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 period ending June 30, 2004

CONVERIUM HOLDING AG

Baarerstrasse 8

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 þ          Form 40-F o

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 o          No þ

If “Yes” is marked, indicate the file number assigned to the registrant in connection with Rule 12g3-2(b): 82-Not Applicable

Half Year Report 2004

Investor Information

Transfer Agent & Registrar
For American Depository Shares (ADS) traded on the New York Stock Exchange:

The Bank of New York
Corporate Trust Office
101 Barclay Street
New York, NY 10286
USA
Telephone +1 646 885 3300

Auditors
PricewaterhouseCoopers Ltd
Stampfenbachstrasse 73
P.O. Box 634
8035 Zurich
Switzerland
Telephone +41 1 630 1111
Fax +41 1 630 1115

Stock Trading

Converium Holding AG common shares are traded on the SWX Swiss Exchange under the trading symbol CHRN and as ADS (0.5 of a common share) on the New York Stock Exchange under the trading symbol CHR.

First listed

December 11, 2001 SWX Swiss Exchange and New York Stock Exchange

Investor Relations Contact
Zuzana Drozd
Head of Investor Relations
Phone +41 1 639 9120
E-mail zuzana.drozd@converium.com

Contents

Financial highlights

2

3

Letter from the Chief Executive Officer

Dear shareholders,

Converium disappointed shareholders and the markets on July 20th by announcing the need to increase reserves substantially. In this letter I will explain what happened, and outline the impact on your company. I will present details of the changes we have and will make at Converium to ensure that such surprises do not happen again, and of the steps we intend to take to recover both the financial strength that has been lost and the confidence which, understandably, has been eroded.

Trends reversed

The reserve strengthening covers adverse development of casualty business written in the United States during the soft market years from 1997 to 2001. Claims development on this business exceeded expectations in the first quarter of 2004. In the second quarter of 2004, the notifications continued and accelerated.

With the sustained increase in claims notifications, I launched a comprehensive review of all Converium’s business of North American origin, including some underwritten in Zurich. This resulted in a reserve increase of US$385 million, which in turn triggered impairments of Deferred Tax Assets and Goodwill of US$364 million; both impairments affect the balance sheet of Converium Reinsurance (North America) Inc. The reserve strengthening, the impairments of intangible balance sheet positions, and additional changes in Converium’s equity resulted in a reduction of Converium’s total tangible equity of US$ 409.4 million since year-end 2003.

Our effort to finally measure the scope of this problem was extensive. I personally led an investigation of over 400 contracts originating from this problematic era, with the assistance of Chief Technical Officer Gary Prestia and staff from his newly formed Underwriting Technical Services team. This was in addition to targeted underwriting reviews, claims audits at our clients’ offices and additional actuarial studies for specific lines of business and clients. Based on the information we gathered during these reviews and on the current level of notifications, the additional reserve strengthening aims to put an end to Converium’s reserving saga, and to restore the clean balance sheet we aimed to set out with. As part of this review and to assist with its assessment, Converium has commissioned a leading firm of consulting actuaries to conduct an external actuarial study of the company’s reserves held in respect of the Zurich and New York businesses, that will be completed before the end of August.

Much has been done since our Initial Public Offering to ensure that such shocks do not happen again. New underwriting and pricing standards were introduced and significant staff changes were made. Additionally, Converium’s new organizational structure, introduced last October, with the new positions of Chief Risk Officer and Chief Technical Officer has contributed to a more robust environment of internal controls. Meanwhile, Converium’s concurrent move away from regional profit centers to global management structures has created greater accountability and transparency by eliminating variations in the use of common tools. Behind that, the reorganization has removed local thinking bias in favor of a consistent, objective global approach to risk management. Finally, we will create a dedicated run-off unit to actively manage this historical business.

The way forward

Following a loss of the magnitude Converium reports in our first half, the way forward cannot be business-as-usual. We will build on the steps taken since Converium’s Initial Public Offering to ensure consistent underwriting quality throughout the global operation. Our extensive file review presented several lessons which, from now on, will be incorporated into our underwriting guidelines and philosophy, as well as into our reserving approach. At the request of the Board, I will be actively engaged in the underwriting process for North American business. I have initiated a dialogue with our underwriting officers in the United States to discuss specific elements of our client and product strategy, to ensure that we avoid repeating past mistakes.

Meanwhile we will take steps to strengthen Converium’s balance sheet. Your management is actively working on various options to rebuild capital strength; these include curtailing underwriting of certain capital-intensive lines of business. Although a drastic downsizing is not in my plans, we will reduce our exposure in the US to so-called national account writers of umbrella liability and excess and surplus lines casualty risks, as well as heavy commercial auto written on an excess basis. Our directors’ and officers’ underwriting will also shrink. This is not necessarily the business that caused the current situation; however, we have begun to observe a trend towards weaker terms and conditions that, if continued, is concerning. As these lines are known to be volatile, they are capital-intensive. Reducing our writings would therefore free up risk capital.

4

Further steps to rebuild Converium’s capital strength may include the purchase of additional reinsurance. Such cover would also improve the solvency ratio by freeing up capital currently allocated to risk. On the asset side, we will minimize risk by reducing our exposure to equities and to interest rate and duration risks.

In order to restore Converium’s competitive position and to allow us to execute our strategy, we may also raise new capital. Further details of our capital planning measures will follow the completion of the reserving study.

