Exhibit 32.1

CERTIFICATION FURNISHED PURSUANT TO 18 U.S.C. SECTION 1350,
AS ADOPTED PURSUANT TO SECTION 906

OF THE SARBANES-OXLEY ACT OF 2002

In connection with thisAmendment No. 1 to Annual Report on Form 10-K/Aof SWS Group, Inc. (the "Company") for the fiscal year ended June 30,  2014as filed with the Securities and Exchange Commission on the date hereof (the "Report"), I, James H. Ross, Chief Executive Officer of the Company, certify, pursuant to 18 U.S.C. § 1350, as adopted pursuant to Section 906 of the Sarbanes-Oxley Act of 2002, to my knowledge 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 Company.

Date: September 26, 2014	/S/ James H. Ross
	James H. Ross
	President and Chief Executive Officer

The foregoing certification is being furnished as an exhibit to the Reportpursuant to Item 601(b)(32) of Regulation S-K and Section 906 of the Sarbanes-Oxley Act of 2002 (subsections (a) and (b) of Section 1350, Chapter 63 of Title 18, United States Code) and, accordingly, is not being filed as part of the Reportfor purposes of Section 18 of the Securities Exchange Act of 1934, as amended, and is not incorporated by reference into any filing of the Company, whether made before or after the date hereof, regardless of any general incorporation language in such filing.