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UNITED STATES

SECURITIES AND EXCHANGE COMMISSION

WASHINGTON, D.C.  20549

FORM 10-Q

(Mark One)

x      QUARTERLY REPORT PURSUANT TO SECTION 13 OR 15(d) OF THE SECURITIES EXCHANGE ACT OF 1934

For the quarterly period ended September 30, 2010

Or

o         TRANSITION REPORT PURSUANT TO SECTION 13 OR 15(d) OF THE SECURITIES EXCHANGE ACT OF 1934

Commission file number: 001-26456

ARCH CAPITAL GROUP LTD.

(Exact name of registrant as specified in its charter)

Bermuda

(State or other jurisdiction of incorporation or organization)

Not Applicable

(I.R.S. Employer Identification No.)

Wessex House, 45 Reid Street

Hamilton HM 12, Bermuda

(Address of principal executive offices)

(441) 278-9250

(Registrant’s telephone number, including area code)

Indicate by check mark whether the registrant (1) has filed all reports required to be filed by Section 13 or 15(d) of the Securities Exchange Act of 1934 during the preceding 12 months (or for such shorter period that the registrant was required to file such reports), and (2) has been subject to such filing requirements for the past 90 days. Yes x   No o

Indicate by check mark whether the registrant has submitted electronically and posted on its corporate Web site, if any, every Interactive Data File required to be submitted and posted pursuant to Rule 405 of Regulation S-T (§232.405 of this chapter) during the preceding 12 months (or for such shorter period that the registrant was required to submit and post such files). Yes x   No o

Indicate by check mark whether the registrant is a large accelerated filer, an accelerated filer, a non-accelerated filer, or a smaller reporting company. See the definitions of “large accelerated filer,” “accelerated filer” and “smaller reporting company” in Rule 12b-2 of the Exchange Act.

Indicate by check mark whether the Registrant is a shell company (as defined in Rule 12b-2 of the Exchange Act). Yes o   No x

The number of the registrant’s common shares (par value, $0.01 per share) outstanding as of November 4, 2010 was 48,887,727.

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ARCH CAPITAL GROUP LTD.

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Report of Independent Registered Public Accounting Firm

To the Board of Directors and Shareholders of

Arch Capital Group Ltd.:

We have reviewed the accompanying consolidated balance sheet of Arch Capital Group Ltd. and its subsidiaries (the “Company”) as of September 30, 2010, and the related consolidated statements of income for the three-month and nine-month periods ended September 30, 2010 and September 30, 2009, and the consolidated statements of changes in shareholders’ equity, comprehensive income and cash flows for each of the nine-month periods ended September 30, 2010 and September 30, 2009.  These interim financial statements are the responsibility of the Company’s management.

We conducted our review in accordance with the standards of the Public Company Accounting Oversight Board (United States).  A review of interim financial information consists principally of applying analytical procedures and making inquiries of persons responsible for financial and accounting matters.  It is substantially less in scope than an audit conducted in accordance with the standards of the Public Company Accounting Oversight Board (United States), the objective of which is the expression of an opinion regarding the financial statements taken as a whole.  Accordingly, we do not express such an opinion.

Based on our review, we are not aware of any material modifications that should be made to the accompanying consolidated interim financial statements for them to be in conformity with accounting principles generally accepted in the United States of America.

We previously audited, in accordance with the standards of the Public Company Accounting Oversight Board (United States), the consolidated balance sheet as of December 31, 2009, and the related consolidated statements of income, changes in shareholders’ equity, comprehensive income, and of cash flows for the year then ended (not presented herein), and in our report dated February 26, 2010, we expressed an unqualified opinion on those consolidated financial statements.  In our opinion, the information set forth in the accompanying consolidated balance sheet information as of December 31, 2009, is fairly stated in all material respects in relation to the consolidated balance sheet from which it has been derived.