Good business

I believe that our continuing strategy is sound and profitable. Although serious legacy issues have masked it, the performance of our recent business has met with expectations. Gross written premium grew at 9.0% in the first six months of the year, and the non-life combined ratio, excluding the reserve strengthening, declined by 4.1 percentage points compared to the first half of 2003. Growth has slowed slightly, reflecting market conditions. Pricing has eased in airline and catastrophe lines, but Converium has not relaxed its rigorous pricing and profitability standards. As a result, underwriters have elected to decline potential business that failed to meet these high standards.

In Standard Property & Casualty Reinsurance, gross written premiums grew by 7.5% and net earned premiums grew by 9.3% as last year’s strong growth flowed through. The combined ratio for the half year was 106.1%, compared to 92.0% in the prior year period, however 2004 reflects US$ 96.0 million worth of reserve strengthening in the second quarter (US$ 106.1 million in the first half), primarily for general third party liability business, which added 12.3 loss ratio points to the combined ratio. The current in-force business achieved a combined ratio of 93.8%, in line with our expectations.

Gross written premiums in Specialty Lines grew by 8.3% and net earned premiums grew by 11.3%. This segment was most affected by the reserve strengthening, primarily for US casualty long-tail risks including professional liability, umbrella, and excess and surplus lines. Here the combined ratio for the first half was 129.7%, with reserve strengthening of US$ 288.7 million in the second quarter (US$ 321.6 million in the first half), adding 35.1 loss ratio points. Without it the combined ratio is 94.6%, which is also in line with expectations. Strong growth in the Life and Health Reinsurance segment saw gross written premiums rise by 18.8% to US$ 264.7 million, resulting in segment income of US$ 5.9 million. This business is once again a positive contributor to Converium’s overall operating performance.

Alongside successful bottom-line underwriting, invested assets performed very much in line with our benchmarks. The overall interest rate environment has had an impact, as did the need to mark to market our fixed income instruments, but performance was sound. Notwithstanding the impact of adverse reserve development, our current underlying underwriting and investment performance is very profitable for Converium. I am confident that prior years’ legacy issues have been adequately addressed and as such I expect a strong operating performance in subsequent periods (although as always, a major catastrophic event could change this for Converium or any reinsurer).

Of course the developments Converium reports today are a great disappointment to me. They raise challenges for all of us, but these are not insurmountable. We are doing everything within our power to right the ship, and will continue to do so. We will demonstrate to our customers and partners that these issues have been fully addressed.

I would especially like to thank our shareholders for their patience and support as we pass through this painful and unexpected period. I remain confident that our platform is strong, and with the past resolutely addressed, our opportunities plentiful.

Yours sincerely,

Dirk Lohmann
Chief Executive Officer

5

The Converium share

The Converium share and ADS

In the first half of 2004, the Converium share moved within a narrow band of the Bloomberg European Insurance Index. In contrast, the Converium ADS underperformed the Bloomberg US Insurance Index in the same period.

The terrorist attack in Madrid, Spain in March 2004 impacted industry share performance. In addition to that, the stock markets, with insurance stocks particularly affected, have been negatively impacted by the prospect of rising interest rates.

After the ad-hoc announcement on July 20, 2004, when Converium published information on their pre-IPO legacy issues, the Converium share and ADS decreased by 46.4% and 44.4%, respectively. On July 23, 2004 the prices of the Converium share and ADS were CHF 27.30 and US$ 10.93, respectively representing a decline of 56%, respectively since the ad-hoc announcement.

6

Key share data for 2004

Major shareholders

In accordance with the notification requirements as set by the SWX Swiss Exchange, the following significant share holdings were notified to Converium Holding AG as of June 30, 2004:

Only one shareholder, a fund managed by Fidelity International Limited (European Growth SICAV Luxembourg: 6.60%), is registered in Converium’s share register with an individual shareholding exceeding the 5% threshold specified in article 663c of the Swiss Code of Obligations.

Fidelity is an investment advisor, which provides investment advisory and management services to non-US investment companies, trusts and institutions. Wellington is an investment advisor and portfolio manager with voting authority for 47 clients, none of which has an individual shareholding in excess of 5%. Converium does not hold any interlocking shareholdings with any other joint-stock companies.

7

Management’s discussion and analysis
of financial condition and results of operations

The following discussion and analysis should be read in conjunction with our financial statements, including the related notes to those financial statements. This discussion contains forward-looking statements that involve risks and uncertainties and actual results may differ materially from the results described or implied by these forward-looking statements. See “Cautionary note regarding forward-looking statements.”

Overview

Converium Holding AG and subsidiaries (“Converium”) is a leading global reinsurer whose business operations are recognized for innovation, professionalism and service. We believe we are accepted as a professional lead reinsurer for all major lines of non-life and life reinsurance. We actively seek to create innovative and efficient reinsurance solutions to complement our clients’ business plans and needs. We focus on core underwriting skills and on developing close client relationships while honoring our and our clients’ relationships with brokers. We have the ability to cover risks globally and to provide meaningful capacity worldwide.

During the second quarter of 2004, Converium has taken actions that resulted in measurable effects on its financial results. These actions include the net strengthening of prior years’ loss reserves (US$ 384.7 million), the establishment of a full valuation allowance against its net deferred tax assets related to its North American operations (second quarter expense of US$ 269.8 million) and an impairment of goodwill (US$ 94.0 million). See “Second Quarter Developments”.

