Exhibit 13.1

Certification

Pursuant to 18 U.S.C. §1350, the undersigned officer of Nomura Holdings, Inc. (the “Company”) hereby certifies, to such officer’s knowledge, that the Company’s annual report on Form 20-F for the year ended March 31, 2004 (the “Report”) fully complies with the requirements of Section 13(a) or 15(d), as applicable, of the Securities Exchange Act of 1934 and that the information contained in the Report fairly presents, in all material respects, the financial condition and results of operation of the Company.

Date: June 25, 2004

/s/    NOBUYUKI KOGA        

Nobuyuki Koga

President and Chief Executive Officer