Form 6-K SECURITIES AND EXCHANGE COMMISSION Washington, D.C. 20549 Report of Foreign Private Issuer Pursuant to Rule 13a-16 or 15d-16 of the Securities Exchange Act of 1934 For the month of August, 2004 CONVERIUM HOLDING AG ----------------------------------------------- (Translation of registrant's name into English) Baarerstrasse 8 CH-6300 Zug Switzerland ---------------------------------------- (Address of principal executive offices) Indicate by check mark whether the registrant files or will file annual reports under cover Form 20-F or Form 40-F. Form 20-F X Form 40-F ----- ----- Indicate by check mark whether the registrant by furnishing the information contained in this Form is also thereby furnishing the information to the Commission pursuant to Rule 12g3-2(b) under the Securities Exchange Act of 1934. Yes No X ----- ----- If "Yes" is marked, indicate the file number assigned to the registrant in connection with Rule 12g3-2(b): 82- Not Applicable Capital Group Companies Inc. adjusts its holding in Converium shares from 4.05% to 5.34% (held and managed in various funds) Converium Holding Ltd has been notified that Capital Group Companies Inc., 333 South Hope Street, Los Angeles, CA, 90071-1406, USA, has increased as a group its holding on behalf of funds managed by Capital Research and Management Company, 333 South Hope Street, Los Angeles, CA, USA, and clients of Capital Guardian Trust Company, 11100 Santa Monica Blvd 15th Floor, Los Angeles, CA, USA, Capital International Ltd., 25 Bedford St., London, England, Capital International Inc., 11100 Santa Monica Blvd 15th Floor, Los Angeles, CA, USA, and Capital International S.A., 3 Place des Bergues, 1201 Geneva, Switzerland, to 2,137,095 registered shares in Converium Holding Ltd, Zug. This corresponds to 5.34% of Converium's registered shares. None of these entities represented by Capital Group Companies Inc. individually holds shares of 5% or more of Converium's registered share capital. Zug, August 10, 2004 Contacts: Zuzana Drozd Head of Investor Relations zuzana.drozd@converium.com +41 (0)1 639 91 20 Michael Schiendorfer Media Relations Manager michael.Schiendorfer@converium.com +41 (0)1 639 96 57 www.converium.com SIGNATURES Pursuant to the requirements of the Securities Exchange Act of 1934, the registrant has duly caused this report to be signed on its behalf by the undersigned, thereunto duly authorized. CONVERIUM HOLDING AG By:/s/ Dirk Lohmann Name: Dirk Lohmann Title: CEO By:/s/ Christian Felderer Name: Christian Felderer Title: Group General Counsel Date: August 13, 2004 Monthly disclosure of equity securities newly created from conditional capital