Results of operations

Net income for the three and six months ended June 30, 2004 declined compared to the same periods in 2003. The decline is primarily due to the net strengthening of prior years’ loss reserves, and a related increase in income tax expense due to the establishment of a full valuation allowance against the net deferred tax assets from our North American operations and an impairment of goodwill.

We reported a decrease in pre-tax operating results (defined as pre-tax income or loss excluding pre-tax net realized capital gains or losses and impairment of goodwill) for the three and six months ended June 30, 2004 as compared to the same period in 2003. We use pre-tax operating results to measure performance, as this measure focuses on the underlying fundamentals of our operations without the influence of realized gains and losses from the sale of investments, or other non-operating items such as goodwill impairment.

For the three months ended June 30, 2004, gross premiums written increased 8.3%, net premiums written increased 5.5% and net premiums earned increased 10.7%. For the six months ended June 30, 2004, gross premiums written increased 9.0%, net premiums written increased 7.8% and net premiums earned increased 11.5%. See “Reinsurance results” and “Business Development”.

Our non-life combined ratio was 140.5% and 118.3% for the three and six months ended June 30, 2004, respectively, as compared to 99.4% and 98.7% for the same periods of 2003. Reserve actions in 2004 increased the combined ratio by 43.3 points for the three months ended June 30, 2004 and 24.1 points for the six months ended June 30, 2004.

We had net realized capital gains of US$ 12.5 million and US$ 15.8 million for the three months ended June 30, 2004 and 2003, respectively. In the second quarter of 2004, we realized capital gains of US$ 16.5 million from the sale of certain equity investments. In the second quarter of 2003, we realized capital gains of US$ 16.0 million on sales of fixed income investments in order to reduce the duration of our bond portfolio as trends of declining interest rates continued. For the three months ended June 30, 2004, US$ 1.5 million in impairment charges were recorded, compared to US$ 6.1 million for the same period of 2003.

We had net realized capital gains of US$ 21.7 million and US$ 7.5 million for the six months ended June 30, 2004 and 2003, respectively. For the six months ended June 30, 2004, US$ 2.6 million in impairment charges were recorded, compared to US$ 21.9 million for the same period of 2003. Included in the impairment charges in the six months ended June 30, 2003 were US$ 19.5 million related to our equity securities portfolio and US$ 2.4 million related to our real estate portfolio.

8

Management’s discussion and analysis
of financial condition and results of operations (continued)

Second Quarter Developments

In the second quarter of 2004, Converium recorded pre-tax charges of US$ 748.5 million, as described below.

Reserve development

The following table presents the net adverse (favorable) reserve development for each of Converium’s non-life segments:

Converium has experienced significant adverse development in its US casualty reinsurance lines for the last several years. Since 2001, Converium has recorded a total of US$ 668.5 million of additional provisions on its non-life business (2001: US$ 123.6 million; 2002: US$ 148.5 million; 2003: US$ –31.3 million; and first half of 2004: US$ 427.7 million). In 2003, the positive development of US$ 31.3 million consisted of positive development on property lines (US$ 113.5 million) and aviation and space (US$ 102.2 million), offset by adverse development on workers’ compensation and professional liability and other special liability lines (US$ 120.3 million) and the motor and general third party liability lines (US$ 64.1 million). The reserve releases in 2003 were primarily from the 2002 underwriting year, while the US business written in 1997 to 2001 mostly saw continued strengthening.

On April 29, 2004, Converium announced that first quarter reported losses from prior year US casualty business had exceeded expected loss emergence. In that release, Converium also stated the expectation that the volatility of longer-tail risks is likely to persist for some time. In the first quarter of 2004, the continuing reserve volatility of old underwriting years resulted in strengthening of prior years’ loss reserves of US$ 43.0 million, consisting of US$ 10.1 million in the Standard Property & Casualty Reinsurance segment (primarily from the Western European motor book) and US$ 32.9 million in the Specialty Lines segment (primarily from the US professional liability and other special liability lines).

This adverse loss reporting trend has continued and accelerated in the second quarter of 2004. In response to the loss development observed in the first and second quarters of 2004, Converium has initiated additional reviews of its US business from an integrated underwriting, claims and actuarial perspective in order to examine the adequacy of prior years’ provisions. The Chief Executive Officer and Chief Technical Officer have conducted underwriting reviews on treaty accounts and lines of business with material loss experience to supplement the claims audits and actuarial reserve reviews that Converium conducts in its ordinary course of business. Through the date of this report, it is performing additional claims audits and actuarial reserve reviews of the largest and most significant ceding companies in order to obtain more information to refine the estimate of the ultimate loss reserves for this book of business. These claims audits and actuarial reserve reviews will continue into the third quarter of 2004. As part of this review and to assist with its assessment, Converium commissioned a leading firm of consulting actuaries to conduct an external actuarial study of the company’s reserves held in respect of the Zurich and New York businesses.

When deriving its estimates of ultimate losses and its selection of loss development patterns as of June 30, 2004, Converium has reflected the accelerated claims development in the more recent periods. Based upon Converium’s ongoing analysis to date, in the second quarter of 2004, Converium recorded strengthening of prior years’ loss reserves of US$ 384.7 million, consisting of US$ 96.0 million in the Standard Property & Casualty Reinsurance segment and US$ 288.7 million in the Specialty Lines segment. In the Standard Property & Casualty Reinsurance segment, the reserve strengthening primarily related to general third party liability lines in the US (US$ 99.3 million). In the Specialty Lines segment, the reserve strengthening arose primarily from the professional liability and other special liability lines, in particular umbrella, professional liability and excess & surplus lines of business in the US (US$ 265.2 million), related to accident years 1997 through 2001.

