acgl-20221026
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UNITED STATES
SECURITIES AND EXCHANGE COMMISSION
Washington, D.C.  20549
 
FORM 8-K
 
Current Report Pursuant to Section 13 or 15(d)
of the Securities Exchange Act of 1934
 
October 26, 2022
Date of Report (Date of earliest event reported) 
Arch Capital Group Ltd.
(Exact name of registrant as specified in its charter)
Bermuda 001-16209 98-0374481
(State or other
jurisdiction of
incorporation or
organization)		 (Commission File Number) (I.R.S. Employer
Identification No.)
 
Waterloo House, Ground Floor, 100 Pitts Bay Road, Pembroke HM 08, Bermuda
(Address of principal executive offices) (Zip Code)
 
Registrant’s telephone number, including area code:
(441) 278-9250
 
N/A
(Former name or former address, if changed since last report)
 
Check the appropriate box below if the Form 8-K filing is intended to simultaneously satisfy the filing obligation of the registrant under any of the following provisions (see General Instruction A.2. below):
 
☐    Written communications pursuant to Rule 425 under the Securities Act (17 CFR 230.425)
 
☐    Soliciting material pursuant to Rule 14a-12 under the Exchange Act (17 CFR 240.14a-12)
 
☐    Pre-commencement communications pursuant to Rule 14d-2(b) under the Exchange Act (17 CFR 240.14d-2(b))
 
☐    Pre-commencement communications pursuant to Rule 13e-4(c) under the Exchange Act (17 CFR 240.13e-4(c))


Securities registered pursuant to Section 12(b) of the Exchange Act:
Title of each classTrading Symbol (s)Name of each exchange on which registered
Common shares, $0.0011 par value per shareACGLNASDAQStock Market
Depositary shares, each representing a 1/1,000th interest in a 5.45% Series F preferred share
ACGLO
NASDAQStock Market
Depositary shares, each representing a 1/1,000th interest in a 4.55% Series G preferred shareACGLNNASDAQStock Market
Indicate by check mark whether the registrant is an emerging growth company as defined in Rule 405 of the Securities Act of 1933 (§230.405 of this chapter) or Rule 12b-2 of the Securities Exchange Act of 1934 (§240.12b-2 of this chapter).

    Emerging growth company     ☐

If an emerging growth company, indicate by check mark if the registrant has elected not to use the extended transition period for complying with any new or revised financial accounting standards provided pursuant to Section 13(a) of the Exchange Act.  o


ITEM 2.02           Results of Operations and Financial Condition.
 
On October 26, 2022, Arch Capital Group Ltd. issued a press release reporting its earnings and the availability of its financial supplement for the quarter ended September 30, 2022. The press release and financial supplement are attached to this Current Report on Form 8-K as Exhibit 99.1 and Exhibit 99.2, respectively, and are incorporated herein by reference.
 
The information in this Current Report on Form 8-K, including the information set forth in Exhibit 99.1 and Exhibit 99.2, shall not be deemed “filed” for purposes of Section 18 of the Securities Exchange Act of 1934, as amended (the “Exchange Act”), or incorporated by reference in any filing under the Securities Act of 1933, as amended, or the Exchange Act, except as shall be expressly set forth by specific reference in such a filing.

ITEM 9.01    Financial Statements and Exhibits.

(d):     The following exhibits are being filed herewith.
EXHIBIT NO. DESCRIPTION
99.1 
99.2 
104Cover Page Interactive Data File (embedded within the Inline XBRL document)
2

SIGNATURES
 
Pursuant to the requirements of the Securities Exchange Act of 1934, as amended, the registrant has duly caused this report to be signed on its behalf by the undersigned hereunto duly authorized.
 
 ARCH CAPITAL GROUP LTD.
   
   
Date: October 26, 2022By:/s/ François Morin
  Name:François Morin
  Title:Executive Vice President, Chief Financial Officer and Treasurer


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EXHIBIT 99.1
PRESS RELEASEArch Capital Group Ltd.
NASDAQ Symbol: ACGLWaterloo House, Ground Floor
For Immediate Release100 Pitts Bay Road
October 26, 2022
Pembroke HM 08 Bermuda


ARCH CAPITAL GROUP LTD. REPORTS 2022 THIRD QUARTER RESULTS

PEMBROKE, BERMUDA--(BUSINESS WIRE)--Arch Capital Group Ltd. (NASDAQ: ACGL; “Arch” or “the Company”) announces its 2022 third quarter results. The results included:
•Net income available to Arch common shareholders of $6.9 million, or $0.02 per share, a 0.2% annualized net income return on average common equity, compared to $388.8 million, or $0.98 per share, for the 2021 third quarter;
•After-tax operating income available to Arch common shareholders(1) of $106.0 million, or $0.28 per share, a 3.8% annualized operating return on average common equity, compared to $294.7 million, or $0.74 per share, for the 2021 third quarter;
•Pre-tax current accident year catastrophic losses for the Company’s insurance and reinsurance segments, net of reinsurance and reinstatement premiums (1), of $550.8 million, primarily related to Hurricane Ian, as well as from a series of other global events that occurred this year, including U.S. convective storms, Typhoon Nanmadol and the June French hailstorms;
•Combined ratio excluding catastrophic activity and prior year development(1) of 82.2%, compared to 80.1% for the 2021 third quarter;
•Favorable development in prior year loss reserves, net of related adjustments(1) of $178.0 million;
•Book value per common share of $29.69 at September 30, 2022, a 5.4% decrease from June 30, 2022.
All earnings per share amounts discussed in this release are on a diluted basis. The following table summarizes the Company’s underwriting results:
(U.S. dollars in thousands)Three Months Ended September 30,
20222021% Change
Gross premiums written$3,860,683 $3,207,415 20.4 
Net premiums written2,723,774 2,075,929 31.2 
Net premiums earned2,470,750 1,929,337 28.1 
Underwriting income68,797 173,745 (60.4)
Underwriting Ratios% Point Change
Loss ratio68.1 %63.5 %4.6 
Underwriting expense ratio29.2 %27.9 %1.3 
Combined ratio97.3 %91.4 %5.9 
Combined ratio excluding catastrophic activity and prior year development (1)
82.2 %80.1 %2.1 
(1)    Presentation represents a “non-GAAP” financial measure as defined in Regulation G. See ‘Comments on Regulation G’ for further details.
1

The following table summarizes the Company’s consolidated financial data, including a reconciliation of net income or loss available to Arch common shareholders to after-tax operating income or loss available to Arch common shareholders and related diluted per share results (see ‘Comments on Regulation G’ for a discussion of non-GAAP financial measures):
(U.S. dollars in thousands, except share data)Three Months Ended
September 30,
20222021
Net income available to Arch common shareholders$6,917 $388,751 
Net realized (gains) losses183,674 25,040 
Equity in net (income) loss of investment funds accounted for using the equity method18,861 (105,398)
Net foreign exchange (gains) losses(90,537)(36,078)
Transaction costs and other76 1,036 
Loss on redemption of preferred shares— 15,101 
Income tax expense (benefit) (1)(13,019)6,236 
After-tax operating income available to Arch common shareholders$105,972 $294,688 
Diluted per common share results:
Net income available to Arch common shareholders$0.02 $0.98 
Net realized (gains) losses0.48 0.05 
Equity in net (income) loss of investment funds accounted for using the equity method0.05 (0.26)
Net foreign exchange (gains) losses(0.24)(0.09)
Transaction costs and other0.00 0.00 
Loss on redemption of preferred shares— 0.04 
Income tax expense (benefit) (1)(0.03)0.02 
After-tax operating income available to Arch common shareholders$0.28 $0.74 
Weighted average common shares and common share equivalents outstanding — diluted373,727,277 397,903,347 
Beginning common shareholders’ equity$11,587,566 $12,706,072 
Ending common shareholders’ equity10,965,110 12,557,526 
Average common shareholders’ equity$11,276,338 $12,631,799 
Annualized net income return on average common equity0.2 %12.3 %
Annualized operating return on average common equity3.8 %9.3 %
(1)    Income tax expense (benefit) on net realized gains or losses, equity in net income (loss) of investment funds accounted for using the equity method, net foreign exchange gains or losses, transaction costs and other and loss on redemption of preferred shares reflects the relative mix reported by jurisdiction and the varying tax rates in each jurisdiction.

