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

In connection with the Annual Report of Diversified Multi-Advisor Futures Fund L.P. II (the “Partnership”) on Form 10-K for the year ended December 31, 2011 as filed with the Securities and Exchange Commission on the date hereof (the “Report”), I, Walter Davis, President and Director of Ceres Managed Futures LLC, certify, pursuant to 18 U.S.C. § 1350, as adopted pursuant to § 906 of the Sarbanes-Oxley Act of 2002, that:

(1) The 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 Report fairly presents, in all material respects, the financial condition and results of operations of the Partnership.

Date: March 30, 2012