Based upon information obtained from Converium’s continuing analysis, including the results of the external actuarial reserve study, and the completion of the claims audits, Converium will update its estimate of its loss reserve position and potential loss exposure and, if the new information indicates the need for further adjustment, it will be recorded in the third quarter of 2004. Based upon the information currently available, Converium does not expect further material strengthening of its loss reserve position.

Income taxes

Converium’s consolidated income tax expense for the three months ended June 30, 2004 reflects an additional expense of US$ 269.8 million, related to the establishment of a full valuation allowance against the net deferred income tax balances previously carried at Converium Reinsurance (North America) Inc. (“CRNA”). CRNA is the legal entity where the majority of the reserve strengthening has occurred.

9

Management’s discussion and analysis
of financial condition and results of operations (continued)

As required under SFAS No. 109, “Accounting for Income Taxes”, Converium is required to assess if it is more likely than not that some or all of the net deferred tax assets will not be realized. In making this assessment, reference is made to, among other things, historical losses. Therefore, a full valuation allowance has been established against CRNA’s net deferred tax assets as of June 30, 2004. CRNA may offset future taxable income against the existing net operating loss carryforwards, resulting in no US federal tax expense on such income until such time as the net operating losses are utilized or expire.

As of June 30, 2004, Converium’s valuation allowance was US$ 455.6 million, comprising net operating loss carryforwards (US$ 313.1 million), loss reserve discount (US$ 133.9 million), and other temporary differences, net (US$ 8.6 million). As of December 31, 2003, the valuation allowance was US$ 47.9 million, all of which related to net operating loss carryforwards.

As of June 30, 2004, Converium had total net operating loss carryforwards of US$ 959.1 million available to offset future taxable income of certain branches and subsidiaries. The majority of these net operating loss carryforwards relate to CRNA and expire in the years 2020 through 2024.

Converium will continue to monitor its tax position and reassess the need for a full valuation allowance on its net deferred tax assets on a periodic basis. Realization of the deferred tax asset related to net operating loss carryforwards is dependent upon generating sufficient taxable income within specified future periods.

Goodwill and other intangible assets

SFAS No. 142, “Goodwill and Other Intangible Assets”, requires impairment testing of goodwill annually or more regularly if any event or change in business circumstances occurs which would indicate that the carrying value of goodwill may be impaired. Due to the reserving actions taken in the second quarter of 2004 in respect of prior year development in the Specialty Lines segment’s business written in North America, and a subsequent decision to take a full valuation allowance against the net deferred tax asset at Converium Reinsurance (North America) Inc., a goodwill impairment test has been conducted to assess the fair value of the reporting units at that date. As a result of this assessment, an impairment charge of US$ 94.0 million has been recorded in the second quarter of 2004.

SFAS No. 142 also requires that useful lives for intangible assets other than goodwill be reassessed and the remaining amortization periods be adjusted accordingly. There are no intangible assets recorded on the Converium Reinsurance (North America) Inc. balance sheet as of June 30, 2004 in respect of any business segment or reporting unit; therefore there is no requirement to perform impairment testing on intangible assets.

The remaining balance of goodwill and other intangible assets as of June 30, 2004 was US$ 76.8 million, which relates to Converium AG’s strategic investments in Global Aerospace Underwriting Managers Limited (“GAUM”) and MDU Services Ltd. As of June 30, 2004, both of these companies have continued to perform in line with management’s expectations.

Ratings and regulatory issues

On July 20, 2004, Standard & Poor’s Ratings Services lowered its long-term counterparty credit and insurer financial strength ratings on Converium AG and its main operating subsidiaries (collectively referred to as Converium) to “A–” from “A”. In addition, Standard & Poor’s lowered its long-term counterparty credit and senior unsecured debt ratings on Converium Holdings (North America) Inc. to “BBB–” from “BBB”, and junior subordinated debt rating on Converium Finance S.A. to “BBB” from “BBB+”. At the same time, all ratings were placed on CreditWatch with negative implications. Standard & Poor’s will also reassess the status (currently core) of Converium Reinsurance (North America) Inc. in the Converium Group. This could result in a lowering of the rating on Converium Reinsurance (North America) Inc. below that of the other core companies.

Also, on July 20, 2004, A.M. Best downgraded the financial strength ratings of Converium AG and its rated core subsidiaries (collectively referred to as Converium) to “A–” from “A”. At the same time, it downgraded all issuer credit ratings and related debt issues and placed all ratings under review with negative implications. In addition, A.M. Best is reviewing the core status of Converium Reinsurance (North America) Inc. and Converium Insurance (North America) Inc.

Converium is fully committed to maintaining a strong capitalization that enables us to continue to execute our strategy. In order to achieve this objective, Converium is currently exploring all options. Converium will specify the full set of capital management measures once the external actuarial reserve study is completed.

Converium has reviewed its contracts for implications of a ratings downgrade. Based upon a preliminary analysis, the significant majority of its contracts that contain a ratings provision are triggered at a rating level below “A–”. In addition, the Company is reviewing its contracts for implications of decreases to certain statutory surplus levels.