2

Segment Information
The following section provides analysis on the Company’s 2022 third quarter performance by operating segment. For additional details regarding the Company’s operating segments, please refer to the Company’s Financial Supplement dated September 30, 2022. The Company’s segment information includes the use of underwriting income (loss) and a combined ratio excluding catastrophic activity and prior year development. Such items are non-GAAP financial measures (see ‘Comments on Regulation G’ for further details).
Insurance Segment
Three Months Ended September 30,
(U.S. dollars in thousands)20222021% Change
Gross premiums written$1,862,026 $1,596,619 16.6 
Net premiums written1,368,759 1,153,813 18.6 
Net premiums earned1,186,908 938,670 26.4 
Underwriting income (loss)$(33,723)$(21,358)(57.9)
Underwriting Ratios% Point Change
Loss ratio69.3 %71.2 %(1.9)
Underwriting expense ratio33.5 %31.0 %2.5 
Combined ratio102.8 %102.2 %0.6 
Catastrophic activity and prior year development:
Current accident year catastrophic events, net of reinsurance and reinstatement premiums13.4 %12.2 %1.2 
Net (favorable) adverse development in prior year loss reserves, net of related adjustments(0.1)%(0.5)%0.4 
Combined ratio excluding catastrophic activity and prior year development89.5 %90.5 %(1.0)
Gross premiums written by the insurance segment in the 2022 third quarter were 16.6% higher than in the 2021 third quarter while net premiums written were 18.6% higher than in the 2021 third quarter. The higher level of net premiums written reflected increases in most lines of business, due in part to rate increases, new business opportunities and growth in existing accounts. Net premiums earned in the 2022 third quarter were 26.4% higher than in the 2021 third quarter, and reflect changes in net premiums written over the previous five quarters.
The 2022 third quarter loss ratio reflected 13.4 points of current year catastrophic activity, primarily related to Hurricane Ian, compared to 12.2 points of catastrophic activity in the 2021 third quarter, primarily related to Hurricane Ida. Estimated net favorable development of prior year loss reserves, before related adjustments, reduced the loss ratio by 0.5 points in the 2022 third quarter consistent with 0.5 in the 2021 third quarter. The improvement in the 2022 third quarter loss ratio also reflected the impact of rate increases and changes in mix of business.
The underwriting expense ratio was 33.5% in the 2022 third quarter, compared to 31.0% in the 2021 third quarter. The increase in the 2022 third quarter was primarily due to growth in lines with higher acquisition costs, such as travel, higher contingent commission accruals on profitable business and a slightly lower ceded premium ratio. Partially offsetting this increase in the acquisition expense ratio was a reduction in the operating expense ratio where the growth in net earned premium outpaced the growth in operating expense.
3

Reinsurance Segment
Three Months Ended September 30,
(U.S. dollars in thousands)20222021% Change
Gross premiums written$1,639,061 $1,251,760 30.9 
Net premiums written1,078,836 621,389 73.6 
Net premiums earned1,001,774 678,702 47.6 
Other underwriting income (loss)452 3,293 (86.3)
Underwriting income (loss)$(196,887)$(38,948)(405.5)
Underwriting Ratios% Point Change
Loss ratio92.6 %80.4 %12.2 
Underwriting expense ratio27.1 %25.8 %1.3 
Combined ratio119.7 %106.2 %13.5 
Catastrophic activity and prior year development:
Current accident year catastrophic events, net of reinsurance and reinstatement premiums39.1 %32.6 %6.5 
Net (favorable) adverse development in prior year loss reserves, net of related adjustments(4.9)%(9.6)%4.7 
Combined ratio excluding catastrophic activity and prior year development85.5 %83.2 %2.3 
Gross premiums written by the reinsurance segment in the 2022 third quarter were 30.9% higher than in the 2021 third quarter, while net premiums written were 73.6% higher than in the 2021 third quarter. Net premiums written for the reinsurance segment in the 2021 third quarter were affected by a one time $161.2 million adjustment, resulting from retrocessions to Somers Re Ltd. (formerly known as Watford Re Ltd.) following its ownership change on July 1, 2021. Absent this item, net premiums written by the reinsurance segment were 37.9% higher than in the 2021 third quarter. The growth in net premiums written reflected increases in all lines of business, primarily related to rate increases, new business opportunities and growth in existing accounts. Net premiums earned in the 2022 third quarter were 47.6% higher than in the 2021 third quarter, and reflect changes in net premiums written over the previous five quarters.
The 2022 third quarter loss ratio reflected 42.8 points of current year catastrophic activity, related to Hurricane Ian and other global events, compared to 34.6 points of catastrophic activity in the 2021 third quarter, primarily related to Hurricane Ida and European floods. Estimated net favorable development of prior year loss reserves, before related adjustments, reduced the loss ratio by 4.9 points in the 2022 third quarter, compared to 10.7 points in the 2021 third quarter. In addition, the improvement in the 2022 third quarter loss ratio reflected the impact of rate increases and changes in mix of business.
The underwriting expense ratio was 27.1% in the 2022 third quarter, compared to 25.8% in the 2021 third quarter (including 1.1 points related to prior year development). The increase in the 2022 third quarter reflected a higher level of pro rata business, which generally has higher ceding commissions than excess of loss business. Such increase in the acquisition expense ratio was partially offset by a lower operating expense ratio due to a higher level of earned premium.
4

Mortgage Segment
Three Months Ended September 30,
(U.S. dollars in thousands)20222021% Change
Gross premiums written$362,409 $360,934 0.4 
Net premiums written276,179 300,727 (8.2)
Net premiums earned282,068 311,965 (9.6)
Other underwriting income2,625 3,981 (34.1)
Underwriting income$299,407 $234,051 27.9 
Underwriting Ratios% Point Change
Loss ratio(24.1)%3.7 %(27.8)
Underwriting expense ratio18.9 %22.5 %(3.6)
Combined ratio(5.2)%26.2 %(31.4)
Prior year development:
Net (favorable) adverse development in prior year loss reserves, net of related adjustments(45.1)%(15.5)%(29.6)
Combined ratio excluding prior year development39.9 %41.7 %(1.8)
Gross premiums written by the mortgage segment in the 2022 third quarter were 0.4% higher than in the 2021 third quarter, while net premiums written were 8.2% lower. The increase in gross premiums written primarily reflected higher volume of credit risk transfer contracts and growth in Australian markets, partially offset by lower volumes of U.S. primary mortgage insurance single premium and monthly premium business. Net premiums written for the 2022 third quarter reflected a higher level of premiums ceded than in the 2021 third quarter, while the reduction in net premiums earned also reflected a reduction in earnings from single premium policy terminations and a lower level of monthly premiums.
Estimated net favorable development of prior year loss reserves, before related adjustments, reduced the loss ratio by 44.7 points, primarily related to the U.S. first lien portfolio from the 2020 and 2021 accident years, compared to 14.5 points in the 2021 third quarter. The percentage of loans in default on U.S. primary mortgage insurance business was 1.73% at September 30, 2022, compared to 1.77% at June 30, 2022.
The underwriting expense ratio was 18.9% in the 2022 third quarter, compared to 22.5% in the 2021 third quarter, with the decrease reflecting lower acquisition expenses on Australian mortgage insurance following the acquisition of Westpac LMI in the 2021 third quarter and profit commissions on business ceded related to favorable development of prior year loss reserves in the U.S. These reductions were partially offset by a higher operating expense ratio due to a lower level of net premiums earned in the U.S. primary mortgage insurance business.

