSCONTINENTAL REALTY          )
INVESTORS, a California                 )
business trust; and INCOME              )
OPPORTUNITY REALTY TRUST, a             )
California business trust;              )
                                        )
        Nominal Defendants.             )
                                        )
--------------------------------------


     This amendment to the Second Amendment to the Modification of Stipulation
of Settlement is made and entered into as of February 4, 2002, by and among (i)
Settlement Counsel; (ii) Transcontinental Realty Investors, Inc. ("TRI") and
Income Opportunity Realty Investors, Inc. ("IORI")(collectively referred to as
the "Dallas Trusts"); and (iii) Gene E. Phillips ("Phillips"), Basic Capital
Management, Inc. ("BCM"), American Realty Investors, Inc. ("ARI"), the parent
corporation of American Realty Trust, Inc. ("ART").

     The above parties, by and through their respective counsel of record,
hereby amend Exhibits B and C of the Second Amendment to the Modification of
Stipulation of Settlement, made and entered into as October 5, 2001, in the
following respects only. In the case of both Exhibits B and C, the first
sentence of


                                       1

AMENDMENT TO THE SECOND AMENDMENT TO THE MODIFICATION OF STIPULATION OF
SETTLEMENT
<PAGE>




the section entitled Conversion Rights shall be deleted and replaced with the
following sentence: "For a 75-day period commencing on the 15th day after the
public issuance of ARI's Form 10-Q to the public following the close date of the
Freeze-Out Merger, the preferred shares herein described may be converted into
shares of ARI common stock."

     In the case of both Exhibits B and C, the second sentence of the section
entitled Redemption Rights shall be deleted and replaced with the following
sentence:  "Redeemable by ARI no earlier than 90 days after the public issuance
of ARI's Form 10-Q to the public following the close date of the Freeze-Out
Merger at the liquidation preference plus any accrued and unpaid dividends
thereon."








                                        2

AMENDMENT TO THE SECOND AMENDMENT TO THE MODIFICATION OF STIPULATION OF
SETTLEMENT
<PAGE>


         In all other respects, the Second Amendment remains unchanged.


                                           LAW OFFICES OF GEORGE DONALDSON
                                           456 Montgomery Street, Suite 1250
                                           San Francisco, CA 94104
                                           Telephone:  (415) 394-8500

                                           By /s/ GEORGE DONALDSON
                                             -----------------------------------
                                              George Donaldson
                                           Settlement Counsel and Attorneys for
                                           the Plaintiffs

                                           COOLEY GODWARD LLP
                                           One Maritime Plaza, Suite 2000
                                           San Francisco, CA 94111
                                           Telephone: (415) 693-2000

                                           SIMON, WARNER & DOBY, L.L.P.
                                           1700 City Center Tower II
                                           301 Commerce Street
                                           Fort Worth, TX 76102
                                           Telephone:  (817) 810-5250

                                           By /s/ HENRY W. SIMON, JR.
                                             -----------------------------------
                                             Henry W. Simon, Jr.

                                           Attorneys for Gene E. Phillips and
                                           Basic Capital Management, Inc.
                                           American Realty Trust, Inc. and
                                           American Realty Investors, Inc.

                                           HELLER EHRMAN WHITE & MCAULIFFE
                                           333 Bush Street, Suite 3000
                                           San Francisco, CA 94104-2878

                                           By /s/ JESSICA S. PERS
                                             -----------------------------------
                                             Jessica S. Pers
                                           Attorneys for the Dallas Trusts



                                       3

AMENDMENT TO THE SECOND AMENDMENT TO THE MODIFICATION OF STIPULATION OF
SETTLEMENT