10

Management’s discussion and analysis
of financial condition and results of operations (continued)

Ratings and surplus triggers typically give rise to a right of termination in favor of the cedent that allows the cedent to terminate the contract on a prospective basis from the date of termination. However, as a commercial matter, the cedent and reinsurer generally renegotiate the terms of the contract. In renegotiating the contract terms, cedents will typically require the reinsurer to post collateral to secure the obligations under the contract.

Reinsurance results

Net premiums written grew in the three and six months ended June 30, 2004 over the same periods in 2003, and was largely due to the market conditions and new client relationships in certain key markets. For the six months ended June 30, 2004, Standard Property & Casualty Reinsurance grew by US$ 47.8 million or 5.1%, Specialty Lines grew by US$ 84.7 million or 9.1%, and Life & Health Reinsurance grew by US$ 31.0 million or 14.6%. We retained 93.2% and 94.2% of our gross premiums written for the six months ended June 30, 2004 and 2003, respectively. See “Business Development” for further information by line of business.

For the six months ended June 30, 2004, based on stable exchange rates, gross premiums written increased by 3.8%, net premiums written increased by 2.6%, and net premiums earned increased by 6.3%.

Net premiums earned for the three and six months ended June 30, 2004 increased at a higher rate compared to the corresponding net premiums written due to a large proportion of business written on January 1 in the German and Austrian market, that is earned throughout the year.

Our losses, loss adjustment expenses and life benefits incurred and non-life loss ratio increased for the three and six months ended June 30, 2004 as compared to the same periods of 2003, mainly due to reserve development as described above.

In the first half of 2003, there was reserve strengthening for the Guaranteed Minimum Death Benefit (GMDB) business in the Life & Health Reinsurance segment, which negatively impacted our results by US$ 12.5 million, while there was no action required in the first half of 2004.

Our net reserves for the September 11th terrorist attacks are capped at US$ 289.2 million by Zurich Financial Services.

11

Management’s discussion and analysis
of financial condition and results of operations (continued)

Underwriting acquisition costs primarily relate to commissions on treaty and individual risk business. Our underwriting acquisition costs increased for the three months and six months ended June 30, 2004 as compared to the same periods in 2003. This increase is mainly related to the growth in earned premiums. During 2003, there was new business production in the Continental European markets which was produced on a direct basis as opposed to through brokers, which resulted in lower underwriting acquisition costs in 2003 as compared to 2004.

Operating and administration expenses increased for the three months and six months ended June 30, 2004 over the same periods in 2003 due to increased expenditures to support the growth in operations, and the weakening of the US dollar. As a result of our premium growth and strong expense management, the non-life administration expense ratio remained stable for the three months ended June 30, 2004 and declined by 0.2 points for the first half of 2004 as compared to 2003.

Investment results

Investment results are an important part of our overall profitability. Our net investment income increased for the three months and six months ended June 30, 2004 as compared to the same periods of 2003. The increase largely resulted from growth in invested assets over 2003, particularly in our fixed maturities portfolio, as well as income received from the transition of a fixed income bond fund to a direct fixed income investment portfolio. The decline in income from the Funds Withheld Asset is due to the declining asset balance. See “Funds Withheld Asset”.

Our average annualized net investment income yield (pre-tax) was 3.8% for both the three and six months ended June 30, 2004 as compared to 3.9% and 3.6% for the same periods of 2003.

Our average annualized total investment income yield (pre-tax) was 4.4% and 4.3% for the three and six months ended June 30, 2004, respectively, as compared to 4.8% and 3.8% for the same periods of 2003. The total investment income yields were positively impacted by the results of our equity portfolio in the first half of 2004 and the results of our bond portfolio in 2003.

Our average annualized total investment return (pre-tax) was (2.6)% and 2.4% for the three and six months ended June 30, 2004 as compared to 10.6% and 6.9% for the same periods of 2003. The return for the three months ended June 30, 2004 was negatively affected by changes in net unrealized gain positions on bonds of US$ 123.3 million resulting from an interest rate increase during the quarter, whereas the impact was opposite for the three months ended June 30, 2003, as interest rate declines increased the net unrealized capital gain positions. The interest rate movements also explain the difference between the average annualized total investment return (pre-tax) for the six months ended June 30, 2004 compared to the six months ended June 30, 2003.

12

Management’s discussion and analysis
of financial condition and results of operations (continued)

Other

Other income for the three months ended June 30, 2004 was US$ 3.0 million as compared to nil for the same period of 2003. Other income for the six months ended June 30, 2004 was US$ 2.9 million as compared to a loss of US$ 4.4 million for the same period of 2003. Other income (loss) includes interest income on reinsurance deposits, interest expense on funds held under reinsurance contracts, fee income, write-off of uncollectible balances and results from private equity funds.

Interest expense remained relatively stable for the three and six months ended June 30, 2004 as compared to the same periods in 2003.

Impairment of goodwill was US$ 94.0 million for the three and six months ended June 30, 2004. See “Second Quarter Developments”.

Converium’s consolidated income tax expense for the three and six months ended June 30, 2004 reflects an expense of US$ 269.8 million, related to the establishment of a full valuation allowance against the net deferred income tax balances carried at CRNA. See “Second Quarter Developments”.

Business Development

Converium’s business is organized around three operating segments: Standard Property & Casualty Reinsurance, Specialty Lines and Life & Health Reinsurance, which are based principally on global lines of business. In addition to the three segments’ financial results, the Corporate Center carries certain administration expenses, such as costs of the Board of Directors, the Global Executive Committee, and other global functions.

