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, Chief Executive Officer of the managing owner as of October 1, 2004, Preferred Investment Solutions Corp., of World Monitor Trust II—Series D (“Series D”), 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 D’s Quarterly Report on Form 10-Q for the period ending September 24, 2004, 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 D.

/s/ Kenneth A. Shewer

Kenneth A. Shewer

Chief Executive Officer
of Preferred Investment Solutions Corp.,
the managing owner as of October 1, 2004

November 8, 2004