<PAGE>
Exhibit 31.01

                                  CERTIFICATION

I, Bruce L. Cleland, Chief Executive Officer of Campbell & Company, Inc., the
managing owner of Campbell Alternative Asset Trust (the "Trust"), do hereby
certify that:

1.   I have reviewed this quarterly report on Form 10-Q of the Trust;

2.   Based on my knowledge, this quarterly report does not contain any untrue
     statement of a material fact or omit to state a material fact necessary to
     make the statements made, in light of the circumstances under which such
     statements were made, not misleading with respect to the period covered by
     this quarterly report;

3.   Based on my knowledge, the financial statements, and other financial
     information included in this quarterly report, fairly present in all
     material respects the financial condition, results of operations and cash
     flows of the registrant as of, and for, the periods presented in this
     quarterly report;

4.   The registrant's other certifying officer and I are responsible for
     establishing and maintaining disclosure controls and procedures (as defined
     in Exchange Act Rules 13a-15(e) and 15d-15(e)) for the registrant and have:

     (a)  Designed such disclosure controls and procedures, or caused such
          disclosure controls and procedures to be designed under our
          supervision, to ensure that material information relating to the
          registrant, including its consolidated subsidiaries, is made known to
          us by others within those entities, particularly during the period in
          which this quarterly report is being prepared;

     (b)  Evaluated the effectiveness of the registrant's disclosure controls
          and procedures and presented in this quarterly report our conclusions
          about the effectiveness of the disclosure controls and procedures, as
          of the end of the period covered by this report based on such
          evaluation; and

     (c)  Disclosed in this report any change in the registrant's internal
          control over financial reporting that occurred during the registrant's
          most recent fiscal quarter (the Registrant's fourth fiscal quarter in
          the case of an annual report) that has materially affected, or is
          reasonable likely to materially affect, the registrant's internal
          control over financial reporting; and

5.   The registrant's other certifying officer and I have disclosed, based on
     our most recent evaluation of internal control over financial reporting, to
     the registrant's auditors and the audit committee of the registrant's board
     of directors (or persons performing the equivalent functions):

     (a)  All significant deficiencies and material weaknesses in the design or
          operation of internal control over financial reporting which are
          reasonably likely to adversely affect the registrant's ability to
          record, process, summarize and report financial information; and


                                      E 2
<PAGE>
     (b)  Any fraud, whether or not material, that involves management or other
          employees who have a significant role in the registrant's internal
          control over financial reporting.



                                                 By:  /s/ Bruce L. Cleland


                                                 -------------------------
                                                 Bruce L. Cleland
                                                 Chief Executive Officer
                                                 November 12, 2004


                                      E 3