CERTIFICATION BY CHIEF EXECUTIVE OFFICER

      I, Bruce Cleland, the Chief Executive Officer of Campbell & Company, Inc.
as managing owner of Campbell Alternative Asset Trust, certify that (i) the Form
10Q for the quarter ended March 31, 2004 of Campbell Alternative Asset Trust
fully complies with the requirements of Section 13(a) or 15(d) of the Securities
Exchange Act of 1934 and (ii) the information contained in the Form 10Q for the
quarter ended March 31, 2004 fairly presents, in all material respects, the
financial condition and results of operations of Campbell Alternative Asset
Trust .

                                    CAMPBELL ALTERNATIVE ASSET TRUST
                                    By: Campbell & Company, Inc., managing owner

                                    By: /s/ Bruce L. Cleland
                                        ---------------------------------
                                        Bruce L. Cleland
                                        Chief Executive Officer
                                        May 14, 2004

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