/s/ PricewaterhouseCoopers LLP

New York, NY

November 8, 2010

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ARCH CAPITAL GROUP LTD. AND SUBSIDIARIES

CONSOLIDATED BALANCE SHEETS

(U.S. dollars in thousands, except share data)

See Notes to Consolidated Financial Statements

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CONSOLIDATED STATEMENTS OF INCOME

(U.S. dollars in thousands, except share data)

See Notes to Consolidated Financial Statements

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CONSOLIDATED STATEMENTS OF CHANGES IN SHAREHOLDERS’ EQUITY

(U.S. dollars in thousands)

(1) Adoption of accounting guidance regarding the recognition and presentation of other-than-temporary impairments.

See Notes to Consolidated Financial Statements

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CONSOLIDATED STATEMENTS OF COMPREHENSIVE INCOME

(U.S. dollars in thousands)

See Notes to Consolidated Financial Statements

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CONSOLIDATED STATEMENTS OF CASH FLOWS

(U.S. dollars in thousands)

See Notes to Consolidated Financial Statements

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NOTES TO CONSOLIDATED FINANCIAL STATEMENTS (UNAUDITED)

1.             General

Arch Capital Group Ltd. (“ACGL”) is a Bermuda public limited liability company which provides insurance and reinsurance on a worldwide basis through its wholly owned subsidiaries.

The interim consolidated financial statements have been prepared in conformity with accounting principles generally accepted in the United States of America (“GAAP”) and include the accounts of ACGL and its wholly owned subsidiaries (together with ACGL, the “Company”). All significant intercompany transactions and balances have been eliminated in consolidation. The preparation of financial statements in conformity with GAAP requires management to make estimates and assumptions that affect the reported amounts of assets and liabilities and disclosure of contingent assets and liabilities at the date of the financial statements and the reported amounts of revenues and expenses during the reporting period. Actual results could differ from those estimates and assumptions. In the opinion of management, the accompanying unaudited interim consolidated financial statements reflect all adjustments (consisting of normally recurring accruals) necessary for a fair statement of results on an interim basis. The results of any interim period are not necessarily indicative of the results for a full year or any future periods.

Certain information and footnote disclosures normally included in financial statements prepared in accordance with GAAP have been condensed or omitted; however, management believes that the disclosures are adequate to make the information presented not misleading. This report should be read in conjunction with the Company’s Annual Report on Form 10-K for the year ended December 31, 2009, including the Company’s audited consolidated financial statements and related notes.

The Company has reclassified the presentation of certain prior year information to conform to the current presentation. Such reclassifications had no effect on the Company’s net income, shareholders’ equity or cash flows. Tabular amounts are in U.S. Dollars in thousands, except share amounts, unless otherwise noted.

2.             Recent Accounting Pronouncements

In October 2010, the Financial Accounting Standards Board (“FASB”) issued an Accounting Standards Update (“ASU”) that modifies the definition of the types of costs incurred by insurance entities that can be capitalized in the acquisition of new or renewal insurance contracts. The amended guidance specifies that certain costs incurred in the successful acquisition of new and renewal insurance contracts should be capitalized. Those costs include incremental direct costs of contract acquisition that result directly from and are essential to the contract transaction and would not have been incurred had the contract transaction not occurred. All other acquisition-related costs, such as costs incurred for soliciting business, administration, and unsuccessful acquisition or renewal efforts should be charged to expense as incurred. Administrative costs, including rent, depreciation, occupancy, equipment, and all other general overhead costs are considered indirect costs and should also be charged to expense as incurred. This ASU is effective for fiscal years, and interim periods within those fiscal years, beginning after December 15, 2011. Earlier adoption is permitted. Retrospective application to all prior periods presented upon the date of adoption is also permitted but is not required. The Company is evaluating the impact this new guidance will have on its consolidated statement of financial position and results of operations.

In March 2010, the Financial Accounting Standards Board (“FASB”) issued an ASU that clarifies the type of embedded credit derivative that is exempt from embedded derivative bifurcation requirements. Only one form of embedded credit derivative qualifies for the exemption—one that is related only to the subordination of one financial instrument to another. As a result, entities that have contracts containing an embedded credit derivative feature in a form other than such subordination may need to separately account for the embedded credit

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derivative feature. This ASU was effective as of July 1, 2010 and its adoption did not have a material impact on the Company’s consolidated financial position or results of operations.

