Exhibit 31.1

                                 CERTIFICATION

I, Kenneth A. Shewer, Co-Chief Executive Officer of Preferred Investment
Solutions Corp., the Managing Owner of World Monitor Trust III, do hereby
certify that:

1.    I have reviewed this quarterly report on Form 10-Q of World Monitor
      Trust III ("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 Trust as of, and for, the periods presented in this
      quarterly report;

4.    The Trust'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 Trust and
      we 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
            Trust, 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 Trust's disclosure controls and
            procedures and presented in this 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 Trust's internal
            control over financial reporting that occurred during the Trust's
            most recent fiscal quarter (the Trust's fourth quarter in the case
            of an annual report) that has materially affected, or is
            reasonably likely to materially affect, the Trust's internal
            control over financial reporting; and

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

      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 Trust's ability to
            record, process, summarize and report financial information; and

      b)    any fraud, whether or not material, that involves management or
            other employees who have a significant role in the Trust's
            internal control over financial reporting.

Date:  May 16, 2005                          /s/ Kenneth A. Shewer
                                             -----------------------------------
                                             Kenneth A. Shewer
                                             Co-Chief Executive Officer

                                     E-2