5

Corporate Segment
The corporate segment results include net investment income, net realized gains or losses (which includes changes in the allowance for credit losses on financial assets), equity in net income or loss of investment funds accounted for using the equity method, other income (loss), corporate expenses, transaction costs and other, amortization of intangible assets, interest expense, net foreign exchange gains or losses, income taxes items, income or loss from operating affiliates and items related to the Company’s non-cumulative preferred shares.
Investment returns were as follows:
(U.S. dollars in thousands, except per share data)Three Months Ended
September 30,June 30,September 30,
202220222021
Pre-tax net investment income$128,640 $106,392 $88,195 
Per diluted share$0.34 $0.28 $0.22 
Pre-tax investment income yield, at amortized cost (1)2.06 %1.76 %1.41 %
Total return on investments (2)(3.01)%(3.02)%0.01 %
(1)    Presented on an annualized basis and excluding the impact of investments for which returns are not included within investment income, such as investments accounted for using the equity method and certain equities.
(2)    Presentation represents a “non-GAAP” financial measure as defined in Regulation G. See ‘Comments on Regulation G’ for further details.
The growth in net investment income in the 2022 third quarter compared to the 2022 second quarter and 2021 third quarter reflected the effects of higher interest rates available in the market. Total return on investments for the 2022 third quarter primarily reflected the impact of rising interest rates on fixed income securities and was consistent with total return for the 2022 second quarter.
Net realized gains or losses reflect sales of investments along with the impact of financial market movements on the Company’s investment portfolio, including realized and unrealized changes in the fair value of equity securities and assets accounted for using the fair value option, realized and unrealized gains and losses on derivative instruments and changes in the allowance for credit losses on financial assets. On a pre-tax basis, net realized losses for the 2022 third quarter were $183.7 million, of which approximately 40% represented unrealized changes in the fair value of equity securities and assets accounted for using the fair value option.
On a pre-tax basis, net foreign exchange gains for the 2022 third quarter were $90.5 million, compared to net foreign exchange gains for the 2021 third quarter of $36.1 million. For both periods, such amounts were primarily unrealized and resulted from the effects of revaluing the Company’s net insurance liabilities required to be settled in foreign currencies at each balance sheet date. Changes in the value of available-for-sale investments held in foreign currencies due to foreign currency rate movements are reflected as a direct increase or decrease to shareholders’ equity and are not included in the consolidated statements of income. Although the Company generally attempts to match the currency of its projected liabilities with investments in the same currencies, the Company may elect to over or underweight one or more currencies from time to time, which could increase the Company’s exposure to foreign currency fluctuations and increase the volatility of the Company’s shareholders’ equity.
The Company’s effective tax rate on income before income taxes (based on the Company’s estimated annual effective tax rate) was 3.0% for the nine months ended September 30, 2022, compared to 5.8% for the 2021 period. The Company’s effective tax rate on pre-tax operating income available to Arch common shareholders was 5.2% for the nine months ended September 30, 2022, compared to a 5.9% for the 2021 period. The Company’s effective tax rate may fluctuate from period to period based upon the relative mix of income or loss reported by jurisdiction and the varying tax rates in each jurisdiction. The effective tax rates for the nine months ended September 30, 2022 and 2021 included discrete income tax benefits of $36.5 million and $28.7 million, respectively. The discrete income tax benefits had the effect of decreasing the nine months ended September 30, 2022 and 2021 effective tax rate on operating income available to Arch common shareholders by 3.3% and 2.8%, respectively. The discrete tax items in the 2022 and 2021 period primarily related to the release of a valuation allowance on U.K. deferred tax assets. The Company’s quarterly tax provision is adjusted to reflect changes in its estimated annual effective tax rate, if any.
Income from operating affiliates for the 2022 third quarter was $8.5 million, or $0.02 per share, compared to $124.1 million, or $0.31 per share, for the 2021 third quarter, and primarily reflects amounts related to Company’s investment in Somers Group Holdings Ltd. (“Somers”) and Coface SA. Results for the 2021 third quarter reflected a one-time gain of $95.7 million recognized from the Company’s previously disclosed acquisition of a 40% share of Somers.
6

Conference Call
The Company will hold a conference call for investors and analysts at 11:00 a.m. Eastern Time on October 27, 2022. A live webcast of this call will be available via the Investors section of the Company’s website at http://www.archgroup.com/investors. A recording of the webcast will be available in the Investors section of the Company’s website approximately two hours after the event concludes and will be archived on the site for one year.
Please refer to the Company’s Financial Supplement dated September 30, 2022, which is available via the Investors section of the Company’s website at http://www.archgroup.com/investors. The Financial Supplement provides additional detail regarding the financial performance of the Company. From time to time, the Company posts additional financial information and presentations to its website, including information with respect to its subsidiaries. Investors and other recipients of this information are encouraged to check the Company’s website regularly for additional information regarding the Company.
Arch Capital Group Ltd., a publicly listed Bermuda exempted company with approximately $14.5 billion in capital at September 30, 2022, provides insurance, reinsurance and mortgage insurance on a worldwide basis through its wholly owned subsidiaries.
Comments on Regulation G
Throughout this release, the Company presents its operations in the way it believes will be the most meaningful and useful to investors, analysts, rating agencies and others who use the Company’s financial information in evaluating the performance of the Company and that investors and such other persons benefit from having a consistent basis for comparison between quarters and for comparison with other companies within the industry. These measures may not, however, be comparable to similarly titled measures used by companies outside of the insurance industry. Investors are cautioned not to place undue reliance on these non-GAAP financial measures in assessing the Company’s overall financial performance.
This presentation includes the use of “after-tax operating income or loss available to Arch common shareholders,” which is defined as net income available to Arch common shareholders, excluding net realized gains or losses (which includes changes in the allowance for credit losses on financial assets and net impairment losses recognized in earnings), equity in net income or loss of investment funds accounted for using the equity method, net foreign exchange gains or losses, transaction costs and other and loss on redemption of preferred shares, net of income taxes, and the use of annualized operating return on average common equity. The presentation of after-tax operating income available to Arch common shareholders and annualized operating return on average common equity are non-GAAP financial measures as defined in Regulation G. The reconciliation of such measures to net income available to Arch common shareholders and annualized net income return on average common equity (the most directly comparable GAAP financial measures) in accordance with Regulation G is included on page 2 of this release.
The Company believes that net realized gains or losses, equity in net income or loss of investment funds accounted for using the equity method, net foreign exchange gains or losses, transaction costs and other and loss on redemption of preferred shares in any particular period are not indicative of the performance of, or trends in, the Company’s business performance. Although net realized gains or losses, equity in net income or loss of investment funds accounted for using the equity method and net foreign exchange gains or losses are an integral part of the Company’s operations, the decision to realize investment gains or losses, the recognition of the change in the carrying value of investments accounted for using the fair value option in net realized gains or losses, the recognition of equity in net income or loss of investment funds accounted for using the equity method and the recognition of foreign exchange gains or losses are independent of the insurance underwriting process and result, in large part, from general economic and financial market conditions. Furthermore, certain users of the Company’s financial information believe that, for many companies, the timing of the realization of investment gains or losses is largely opportunistic. In addition, changes in the allowance for credit losses and net impairment losses recognized in earnings on the Company’s investments represent other-than-temporary declines in expected recovery values on securities without actual realization. The use of the equity method on certain of the Company’s investments in certain funds that invest in fixed maturity securities is driven by the ownership structure of such funds (either limited partnerships or limited liability companies). In applying the equity method, these investments are initially recorded at cost and are subsequently adjusted based on the Company’s proportionate share of the net income or loss of the funds (which include changes in the fair value of the underlying securities in the funds). This method of accounting is different from the way the Company accounts for its other fixed maturity securities and the timing of the recognition of equity in net income or loss of investment funds accounted for using the equity method may differ from gains or losses in the future upon sale or maturity of such investments. Transaction costs and other include advisory, financing, legal, severance, incentive compensation and other costs related to acquisitions. The Company believes that transaction costs and other, due to their non-recurring nature, are not indicative of the performance of, or trends in, the Company’s business performance. The loss on redemption of preferred shares related to
7