Our principal lines of non-life reinsurance include general third party liability, motor, personal accident, property, agribusiness, aviation and space, credit and surety, engineering, marine and energy, professional liability and other special liability and workers’ compensation. The principal life reinsurance products are ordinary life and disability reinsurance, including quota share, surplus coverage and financing contracts, and accident and health.

Converium’s financial results for the first half of 2004 have been considerably affected by the recording of additional net strengthening of prior years’ loss reserves (US$ 427.7 million). The following table compares Converium’s segment results for the three months and six months ended June 30, 2004 and 2003 and reconciles segment results to (loss) income before taxes:

13

Management’s discussion and analysis
of financial condition and results of operations (continued)

Standard Property & Casualty Reinsurance

Standard Property & Casualty Reinsurance reported a segment loss for the three months ended June 30, 2004 as compared to segment income for the same period in 2003. For the six months ended June 30, 2004, Standard Property & Casualty Reinsurance reported a decrease in segment income of US$ 100.9 million as compared to the same period in 2003. The decrease in 2004 was primarily attributable to the following:

For the six months ended June 30, 2004, gross premiums written increased 7.5% to US$ 1,076.1 million, net premiums written increased 5.1% to US$ 988.5 million and net premiums earned increased 9.3% to US$ 860.2 million.

For the six months ended June 30, 2004, net premiums written growth in the Standard Property & Casualty Reinsurance segment by line of business included:

These increases were offset by a decrease in net written premiums within the Property line of business. The Property line of business decreased by 12.3% or US$ 53.0 million to US$ 377.2 million, which was primarily driven by the softening of property rates and a consequent non-renewal of several large contracts in North America, and reduced premium writings with cedents in Asia and Latin America.

14

Management’s discussion and analysis
of financial condition and results of operations (continued)

Specialty Lines

Specialty Lines reported a segment loss for the three and six months ended June 30, 2004 as compared to segment income for the same periods in 2003. The segment loss in 2004 was primarily attributable to the following:

For the six months ended June 30, 2004, gross premiums written increased 8.3% to US$ 1,070.4 million, net premiums written increased 9.1% to US$ 1,015.6 million and net premiums earned increased 11.3% to US$ 916.9 million.

For the six months ended June 30, 2004, the Specialty Lines segment included net premiums written growth within:

These increases were offset by a decrease of US$ 66.9 million in net premiums written in the workers’ compensation line of business. This mainly resulted from lower premium accruals related to the 2003 underwriting year based on revised estimated premiums received from a large cedent who reports on a lag, as well as a decrease in run-off premiums from older underwriting years. In addition, there was a reduction of participation on premiums written through the involuntary market with one of our ceding companies.

15

Management’s discussion and analysis
of financial condition and results of operations (continued)

Life & Health Reinsurance

Life & Health Reinsurance reported a decrease in segment income for the three months ended June 30, 2004 as compared to the same period in 2003. Technical result for the three months ended June 30, 2004 was US$ 3.6 million compared to US$ 10.0 million for the same period in 2003. Technical result is defined as net premiums earned minus losses, loss adjustment expenses and life benefits minus underwriting acquisition costs plus technical interest. This decrease was primarily attributable to an increase in underwriting acquisition costs in 2004 as compared to 2003 due to the revision of profit commission accruals on North American Accident & Health business. In addition, there were increases in commissions related to premium growth in financing reinsurance transactions in Continental Europe.

Life & Health Reinsurance reported an increase in segment income for the six months ended June 30, 2004 as compared to the same period in 2003. Technical result increased from US$ 1.5 million to US$ 8.5 million for the same period. The increase in 2004 was primarily attributable to:

For the six months ended June 30, 2004, gross premiums written increased 18.8% to US$ 264.7 million, net premiums written increased 14.6% to US$ 243.3 million and net premiums earned increased 21.3% to US$ 225.8 million.

Corporate Center

The Corporate Center carries certain administration expenses, such as costs of the Board of Directors, the Global Executive Committee, and other global functions. The Corporate Center reported an increase in operating and administration expenses for the six months ended June 30, 2004 as compared to 2003. The increases primarily arose from expenditures to support the growth in operations, and the weakening of the US dollar.

16

Management’s discussion and analysis
of financial condition and results of operations (continued)

Financial Condition and Liquidity

Invested Assets

As of June 30, 2004, total invested assets (excluding cash and cash equivalents) were US$ 7.8 billion compared to US$ 7.5 billion as of December 31, 2003, an increase of US$ 317.5 million, or 4.2%. This increase is mainly due to the deployment of a substantial portion of our cash and cash equivalents balance, as well as operating cash flow, into fixed maturity securities during the second quarter of 2004, offset by a reduction in unrealized capital gains on our bond portfolio due to increasing interest rates during the second quarter of 2004.

Our asset mix, including cash and cash equivalents, consisted of the following at June 30, 2004 and December 31, 2003:

Our investments are managed mainly by external investment managers and their performance is measured against benchmarks. The table below presents our investments in the major managed portfolios, as well as the applicable benchmark and benchmark return for the second quarter of 2004. The balances at June 30, 2004 are shown in original currencies.

