EXHIBIT 32.1

CERTIFICATION PURSUANT TO

18 U.S.C. SECTION 1350

AS ADOPTED PURSUANT TO

SECTION 906 OF THE SARBANES-OXLEY ACT OF 2002

The undersigned, Kenneth A. Shewer, Co-Chief Executive Officer of the Managing Owner, Preferred Investment Solutions Corp. (the “Managing Owner”), of World Monitor Trust III – Series H (“Series H”), hereby certifies pursuant to 18 U.S.C. 1350, as adopted pursuant to Section 906 of the Sarbanes-Oxley Act of 2002, that:

(1)

Series H’s Quarterly Report on Form 10-Q for the period ended June 30, 2006, as filed with the Securities and Exchange Commission on the date hereof (the “Quarterly Report”), fully complies with the requirements of Section 13(a) or 15(d) of the Securities Exchange Act of 1934; and

(2)

The information contained in the Quarterly Report fairly presents, in all material respects, the financial condition and results of operations of Series H.

/s/ Kenneth A. Shewer

Kenneth A. Shewer

Co-Chief Executive Officer

August 14, 2006

World Monitor Trust III - Series H 10-Q