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, hereby certifies pursuant to 18 U.S.C. 1350, as adopted pursuant to Section 906 of the Sarbanes-Oxley Act of 2002, that:

(1) The Quarterly Report on Form 10-Q of World Monitor Trust III – Series J for the period ended September 30, 2012, 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 Registrant.

/s/ Kenneth A. Shewer
Name:	Kenneth A. Shewer
Title:	Co-Chief Executive Officer
	(Principal Executive Officer)
	Kenmar Preferred Investments, L.P.,
	Managing Owner of
	World Monitor Trust III – Series J
Date:	November 14, 2012