the redemption of the Company's Series E preferred shares in September 2021 had no impact on shareholders' equity or cash flows. Due to these reasons, the Company excludes net realized gains or losses, equity in net income or loss of investment funds accounted for using the equity method, net foreign exchange gains or losses and transaction costs and other from the calculation of after-tax operating income or loss available to Arch common shareholders.
The Company believes that showing net income available to Arch common shareholders exclusive of the items referred to above reflects the underlying fundamentals of the Company’s business since the Company evaluates the performance of and manages its business to produce an underwriting profit. In addition to presenting net income available to Arch common shareholders, the Company believes that this presentation enables investors and other users of the Company’s financial information to analyze the Company’s performance in a manner similar to how the Company’s management analyzes performance. The Company also believes that this measure follows industry practice and, therefore, allows the users of the Company’s financial information to compare the Company’s performance with its industry peer group. The Company believes that the equity analysts and certain rating agencies which follow the Company and the insurance industry as a whole generally exclude these items from their analyses for the same reasons.
The Company’s segment information includes the presentation of consolidated underwriting income or loss and a subtotal of underwriting income or loss. Such measures represent the pre-tax profitability of its underwriting operations and include net premiums earned plus other underwriting income, less losses and loss adjustment expenses, acquisition expenses and other operating expenses. Other operating expenses include those operating expenses that are incremental and/or directly attributable to the Company’s individual underwriting operations. Underwriting income or loss does not incorporate items included in the Company’s corporate segment. While these measures are presented in the Segment Information footnote to the Company’s Consolidated Financial Statements, they are considered non-GAAP financial measures when presented elsewhere on a consolidated basis. The reconciliations of underwriting income or loss to income before income taxes (the most directly comparable GAAP financial measure) on a consolidated basis, in accordance with Regulation G, is shown on the following pages.
Management measures segment performance for its three underwriting segments based on underwriting income or loss. The Company does not manage its assets by underwriting segment and, accordingly, investment income, income from operating affiliates and other corporate segment related items are not allocated to each underwriting segment.
In addition, the Company’s segment information includes the use of a combined ratio excluding catastrophic activity and prior year development, for the insurance and reinsurance segments, and a combined ratio excluding prior year development, for the mortgage segment. These ratios are non-GAAP financial measures as defined in Regulation G. The reconciliation of such measures to the combined ratio (the most directly comparable GAAP financial measure) in accordance with Regulation G are shown on the individual segment pages. The Company’s management utilizes the adjusted combined ratios excluding current accident year catastrophic events and favorable or adverse development in prior year loss reserves in its analysis of the underwriting performance of each of its underwriting segments.
Total return on investments includes investment income, equity in net income or loss of investment funds accounted for using the equity method, net realized gains and losses (excluding changes in the allowance for credit losses on non-investment related financial assets) and the change in unrealized gains and losses generated by Arch’s investment portfolio. Total return is calculated on a pre-tax basis and before investment expenses and reflects the effect of financial market conditions along with foreign currency fluctuations. Management uses total return on investments as a key measure of the return generated to Arch common shareholders, and compares the return generated by the Company’s investment portfolio against benchmark returns during the periods presented.
8

The following tables summarize the Company’s results by segment for the 2022 third quarter and 2021 third quarter and a reconciliation of underwriting income or loss to income or loss before income taxes and net income or loss available to Arch common shareholders:
(U.S. Dollars in thousands)Three Months Ended
September 30, 2022
 InsuranceReinsuranceMortgageTotal
Gross premiums written (1)$1,862,026 $1,639,061 $362,409 $3,860,683 
Premiums ceded(493,267)(560,225)(86,230)(1,136,909)
Net premiums written1,368,759 1,078,836 276,179 2,723,774 
Change in unearned premiums(181,851)(77,062)5,889 (253,024)
Net premiums earned1,186,908 1,001,774 282,068 2,470,750 
Other underwriting income (loss)— 452 2,625 3,077 
Losses and loss adjustment expenses(822,663)(927,911)67,878 (1,682,696)
Acquisition expenses(232,469)(208,425)(6,693)(447,587)
Other operating expenses(165,499)(62,777)(46,471)(274,747)
Underwriting income (loss)$(33,723)$(196,887)$299,407 68,797 
Net investment income128,640 
Net realized gains (losses)(183,673)
Equity in net income (loss) of investment funds accounted for using the equity method(18,861)
Other income (loss)(13,684)
Corporate expenses (2)(17,634)
Transaction costs and other (2)(76)
Amortization of intangible assets(26,104)
Interest expense(33,063)
Net foreign exchange gains (losses)90,509 
Income (loss) before income taxes and income (loss) from operating affiliates(5,149)
Income tax expense14,900 
Income (loss) from operating affiliates8,507 
Net income (loss)18,258 
Dividends attributable to redeemable noncontrolling interests(1,157)
Net income (loss) available to Arch17,101 
Preferred dividends(10,184)
Net income (loss) available to Arch common shareholders$6,917 
Underwriting Ratios
Loss ratio69.3 %92.6 %(24.1)%68.1 %
Acquisition expense ratio19.6 %20.8 %2.4 %18.1 %
Other operating expense ratio13.9 %6.3 %16.5 %11.1 %
Combined ratio102.8 %119.7 %(5.2)%97.3 %
Net premiums written to gross premiums written73.5 %65.8 %76.2 %70.6 %
(1)    Certain amounts included in the gross premiums written of each segment are related to intersegment transactions and are included in the gross premiums written of each segment. 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.
(2)    Certain expenses have been excluded from ‘corporate expenses’ and reflected in ‘Transaction costs and other.’ See ‘Comments on Regulation G’ for a further discussion of such items.
9

(U.S. Dollars in thousands)Three Months Ended
September 30, 2021
 InsuranceReinsuranceMortgageTotal
Gross premiums written (1)$1,596,619 $1,251,760 $360,934 $3,207,415 
Premiums ceded(442,806)(630,371)(60,207)(1,131,486)
Net premiums written1,153,813 621,389 300,727 2,075,929 
Change in unearned premiums(215,143)57,313 11,238 (146,592)
Net premiums earned938,670 678,702 311,965 1,929,337 
Other underwriting income (loss)— 3,293 3,981 7,274 
Losses and loss adjustment expenses(668,630)(545,846)(11,543)(1,226,019)
Acquisition expenses(152,467)(129,450)(24,098)(306,015)
Other operating expenses(138,931)(45,647)(46,254)(230,832)
Underwriting income (loss)$(21,358)$(38,948)$234,051 173,745 
Net investment income88,195 
Net realized gains (losses)(25,040)
Equity in net income (loss) of investment funds accounted for using the equity method105,398 
Other income (loss)(3,960)
Corporate expenses (2)(18,636)
Transaction costs and other (2)(1,036)
Amortization of intangible assets(20,135)
Interest expense(33,176)
Net foreign exchange gains (losses)36,078 
Income (loss) before income taxes and income (loss) from operating affiliates301,433 
Income tax expense(4,137)
Income (loss) from operating affiliates124,119 
Net income (loss)421,415 
Dividends attributable to redeemable noncontrolling interests(1,473)
Net income (loss) available to Arch419,942 
Preferred dividends(16,090)
Loss on redemption of preferred shares(15,101)
Net income (loss) available to Arch common shareholders$388,751 
Underwriting Ratios
Loss ratio71.2 %80.4 %3.7 %63.5 %
Acquisition expense ratio16.2 %19.1 %7.7 %15.9 %
Other operating expense ratio14.8 %6.7 %14.8 %12.0 %
Combined ratio102.2 %106.2 %26.2 %91.4 %
Net premiums written to gross premiums written72.3 %49.6 %83.3 %64.7 %
 