In January 2010, the FASB issued an ASU to improve disclosure requirements related to fair value measurements. The ASU requires more robust disclosures about (i) different classes of assets and liabilities measured at fair value, (ii) the valuation techniques and inputs to fair value measurements for both Levels 2 and 3, (iii) the activity within Level 3 fair value measurements (i.e., in the reconciliation for fair value measurements using significant unobservable inputs activity should be presented on a gross basis), and (iv) the transfers between Levels 1, 2 and 3, (i.e., include the reasons for significant transfers in and out of Levels 1 and 2 ).The ASU is effective for interim and annual reporting periods beginning after December 15, 2009, except for the disclosures about purchases, sales, issuances, and settlements in the roll forward activity in Level 3 fair value measurements, which will become effective for fiscal years beginning after December 15, 2010. Accordingly, the Company adopted the appropriate disclosure provisions of the ASU on January 1, 2010.

3.             Share Transactions

Share Repurchases

The board of directors of ACGL has authorized the investment of up to $2.5 billion in ACGL’s common shares through a share repurchase program, consisting of a $1.0 billion authorization in February 2007, a $500 million authorization in May 2008, and a $1.0 billion authorization in November 2009. Repurchases under the program may be effected from time to time in open market or privately negotiated transactions through December 2011. Since the inception of the share repurchase program, ACGL has repurchased 28.8 million common shares for an aggregate purchase price of $2.01 billion. During the 2010 third quarter, ACGL repurchased 0.7 million common shares for an aggregate purchase price of $53.4 million, compared to 1.5 million common shares for an aggregate purchase price of $98.2 million during the 2009 third quarter. During the nine months ended September 30, 2010, ACGL repurchased 6.9 million common shares for an aggregate purchase price of $503.7 million, compared to 1.6 million common shares for an aggregate purchase price of $99.7 million during the 2009 period.

At September 30, 2010, approximately $487.7 million of share repurchases were available under the program. The timing and amount of the repurchase transactions under this program will depend on a variety of factors, including market conditions and corporate and regulatory considerations.

Treasury Shares

In May 2010, ACGL’s shareholders approved amendments to the bye-laws to permit ACGL to hold its own acquired shares as treasury shares in lieu of cancellation, as determined by ACGL’s board of directors. From May 5 to September 30, 2010, all repurchases of ACGL’s common shares in connection with the share repurchase plan noted above and other share-based transactions were held in the treasury under the cost method, and the cost of the common shares acquired is included in ‘Common shares held in treasury, at cost.’  Prior to May 5, 2010, such acquisitions were reflected as a reduction in additional paid-in capital. At September 30, 2010, the Company held 3.9 million shares for an aggregate cost of $291.5 million in treasury, at cost.

Non-Cumulative Preferred Shares

ACGL’s outstanding non-cumulative preferred shares consist of $200.0 million principal amount of 8.0% series A non-cumulative preferred shares (“Series A Preferred Shares”) and $125.0 million principal amount of 7.875% series B non-cumulative preferred shares (“Series B Preferred Shares” and together with the Series A Preferred Shares, the “Preferred Shares”). ACGL has the right to redeem all or a portion of each series of

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Preferred Shares at a redemption price of $25.00 per share on or after (1) February 1, 2011 for the Series A Preferred Shares and (2) May 15, 2011 for the Series B Preferred Shares. During the nine month periods ended September 30, 2010 and 2009, the Company paid $19.4 million to holders of the Preferred Shares. At September 30, 2010, the Company had declared an aggregate of $3.3 million of dividends to be paid to holders of the Preferred Shares.

4.             Debt and Financing Arrangements

Senior Notes

On May 4, 2004, ACGL completed a public offering of $300 million principal amount of 7.35% senior notes (“Senior Notes”) due May 1, 2034 and received net proceeds of $296.4 million. ACGL used $200 million of the net proceeds to repay all amounts outstanding under a revolving credit agreement. The Senior Notes are ACGL’s senior unsecured obligations and rank equally with all of its existing and future senior unsecured indebtedness. Interest payments on the Senior Notes are due on May 1st and November 1st of each year. ACGL may redeem the Senior Notes at any time and from time to time, in whole or in part, at a “make-whole” redemption price. For the nine month periods ended September 30, 2010 and 2009, interest expense on the Senior Notes was $16.5 million. The market value of the Senior Notes at September 30, 2010 and December 31, 2009 was $321.9 million and $298.6 million, respectively.