17

Management’s discussion and analysis
of financial condition and results of operations (continued)

Fixed Maturities

As of June 30, 2004, our fixed maturities portfolio, excluding the Funds Withheld Asset (described more fully below), had a carrying value of US$ 5.3 billion and represented 67.1% of total investment portfolio including cash and cash equivalents (84.4% including the Funds Withheld Asset). This represents an increase in carrying value of US$ 391.4 million, or 7.9%, from December 31, 2003. This increase is mainly due to the deployment of a substantial portion of our cash and cash equivalents balance, as well as operating cash flow, into fixed maturity securities during the second quarter of 2004, offset by a reduction in unrealized capital gains on our bond portfolio due to increasing interest rates during the second quarter of 2004.

We invest in government, agency and corporate fixed income securities of issuers from around the world that meet our liquidity and credit standards. We place an emphasis on investing in listed fixed income securities that we believe to be liquid.

The table below presents the composition of our fixed income securities portfolio, excluding short-term investments, based on carrying value by scheduled maturity.

Most of our fixed income securities are rated by Standard & Poor’s, Moody’s or similar rating agencies. As of June 30, 2004, approximately 99.8% of our fixed income securities portfolio was invested in securities rated A or better by these agencies and approximately 83.1% was invested in AAA/Aaa-rated securities.

The table below presents the composition of our fixed income securities portfolio by rating, using the lower of these ratings for any security where there is a split rating.

Equity Securities

As of June 30, 2004, our equity securities portfolio had a carrying value of US$ 862.4 million (including PSP Swiss Property AG). This represents an increase in carrying value of US$ 22.2 million, or 2.6%, from December 31, 2003. Equity securities were approximately 9.8% and 9.7% of our total investment portfolio as of June 30, 2004 and December 31, 2003, respectively, including cash and cash equivalents and excluding PSP Swiss Property AG.

Substantially our entire equity portfolio consists of listed securities held directly or through funds. All the equity portfolios are in developed markets. As experienced in recent years, the equity markets around the world can produce highly volatile and significantly varied results due to local and worldwide economic and political conditions.

Funds Withheld Asset

The transfer of certain historical reinsurance business to Converium was effected as of July 1, 2001 by means of the Quota Share Retrocession Agreement with Zurich Financial Services. In addition, on that date, the Funds Withheld Asset was established. Its initial balance was set to match the net balance of the liabilities, less the premium receivables (including outstanding collectible balances and reinsurance deposits) on the business to which the Quota Share Retrocession Agreement applies. As of June 30, 2004, the Funds Withheld Asset was US$ 1,370.5 million. The decrease of US$ 160.1 million over 2003 was substantially due to paid claims.

18

Management’s discussion and analysis
of financial condition and results of operations (continued)

The table below shows the distribution of the Funds Withheld Asset by currency as of June 30, 2004 and December 31, 2003.

In general, the Funds Withheld Asset is reduced by paid claims, profit commissions, amounts paid to maintain the retrocession agreements and other amounts paid on the business subject to the Quota Share Retrocession Agreement, and is increased by premiums (less premium refunds), salvage and subrogation, recoveries under retrocession agreements, profit commissions and other amounts received for the business subject to the Quota Share Retrocession Agreement. The balance of the Funds Withheld Asset will decrease over time. However, business historically written on the Zurich Insurance Company (“ZIC”) and Zurich International Bermuda Ltd (“ZIB”) balance sheets is being renewed and written on the Converium balance sheet. As a result, we will generate operating cash flow from the new and renewal business written by Converium, which will be invested in accordance with our approved investment guidelines. We do not expect the Funds Withheld Asset to have a material impact on our liquidity, as we will not be required to access our own liquidity sources for claims under the Quota Share Retrocession Agreement.

Short-term Investments

Our short-term investment portfolio includes investments in fixed-term deposits and fiduciary investments. These investments generally have maturities of between three months and one year. As of June 30, 2004, we had short-term investments with a carrying value of US$ 90.2 million, representing 1.1% of our total investment portfolio, including cash and cash equivalents. Short-term investments at December 31, 2003 were US$ 55.8 million or 0.7% of our total investment portfolio, including cash and cash equivalents.

Real Estate and Other Investments

At June 30, 2004, we had real estate held for investment of US$ 127.9 million, consisting primarily of investments in residential and commercial rental properties located in Switzerland. Our direct real estate portfolio represented 1.6% of our total investment portfolio, including cash and cash equivalents.

In addition to these properties, Converium owns a 4.9% participation in PSP Swiss Property AG (an indirect real estate investment, included in equity securities) with a market value of US $82.7 million as of June 30, 2004. The ownership in PSP Swiss Property AG decreased from 7.4% as of December 31, 2003, due to the merger of PSP Swiss Property AG with REG Real Estate Group, another Swiss real estate company, on April 5, 2004.

During the second quarter of 2004, we invested US$ 49.8 million in funds of hedge funds. This investment is included under the caption “Other investments” in the balance sheet.

Premiums Receivable

We had premiums receivable of US$ 2.4 billion at June 30, 2004 compared to US$ 2.0 billion at December 31, 2003, an increase of US$ 349.9 million, or 17.4%. This increase is due to premiums written in 2004. Premiums receivable include those currently due, as well as deferred premiums receivable, which is comprised primarily of accruals on premium balances which have not yet been reported and which are not contractually due to be paid until some time in the future. Current premiums receivable represented 9.4% and 9.1% of total premiums receivable at June 30, 2004 and December 31, 2003, respectively, and accrued premiums receivable represented 90.6% and 90.9%, respectively.