(1)    Certain amounts included in the gross premiums written of each segment are related to intersegment transactions and are included in the gross premiums written of each segment. 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.
(2)    Certain expenses have been excluded from ‘corporate expenses’ and reflected in ‘Transaction costs and other.’ See ‘Comments on Regulation G’ for a further discussion of such items.

10

Cautionary Note Regarding Forward-Looking Statements
The Private Securities Litigation Reform Act of 1995 (“PSLRA”) provides a “safe harbor” for forward-looking statements. This release or any other written or oral statements made by or on behalf of the Company may include forward-looking statements, which reflect the Company’s current views with respect to future events and financial performance. All statements other than statements of historical fact included in or incorporated by reference in this release are forward-looking statements. Forward-looking statements, for purposes of the PSLRA or otherwise, can generally be identified by the use of forward-looking terminology such as “may,” “will,” “expect,” “intend,” “estimate,” “anticipate,” “believe” or “continue” and similar statements of a future or forward-looking nature or their negative or variations or similar terminology.
Forward-looking statements involve the Company’s current assessment of risks and uncertainties. Actual events and results may differ materially from those expressed or implied in these statements. Important factors that could cause actual events or results to differ materially from those indicated in such statements are discussed below and elsewhere in this release and in the Company’s periodic reports filed with the Securities and Exchange Commission (the “SEC”), and include:
•the Company’s ability to successfully implement its business strategy during “soft” as well as “hard” markets;
•acceptance of the Company’s business strategy, security and financial condition by rating agencies and regulators, as well as by brokers and its insureds and reinsureds;
•the Company’s ability to consummate acquisitions and integrate any businesses it has acquired or may acquire into its existing operations;
•the Company’s ability to maintain or improve its ratings, which may be affected by its ability to raise additional equity or debt financings, by ratings agencies’ existing or new policies and practices, as well as other factors described herein;
•general economic and market conditions (including inflation, interest rates, unemployment, housing prices, foreign currency exchange rates, prevailing credit terms and the depth and duration of a recession, including those resulting from COVID-19) and conditions specific to the reinsurance and insurance markets in which the Company operates;
•competition, including increased competition, on the basis of pricing, capacity (including alternative sources of capital), coverage terms or other factors;
•developments in the world’s financial and capital markets and the Company’s access to such markets;
•the Company’s ability to successfully enhance, integrate and maintain operating procedures (including information technology) to effectively support its current and new business;
•the loss and addition of key personnel;
•material differences between actual and expected assessments for guaranty funds and mandatory pooling arrangements;
•accuracy of those estimates and judgments utilized in the preparation of the Company’s financial statements, including those related to revenue recognition, insurance and other reserves, reinsurance recoverables, investment valuations, intangible assets, bad debts, income taxes, contingencies and litigation, and any determination to use the deposit method of accounting;
•greater than expected loss ratios on business written by the Company and adverse development on claim and/or claim expense liabilities related to business written by its insurance and reinsurance subsidiaries;
•the adequacy of the Company’s loss reserves;
•severity and/or frequency of losses;
•greater frequency or severity of unpredictable natural and man-made catastrophic events;
•claims resulting from natural or man-made catastrophic events or severe economic events in the Company’s insurance, reinsurance and mortgage businesses could cause large losses and substantial volatility in the Company’s results of operations;
•the effect of climate change on the Company’s business;
•the effect of contagious diseases (including COVID-19) on the Company’s business;
•acts of terrorism, political unrest and other hostilities or other unforecasted and unpredictable events;
•availability to the Company of reinsurance to manage its gross and net exposures and the cost of such reinsurance;
•the failure of reinsurers, managing general agents, third party administrators or others to meet their obligations to the Company;
11

•the timing of loss payments being faster or the receipt of reinsurance recoverables being slower than anticipated by the Company;
•the Company’s investment performance, including legislative or regulatory developments that may adversely affect the fair value of the Company’s investments;
•changes in general economic conditions, including new or continued sovereign debt concerns or downgrades of U.S. securities by credit rating agencies, which could affect the Company’s business, financial condition and results of operations;
•changes in the method for determining the London Inter-bank Offered Rate (“LIBOR”) and the replacement of LIBOR with alternative benchmark rates;
•the volatility of the Company’s shareholders’ equity from foreign currency fluctuations, which could increase due to us not matching portions of the Company’s projected liabilities in foreign currencies with investments in the same currencies;
•changes in accounting principles or policies or in the Company’s application of such accounting principles or policies;
•changes in the political environment of certain countries in which the Company operates, underwrites business or invests;
•a disruption caused by cyber-attacks or other technology breaches or failures on the Company or the Company’s business partners and service providers, which could negatively impact the Company’s business and/or expose the Company to litigation;
•statutory or regulatory developments, including as to tax policy matters and insurance and other regulatory matters such as the adoption of proposed legislation that would affect Bermuda-headquartered companies and/or Bermuda-based insurers or reinsurers and/or changes in regulations or tax laws applicable to the Company, its subsidiaries, brokers or customers, including new guidance implementing the Tax Cuts and Jobs Act of 2017 and the possible implementation of the Organization for Economic Cooperation and Development (“OECD”) Pillar I and Pillar II initiative; and
•the other matters set forth under Item 1A “Risk Factors”, Item 7 “Management’s Discussion and Analysis of Financial Condition and Results of Operations” and other sections of the Company’s Annual Report on Form 10-K, as well as the other factors set forth in the Company’s other documents on file with the SEC, and management’s response to any of the aforementioned factors.

All subsequent written and oral forward-looking statements attributable to the Company or persons acting on its behalf are expressly qualified in their entirety by these cautionary statements. The foregoing review of important factors should not be construed as exhaustive and should be read in conjunction with other cautionary statements that are included herein or elsewhere. The Company undertakes no obligation to publicly update or revise any forward-looking statement, whether as a result of new information, future events or otherwise.
Contacts
Arch Capital Group Ltd.Investor Relations
François Morin: (441) 278-9250Donald Watson: (914) 872-3616; dwatson@archgroup.com
Source - Arch Capital Group Ltd.
arch-corporate

12

EXHIBIT 99.2
Arch Capital Group Ltd.
Waterloo House, Ground Floor
100 Pitts Bay Road
Pembroke HM 08 Bermuda


Financial Supplement
September 30, 2022
 
The following financial supplement is provided to assist in your understanding of Arch Capital Group Ltd. (“Arch”) and its subsidiaries (collectively, the “Company”).
 
This report is for informational purposes only. It should be read in conjunction with documents filed by Arch with the U.S. Securities and Exchange Commission, including the most recent Annual Report on Form 10-K and the Quarterly Reports on Form 10-Q. Please refer to the Company’s website at www.archgroup.com for further information describing Arch.