Letter of Credit and Revolving Credit Facilities

As of September 30, 2010, the Company had a $300 million unsecured revolving loan and letter of credit facility and a $1.0 billion secured letter of credit facility (the “Credit Agreement”). Under the terms of the agreement, Arch Reinsurance Company (“Arch Re U.S.”) is limited to issuing $100 million of unsecured letters of credit as part of the $300 million unsecured revolving loan. Borrowings of revolving loans may be made by ACGL and Arch Re U.S. at a variable rate based on LIBOR or an alternative base rate at the option of the Company. Secured letters of credit are available for issuance on behalf of the Company’s insurance and reinsurance subsidiaries. The Credit Agreement and related documents are structured such that each party that requests a letter of credit or borrowing does so only for itself and for only its own obligations. Issuance of letters of credit and borrowings under the Credit Agreement are subject to the Company’s compliance with certain covenants and conditions, including absence of a material adverse change. These covenants require, among other things, that the Company maintain a debt to total capital ratio of not greater than 0.35 to 1 and shareholders’ equity in excess of $1.95 billion plus 25% of future aggregate net income for each quarterly period (not including any future net losses) beginning after June 30, 2006 and 25% of future aggregate proceeds from the issuance of common or preferred equity and that the Company’s principal insurance and reinsurance subsidiaries maintain at least a “B++” rating from A.M. Best. In addition, certain of the Company’s subsidiaries which are party to the Credit Agreement are required to maintain minimum shareholders’ equity levels. The Company was in compliance with all covenants contained in the Credit Agreement at September 30, 2010. The Credit Agreement expires on August 30, 2011.

Including the secured letter of credit portion of the Credit Agreement, the Company has access to letter of credit facilities for up to a total of $1.45 billion. Arch Reinsurance Ltd. (“Arch Re Bermuda”) also has access to other letter of credit facilities, some of which are available on a limited basis and for limited purposes (together with the secured portion of the Credit Agreement and these letter of credit facilities, the “LOC Facilities”). The principal purpose of the LOC Facilities is to issue, as required, evergreen standby letters of credit in favor of primary insurance or reinsurance counterparties with which the Company has entered into reinsurance arrangements to ensure that such counterparties are permitted to take credit for reinsurance obtained from the Company’s reinsurance subsidiaries in United States jurisdictions where such subsidiaries are not licensed or otherwise admitted as an insurer, as required under insurance regulations in the United States, and to comply

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with requirements of Lloyd’s of London in connection with qualifying quota share and other arrangements. The amount of letters of credit issued is driven by, among other things, the timing and payment of catastrophe losses, loss development of existing reserves, the payment pattern of such reserves, the further expansion of the Company’s business and the loss experience of such business. When issued, certain letters of credit are secured by a portion of the Company’s investment portfolio. In addition, the LOC Facilities also require the maintenance of certain covenants, which the Company was in compliance with at September 30, 2010. At such date, the Company had $703.2 million in outstanding letters of credit under the LOC Facilities, which were secured by investments with a market value of $785.4 million. At September 30, 2010, the Company had $125.0 million of borrowings outstanding under the Credit Agreement at a Company-selected variable interest rate that is based on 1 month, 3 month or 6 month reset option terms and their corresponding term LIBOR rates plus 27.5 basis points.

TALF Program

The Company participates in the Federal Reserve Bank of New York’s (“FRBNY”) Term Asset-Backed Securities Loan Facility (“TALF”). TALF provides secured financing for asset-backed securities backed by certain types of consumer and small business loans and for legacy commercial mortgage-backed securities. TALF financing is non-recourse to the Company, except in certain limited instances, and is collateralized by the purchased securities and provides financing for the purchase price of the securities, less a ‘haircut’ that varies based on the type of collateral. The Company can deliver the collateralized securities to a special purpose vehicle created by the FRBNY in full defeasance of the borrowings.

The Company elected to carry the securities and related borrowings at fair value under the fair value option afforded by accounting guidance regarding the fair value option for financial assets and financial liabilities. As of September 30, 2010, the Company had $410.9 million of securities under TALF which are reflected as “TALF investments, at market value” and $331.8 million of secured financing from the FRBNY which is reflected as “TALF borrowings, at market value.” As of December 31, 2009, the Company had $250.3 million of securities under TALF which are reflected as “TALF investments, at market value” and $217.6 million of secured financing from the FRBNY which is reflected as “TALF borrowings, at market value.” The original maturity dates for the TALF borrowings vary between 1.5 to 4.5 years with floating or fixed coupons depending on the related TALF investments.

Interest Paid

During the nine months ended September 30, 2010, the Company made interest payments of $17.1 million related to its debt and financing arrangements, compared to $12.0 million for the nine months ended September 30, 2009. The growth was primarily attributable to payments on the Company’s TALF borrowings.

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5.             Segment Information

The Company classifies its businesses into two underwriting segments — insurance and reinsurance — and corporate and other (non-underwriting). The Company’s insurance and reinsurance operating segments each have segment managers who are responsible for the overall profitability of their respective segments and who are directly accountable to the Company’s chief operating decision makers, the Chairman, President and Chief Executive Officer of ACGL and the Chief Financial Officer of ACGL. The chief operating decision makers do not assess performance, measure return on equity or make resource allocation decisions on a line of business basis. The Company determined its reportable operating segments using the management approach described in accounting guidance regarding disclosures about segments of an enterprise and related information.

Management measures segment performance based on underwriting income or loss. The Company does not manage its assets by segment and, accordingly, investment income is not allocated to each underwriting segment. In addition, other revenue and expense items are not evaluated by segment. The accounting policies of the segments are the same as those used for the preparation of the Company’s consolidated financial statements. Intersegment business is allocated to the segment accountable for the underwriting results.

The insurance segment consists of the Company’s insurance underwriting subsidiaries which primarily write on both an admitted and non-admitted basis. Specialty product lines include: casualty; construction; executive assurance; healthcare; national accounts casualty; professional liability; programs; property, energy, marine and aviation; surety; travel and accident; and other (consisting of excess workers’ compensation, employers’ liability, collateral protection and alternative markets business).

The reinsurance segment consists of the Company’s reinsurance underwriting subsidiaries. The reinsurance segment generally seeks to write significant lines on specialty property and casualty reinsurance contracts. Classes of business include: casualty; marine and aviation; other specialty; property catastrophe; property excluding property catastrophe (losses on a single risk, both excess of loss and pro rata); and other (consisting of non-traditional and casualty clash business).

Corporate and other (non-underwriting) includes net investment income, other income (loss), other expenses incurred by the Company, interest expense, net realized gains or losses, net impairment losses recognized in earnings, equity in net income (loss) of investment funds accounted for using the equity method, net foreign exchange gains or losses, income taxes and dividends on the Company’s non-cumulative preferred shares.

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The following tables set forth an analysis of the Company’s underwriting income by segment, together with a reconciliation of underwriting income to net income available to common shareholders, summary information regarding net premiums written and earned by major line of business and net premiums written by location:

(1)        Certain amounts included in the gross premiums written of each segment are related to intersegment transactions. Accordingly, the sum of gross premiums written for each segment does not agree to the total gross premiums written as shown in the table above due to the elimination of intersegment transactions in the total. The insurance segment and reinsurance segment results include nil and $1.5 million, respectively, of gross and net premiums written and $0.3 million and $2.7 million, respectively, of net premiums earned assumed through intersegment transactions.

(2)        The acquisition expense ratio is adjusted to include policy-related fee income.

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(1)        Certain amounts included in the gross premiums written of each segment are related to intersegment transactions. Accordingly, the sum of gross premiums written for each segment does not agree to the total gross premiums written as shown in the table above due to the elimination of intersegment transactions in the total. The insurance segment and reinsurance segment results include nil and $2.8 million, respectively, of gross and net premiums written and $0.4 million and $3.0 million, respectively, of net premiums earned assumed through intersegment transactions.

(2)        The acquisition expense ratio is adjusted to include policy-related fee income.

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