Reinsurance Assets

Retrocessional reinsurance arrangements generally do not relieve Converium from its direct obligations to its reinsureds. Thus, a credit exposure exists with respect to reinsurance ceded to the extent that any retrocessionaire is unable or unwilling to meet the obligations assumed under the retrocessional agreements. At June 30, 2004, Converium held US$ 557.6 million in collateral as security under related retrocessional agreements in the form of deposits, securities and/or letters of credit.

As of June 30, 2004, we had reinsurance recoverables from retrocessionaires of approximately US$ 1.6 billion on paid and unpaid losses and loss adjustment expenses, unearned premium reserves and future life benefits balances, compared to US$ 1.7 billion at December 31, 2003. Recoverables from retrocessionaires relating to contracts in arbitration were 5.8% of equity at June 30, 2004. Allowances of US$ 54.6 million have been recorded for estimated uncollectible receivables and reinsurance recoverables at June 30, 2004, compared to US$ 35.4 million at December 31, 2003.

19

Management’s discussion and analysis
of financial condition and results of operations (continued)

Deferred Income Taxes

As of June 30, 2004, deferred income tax assets were US$ 82.9 million as compared to US$ 345.1 million at December 31, 2003, a decrease of US$ 262.2 million. The decrease is due to a full valuation allowance established against CRNA’s net deferred income tax assets as of June 30, 2004. See “Second Quarter Developments”. As of June 30, 2004, deferred income tax liabilities were US$ 133.3 million as compared to US$ 158.3 million at December 31, 2003.

Loss and Loss Adjustment Expense Reserves

We had gross loss and loss adjustment expense (“LAE”) reserves of US$ 8.5 billion at June 30, 2004, compared to US$ 7.8 billion at December 31, 2003, an increase of US$ 678.0 million, or 8.6%. The increase in our reserve position is mainly attributable to the recording of US$ 427.7 million of strengthening of prior years’ loss reserves during the first half of 2004. See “Second Quarter Developments”. Loss and loss adjustment expense reserves, net of reinsurance recoverables for paid and unpaid losses were US$ 7.2 billion at June 30, 2004, compared to US$ 6.5 billion at December 31, 2003, an increase of US$ 771.7 million, or 12.0%. Gross reserves for future life benefits were US$ 498.9 million at June 30, 2004 compared to US$ 483.5 million at December 31, 2003.

Shareholders’ Equity

As of June 30, 2004, we had total shareholders’ equity of US$ 1,349.2 million (US$ 33.90 per share) compared to US$ 2,083.3 million (US$ 52.38 per share) as of December 31, 2003, a decrease of US$ 734.1 million (US$ 18.48 per share). This decrease is mainly comprised of the 2004 net loss of US$ 594.3 million, a reduction in net unrealized gains on investments, net of taxes of US$ 86.0 million, due to an increase in interest rates, and US$ 47.9 million of dividends to shareholders paid in the second quarter of 2004.

Converium is fully committed to maintaining a strong capitalization that enables us to continue to execute our strategy. In order to achieve this objective, Converium is currently exploring all options. Converium will specify the full set of capital management measures once the external actuarial reserve study is completed.

Cash Flows and Liquidity Sources

We held cash and cash equivalents of US$ 80.2 million as of June 30, 2004 compared to US$ 280.8 million as of December 31, 2003. Our cash position at June 30, 2004 decreased due to the deployment of a substantial portion of cash into investments in fixed maturity securities.

Our cash flows from operating activities result principally from premiums, collections on losses recoverable and investment income, net of paid losses, acquisition costs and underwriting expenses. Our cash provided by operating activities was US$ 442.5 million for the six months ended June 30, 2004 compared to US$ 572.6 million for the six months ended June 30, 2003, a decrease of US$ 130.1 million, or 22.7%. This decrease was due to the slowing down of new business growth as a result of active cycle management. This decrease also reflects increased claims payment activity.

The charges in the second quarter of 2004 for reserves, deferred income taxes, and impairment of goodwill do not have a current impact on cash provided by operating activities. However, future periods may be affected by higher claim payments on those reserves, offset by lower tax payments (due to net operating loss carry forwards).

20

Management’s discussion and analysis
of financial condition and results of operations (continued)

Critical Accounting Policies

Our consolidated financial statements include amounts that, either by their nature or due to requirements of accounting principles generally accepted in the United States (US GAAP), are determined using best estimates and assumptions. While we believe that the amounts included in our consolidated financial statements reflect our best judgment, actual amounts could ultimately differ materially from those currently presented in our consolidated financial statements. We believe the items that require the most subjective and complex estimates are:

More information regarding the estimates and assumptions required to arrive at the amounts recorded is included in the section entitled “Critical Accounting Policies” in our Management’s Discussion and Analysis of Financial Condition and Results of Operations in our Annual Report 2003.

Cautionary note regarding forward-looking statements

This document contains certain forward-looking statements. Forward-looking statements are necessarily based on estimates and assumptions that are inherently subject to significant business, economic and competitive uncertainties and contingencies, many of which, with respect to future business decisions, are subject to change. These uncertainties and contingencies can affect actual results and could cause actual results to differ materially from those expressed in any forward-looking statements. In particular, statements using words such as “expect,” “anticipate,” “intend,” “believe” or words of similar import generally involve forward-looking statements. The specific forward-looking statements cover, among other matters, our reserve position, loss reporting trends and our business and capital plans. In light of the risks and uncertainties inherent in all future projections, the inclusion of forward-looking statements should not be considered a representation by us that our objectives or plans will be achieved. Numerous factors could cause our actual results to differ materially from those in the forward-looking statements, including the following: