WORLD MONITOR TRUST III – SERIES J 10-K 

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, Jim Parrish, 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 Annual Report on Form 10-K of World Monitor Trust III – Series J for the period January 1, 2014 to December 31, 2014, as filed with the Securities and Exchange Commission on the date hereof (the “Annual 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 Annual Report fairly presents, in all material respects, the financial condition and results of operations of the Registrant.

	/s/ Jim Parrish
Name:	Jim Parrish
Title:	President
	(Principal Executive Officer)
	Kenmar Preferred Investments, LLC
	Managing Owner of
	World Monitor Trust III – Series J
Date: March 17, 2015