Arch Capital Group Ltd.Investor Relations
François Morin: (441) 278-9250Donald Watson: (914) 872-3616; dwatson@archgroup.com


Arch Capital Group Ltd. and Subsidiaries
Table of Contents

  Page
   
I.Financial Highlights
  
II.Consolidated Financial Statements
 a.Consolidated Statements of Income
 b.Consolidated Balance Sheets
 c.Consolidated Statements of Changes in Shareholders’ Equity
 d.Consolidated Statements of Cash Flows
  
III.Segment Information
 a.Overview
 b.Consolidated Results
 c.Insurance Segment Results
 d.Reinsurance Segment Results
e.Mortgage Segment Results
f.Consolidated Results Excluding ‘Other’ Segment
g.Selected Information on Losses and Loss Adjustment Expenses
  
IV.Investment Information
 a.Investable Asset Summary and Investment Portfolio Metrics
b.Composition of Net Investment Income, Yield and Total Return
 c.Composition of Fixed Maturities
d.Credit Quality Distribution and Maturity Profile
e.Analysis of Corporate Exposures
 f.Structured Securities
  
V.Other
 a.Comments on Regulation G
 b.Operating Income Reconciliation and Annualized Operating Return on Average Common Equity
c.Operating Income and Effective Tax Rate Calculations
 d.Capital Structure and Share Repurchase Activity

1
Arch Capital Group Ltd. and Subsidiaries
Basis of Presentation

Basis of Presentation

All financial information contained herein is unaudited, however, certain information relating to the consolidated balance sheet at December 31, 2021 is derived from or agrees to audited financial information. During the 2021 first quarter, the Company changed its presentation of ‘income (loss) from operating affiliates’ on its consolidated statements of income for all periods presented to reclass such item from ‘other income (loss)’. The Company also changed its presentation of ‘investment in operating affiliates’ on its consolidated balance sheet for all periods presented to reclass such item from ‘other assets’. Unless otherwise noted, all data is in thousands, except for share and per share amounts and ratio information.

In March 2014, the Company invested $100.0 million to acquire common equity and a warrant to purchase additional common equity of Somers Group Holdings Ltd. (formerly Watford Holdings Ltd.), (“Somers”). In accordance with GAAP, the Company consolidated the results of Somers in its financial statements. Somers was considered a variable interest entity and the Company concluded that it was the primary beneficiary of Somers, through June 30, 2021. As such, 100% of the results of Somers were included in the Company’s consolidated financial statements as of and for the periods ended June 30, 2021. The portion of Somers’ earnings owned by third parties was recorded in the consolidated statements of income as ‘amounts attributable to noncontrolling interests.’ In addition, through June 30, 2021 the Company reflected Somers’ redeemable preference shares in the mezzanine section of the Company’s consolidated balance sheets as ‘redeemable noncontrolling interests’. In July 2021, the Company announced the completion of the previously disclosed acquisition of Somers by Greysbridge. Based on the governing documents of Greysbridge, the Company has concluded that, while it will retain significant influence over Somers, Somers no longer constitutes a variable interest entity. Accordingly, effective July 1, 2021, Arch no longer consolidates the results of Somers in its consolidated financial statements and footnotes.

Cautionary Note Regarding Forward-Looking Statements

The Private Securities Litigation Reform Act of 1995 provides a “safe harbor” for forward-looking statements. This release or any other written or oral statements made by or on behalf of Arch and its subsidiaries may include forward-looking statements, which reflect the Company’s current views with respect to future events and financial performance. All statements other than statements of historical fact included in or incorporated by reference in this release are forward-looking statements.
 
Forward-looking statements can generally be identified by the use of forward-looking terminology such as “may,” “will,” “expect,” “intend,” “estimate,” “anticipate,” “believe” or “continue” or their negative or variations or similar terminology. Forward-looking statements involve the Company’s current assessment of risks and uncertainties. Actual events and results may differ materially from those expressed or implied in these statements. A non-exclusive list of the important factors that could cause actual results to differ materially from those in such forward-looking statements includes the following: adverse general economic and market conditions; increased competition; pricing and policy term trends; fluctuations in the actions of rating agencies and the Company’s ability to maintain and improve the Company’s ratings; investment performance; the loss and addition of key personnel; the adequacy of the Company’s loss reserves, severity and/or frequency of losses, greater than expected loss ratios and adverse development on claim and/or claim expense liabilities; greater frequency or severity of unpredictable natural and man-made catastrophic events; including pandemics such as COVID-19; the impact of acts of terrorism and acts of war; changes in regulations and/or tax laws in the United States or elsewhere; the Company’s ability to successfully integrate, establish and maintain operating procedures as well as integrate the businesses we have acquired or may acquire into the existing operations; changes in accounting principles or policies; material differences between actual and expected assessments for guaranty funds and mandatory pooling arrangements; availability and cost to the Company of reinsurance to manage gross and net exposures; the failure of others to meet their obligations to the Company; changes in the method for determining the London Inter-bank Offered Rate (“LIBOR”) and the replacement of LIBOR with alternative benchmark rates and other factors identified in the Company’s filings with the U.S. Securities and Exchange Commission.
 
The foregoing review of important factors should not be construed as exhaustive and should be read in conjunction with other cautionary statements that are included herein or elsewhere. All subsequent written and oral forward-looking statements attributable to the Company or persons acting on the Company’s behalf are expressly qualified in their entirety by these cautionary statements. The Company undertakes no obligation to publicly update or revise any forward-looking statement, whether as a result of new information, future events or otherwise.
2
Arch Capital Group Ltd. and Subsidiaries
Financial Highlights
The following table presents financial highlights (1):
(U.S. Dollars in thousands, except share data)Three Months EndedNine Months Ended
September 30,September 30,
20222021Change20222021Change
Underwriting results:
Gross premiums written$3,860,683 $3,207,415 20.4 %$11,531,185 $9,602,213 20.1 %
Net premiums written2,723,774 2,075,929 31.2 %8,042,553 6,629,208 21.3 %
Net premiums earned2,470,750 1,929,337 28.1 %6,917,158 5,666,700 22.1 %
Underwriting income (loss) (2)68,797 173,745 (60.4)%1,061,768 768,129 38.2 %
Loss ratio68.1 %63.5 %4.6 54.7 %58.8 %(4.1)
Acquisition expense ratio18.1 %15.9 %2.2 17.9 %15.6 %2.3 
Other operating expense ratio11.1 %12.0 %(0.9)12.2 %12.4 %(0.2)
Combined ratio97.3 %91.4 %5.9 84.8 %86.8 %(2.0)
Net investment income$128,640 $88,195 45.9 %$315,468 $256,354 23.1 %
Per diluted share$0.34 $0.22 54.5 %$0.83 $0.63 31.7 %
Net income available to Arch common shareholders$6,917 $388,751 (98.2)%$586,693 $1,480,324 (60.4)%
Per diluted share$0.02 $0.98 (98.0)%$1.55 $3.66 (57.7)%
After-tax operating income available to Arch common shareholders (2)$105,972 $294,688 (64.0)%$1,034,467 $941,673 9.9 %
Per diluted share$0.28 $0.74 (62.2)%$2.73 $2.33 17.2 %
Comprehensive income (loss) available to Arch$(616,461)$239,078 (357.8)%$(1,209,982)$1,093,872 (210.6)%
Net cash provided by operating activities$1,379,749 $1,014,979 35.9 %$2,833,717 $2,580,697 9.8 %
Weighted average common shares and common share equivalents outstanding — diluted373,727,277 397,903,347 (6.1)%378,373,180 404,260,485 (6.4)%
Financial measures:      
Change in book value per common share during period(5.4)%1.3 %(6.7)(11.5)%7.0 %(18.5)
Annualized net income return on average common equity0.2 %12.3 %(12.1)6.6 %15.9 %(9.3)
Annualized operating return on average common equity (2)3.8 %9.3 %(5.5)11.6 %10.1 %1.5 
Total return on investments (3)(3.01)%0.01 %-302 bps(8.83)%1.50 %-1033 bps
 
(1)Presented on a ‘core’ basis which excludes amounts related to the ‘other’ segment (i.e., results of Somers). See ‘Comments on Regulation G’ for a further discussion of the presentation of ‘core’ results.
(2)See ‘Comments on Regulation G’ for a further discussion of consolidated underwriting income or loss, after-tax operating income or loss available to Arch common shareholders and annualized operating return on average common equity.
(3)Total return on investments includes investment income, equity in net income (loss) of investment funds accounted for using the equity method, net realized gains and losses and the change in unrealized gains and losses and is calculated on a pre-tax basis and before investment expenses. See ‘Comments on Regulation G’ for a further discussion of the presentation of total return on investments.
3
Arch Capital Group Ltd. and Subsidiaries
Consolidated Statements of Income
(U.S. Dollars in thousands, except share data)Three Months EndedNine Months Ended
 September 30,June 30,March 31,December 31,September 30,September 30,September 30,
 2022202220222021202120222021
Revenues       
Net premiums earned$2,470,750 $2,325,775 $2,120,633 $2,083,630 $1,929,337 $6,917,158 $5,998,668 
Net investment income128,640 106,392 80,436 90,454 88,195 315,468 298,664 
Net realized gains (losses)(183,673)(266,579)(292,414)59,517 (25,040)(742,666)320,328 
Other underwriting income3,077 2,970 5,897 3,160 7,274 11,944 18,913 
Equity in net income (loss) of investment funds accounted for using the equity method(18,861)58,061 36,305 67,132 105,398 75,505 299,270 
Other income (loss)(13,684)(11,777)(9,025)9,093 (3,960)(34,486)1,151 
Total revenues2,386,249 2,214,842 1,941,832 2,312,986 2,101,204 6,542,923 6,936,994 
Expenses
Losses and loss adjustment expenses(1,682,696)(1,102,656)(1,000,835)(995,853)(1,226,019)(3,786,187)(3,588,950)
Acquisition expenses(447,587)(413,319)(378,159)(357,539)(306,015)(1,239,065)(945,639)
Other operating expenses(274,747)(277,392)(289,943)(261,787)(230,832)(842,082)(736,808)
Corporate expenses(17,710)(27,620)(32,332)(18,150)(19,672)(77,662)(61,007)
Amortization of intangible assets(26,104)(27,207)(27,167)(33,132)(20,135)(80,478)(49,823)
Interest expense(33,063)(32,795)(32,708)(32,248)(33,176)(98,566)(107,222)
Net foreign exchange gains (losses)90,509 87,775 3,845 3,163 36,078 182,129 38,366 
Total expenses(2,391,398)(1,793,214)(1,757,299)(1,695,546)(1,799,771)(5,941,911)(5,451,083)
Income (loss) before income taxes and income (loss) from operating affiliates(5,149)421,628 184,533 617,440 301,433 601,012 1,485,911 
Income tax (expense) benefit14,900 (22,323)(11,619)(34,406)(4,137)(19,042)(94,176)
Income (loss) from operating affiliates8,507 4,640 24,518 40,641 124,119 37,665 224,052 
Net income (loss)18,258 403,945 197,432 623,675 421,415 619,635 1,615,787 
Net (income) loss attributable to noncontrolling interests(1,157)399 (1,632)(410)(1,473)(2,390)(82,203)
Net income (loss) attributable to Arch17,101 404,344 195,800 623,265 419,942 617,245 1,533,584 
Preferred dividends(10,184)(10,184)(10,184)(10,184)(16,090)(30,552)(38,159)
Loss on redemption of preferred shares— — — — (15,101)— (15,101)
Net income (loss) available to Arch common shareholders$6,917 $394,160 $185,616 $613,081 $388,751 $586,693 $1,480,324 
Comprehensive income (loss) available to Arch$(616,461)$(204,476)$(389,045)$509,482 $239,078 $(1,209,982)$1,093,872 
Net income (loss) per common share and common share equivalent
Basic$0.02 $1.07 $0.50 $1.62 $1.00 $1.59 $3.74 
Diluted$0.02 $1.04 $0.48 $1.58 $0.98 $1.55 $3.66 
Weighted average common shares and common share equivalents outstanding
Basic365,190,527 369,241,193 374,243,812 379,431,442 389,274,220 369,525,348 395,899,591 
Diluted373,727,277 377,952,988 384,194,363 388,869,378 397,903,347 378,373,180 404,260,485 



4
Arch Capital Group Ltd. and Subsidiaries
Consolidated Balance Sheets

(U.S. Dollars in thousands, except share data)September 30,June 30,March 31,December 31,September 30,
20222022202220212021
Assets     
Investments:     
Fixed maturities available for sale, at fair value$18,120,727 $17,585,029 $17,648,853 $17,998,109 $16,768,363 
Short-term investments available for sale, at fair value1,940,857 2,227,874 2,332,624 1,734,716 3,069,965 
Equity securities, at fair value809,869 772,689 1,002,572 1,804,170 1,790,640 
Other investments1,578,751 1,634,368 1,686,666 1,973,550 2,043,970 
Investments accounted for using the equity method3,565,946 3,496,341 3,325,543 3,077,611 2,741,293 
Total investments26,016,150 25,716,301 25,996,258 26,588,156 26,414,231 
Cash813,583 813,548 812,917 858,668 1,137,721 
Accrued investment income116,263 116,102 82,607 85,453 75,832 
Investment in operating affiliates891,212 967,603 1,144,255 1,135,655 1,111,825 
Premiums receivable3,579,380 3,634,182 3,223,504 2,633,280 2,807,720 
Reinsurance recoverable on unpaid and paid losses and loss adjustment expenses6,356,456 5,938,511 5,941,000 5,880,735 5,358,852 
Contractholder receivables1,735,730 1,758,018 1,810,199 1,828,691 1,824,990 
Ceded unearned premiums2,115,539 2,123,915 1,951,960 1,729,455 1,824,910 
Deferred acquisition costs1,122,711 1,069,845 1,001,866 901,841 893,665 
Receivable for securities sold27,042 157,329 116,633 60,179 84,019 
Goodwill and intangible assets806,655 868,014 926,427 944,983 963,322 
Other assets2,756,383 2,555,826 2,670,315 2,453,849 2,286,649 
Total assets$46,337,104 $45,719,194 $45,677,941 $45,100,945 $44,783,736 
Liabilities     
Reserve for losses and loss adjustment expenses$19,288,291 $18,194,324 $18,109,107 $17,757,156 $17,331,047 
Unearned premiums7,271,279 7,145,297 6,737,779 6,011,942 6,165,114 
Reinsurance balances payable1,669,592 1,634,700 1,510,906 1,583,253 1,403,929 
Contractholder payables1,738,089 1,761,023 1,813,930 1,832,127 1,828,474 
Collateral held for insured obligations254,720 251,063 244,502 242,352 254,259 
Senior notes2,725,153 2,724,896 2,724,642 2,724,394 2,724,149 
Payable for securities purchased174,769 292,106 176,452 64,850 357,531 
Other liabilities1,411,193 1,289,760 1,431,271 1,329,742 1,321,470 
Total liabilities34,533,086 33,293,169 32,748,589 31,545,816 31,385,973 
Redeemable noncontrolling interests8,908 8,459 9,763 9,233 10,237 
Shareholders’ equity     
Non-cumulative preferred shares830,000 830,000 830,000 830,000 830,000 
Common shares652 652 651 648 648 
Additional paid-in capital2,186,599 2,170,661 2,134,241 2,085,075 2,061,906 
Retained earnings15,042,561 15,035,644 14,641,484 14,455,868 13,842,787 
Accumulated other comprehensive income (loss), net of deferred income tax(1,891,827)(1,258,265)(649,445)(64,600)49,184 
Common shares held in treasury, at cost(4,372,875)(4,361,126)(4,037,342)(3,761,095)(3,396,999)
Total shareholders’ equity11,795,110 12,417,566 12,919,589 13,545,896 13,387,526 
Total liabilities, noncontrolling interests and shareholders’ equity$46,337,104 $45,719,194 $45,677,941 $45,100,945 $44,783,736 
Common shares and common share equivalents outstanding, net of treasury shares369,321,990 369,346,815 375,730,891 378,923,894 387,257,752 
Book value per common share (1)$29.69 $31.37 $32.18 $33.56 $32.43 
(1) Excludes the effects of stock options and restricted stock units outstanding.
5
Arch Capital Group Ltd. and Subsidiaries
Consolidated Statements of Changes in Shareholders’ Equity

(U.S. Dollars in thousands)Three Months EndedNine Months Ended
 September 30,June 30,March 31,December 31,September 30,September 30,September 30,
 2022202220222021202120222021
Non-cumulative preferred shares       
Balance at beginning of period$830,000 $830,000 $830,000 $830,000 $1,280,000 $830,000 $780,000 
Preferred shares issued— — — — — — 500,000 
Preferred shares redeemed— — — — (450,000)— (450,000)
Balance at beginning and end of period$830,000 $830,000 $830,000 $830,000 $830,000 $830,000 $830,000 
Common shares
Balance at beginning of period652 651 648 648 647 648 643 
Common shares issued, net— 1 3 — 1 4 5 
Balance at end of period652 652 651 648 648 652 648 
Additional paid-in capital
Balance at beginning of period2,170,661 2,134,241 2,085,075 2,061,906 2,028,919 2,085,075 1,977,794 
Issue costs on preferred shares— — — — — — (14,179)
Reversal of original issue costs on redeemed preferred shares— — — — 15,101 — 15,101 
Amortization of share-based compensation13,518 21,137 45,368 14,774 14,216 80,023 71,279 
All other2,420 15,283 3,798 8,395 3,670 21,501 11,911 
Balance at end of period2,186,599 2,170,661 2,134,241 2,085,075 2,061,906 2,186,599 2,061,906 
Retained earnings
Balance at beginning of period15,035,644 14,641,484 14,455,868 13,842,787 13,454,036 14,455,868 12,362,463 
Net income18,258 403,945 197,432 623,675 421,415 619,635 1,615,787 
Amounts attributable to noncontrolling interests(1,157)399 (1,632)(410)(1,473)(2,390)(82,203)
Preferred share dividends(10,184)(10,184)(10,184)(10,184)(16,090)(30,552)(38,159)
Loss on redemption of preferred shares— — — — (15,101)— (15,101)
Balance at end of period15,042,561 15,035,644 14,641,484 14,455,868 13,842,787 15,042,561 13,842,787 
Accumulated other comprehensive income (loss), net of deferred income tax
Balance at beginning of period(1,258,265)(649,445)(64,600)49,184 230,048 (64,600)488,895 
Change in unrealized appreciation (decline) in value of available-for-sale investments(563,174)(540,295)(582,077)(103,391)(147,825)(1,685,546)(384,418)
Change in foreign currency translation adjustments(70,388)(68,525)(2,768)(10,393)(33,039)(141,681)(55,293)
Balance at end of period(1,891,827)(1,258,265)(649,445)(64,600)49,184 (1,891,827)49,184 
Common shares held in treasury, at cost
Balance at beginning of period(4,361,126)(4,037,342)(3,761,095)(3,396,999)(3,007,578)(3,761,095)(2,503,909)
Shares repurchased for treasury(11,749)(323,784)(276,247)(364,096)(389,421)(611,780)(893,090)
Balance at end of period(4,372,875)(4,361,126)(4,037,342)(3,761,095)(3,396,999)(4,372,875)(3,396,999)
Total shareholders’ equity$11,795,110 $12,417,566 $12,919,589 $13,545,896 $13,387,526 $11,795,110 $13,387,526 

6
Arch Capital Group Ltd. and Subsidiaries
Consolidated Statements of Cash Flows
(U.S. Dollars in thousands)Three Months EndedNine Months Ended
September 30,June 30,March 31,December 31,September 30,September 30,September 30,
2022202220222021202120222021
Operating Activities       
Net income (loss)$18,258 $403,945 $197,432 $623,675 $421,415 $619,635 $1,615,787 
Adjustments to reconcile net income to net cash provided by operating activities:
Net realized (gains) losses187,407 266,060 289,213 (60,054)11,736 742,680 (367,313)
Equity in net (income) or loss of investment. funds accounted for using the equity method and other income or loss62,590 55,235 (11,420)(91,400)(191,622)106,405 (372,650)
Amortization of intangible assets26,104 27,207 27,167 33,132 20,135 80,478 49,823 
Share-based compensation13,511 21,139 45,379 14,791 14,739 80,029 72,303 
Changes in:
Reserve for losses and loss adjustment expenses, net918,602 358,528 275,954 213,979 599,706 1,553,084 1,548,211 
Unearned premiums, net253,024 358,864 513,507 (49,203)146,592 1,125,395 985,242 
Premiums receivable(9,951)(485,099)(600,691)161,884 (65,707)(1,095,741)(847,098)
Deferred acquisition costs(68,466)(76,912)(96,999)(15,277)(33,073)(242,377)(247,966)
Reinsurance balances payable56,323 146,117 (74,022)(118,506)287,110 128,418 618,571 
Other items, net(77,653)(172,679)(13,957)86,983 (196,052)(264,289)(427,359)
Net cash provided by operating activities1,379,749 902,405 551,563 800,004 1,014,979 2,833,717 2,627,551 
Investing Activities       
Purchases of fixed maturity investments(3,359,345)(2,978,292)(6,727,665)(5,581,835)(6,315,639)(13,065,302)(29,870,023)
Purchases of equity securities(131,160)(246,958)(408,615)(196,529)(358,177)(786,733)(978,951)
Purchases of other investments(349,715)(303,725)(616,659)(509,040)(316,922)(1,270,099)(1,350,056)
Proceeds from sales of fixed maturity investments1,911,450 2,025,616 6,053,352 3,509,653 6,937,404 9,990,418 30,067,792 
Proceeds from sales of equity securities49,596 389,956 1,100,256 222,512 153,343 1,539,808 695,633 
Proceeds from sales, redemptions and maturities of other investments212,346 292,992 570,341 277,614 715,370 1,075,679 1,487,919 
Proceeds from redemptions and maturities of fixed maturity investments133,791 203,320 240,753 394,343 428,576 577,864 1,234,412 
Net settlements of derivative instruments(61,509)(42,328)(2,510)27,758 (85,116)(106,347)(67,830)
Net (purchases) sales of short-term investments288,012 70,760 (510,752)1,338,070 (794,712)(151,980)(1,172,798)
Change in cash collateral related to securities lending— — — — 826 — — 
Purchase of operating affiliate, net— — — — (207,567)— (753,916)
Impact of the deconsolidation of a variable interest entity— — — — (349,202)— (349,202)
Purchases of fixed assets(14,553)(12,060)(11,770)(6,987)(10,822)(38,383)(34,407)
Other29,968 97,836 550 (162,007)(156,968)128,354 (361,857)
Net cash provided by (used for) investing activities(1,291,119)(502,883)(312,719)(686,448)(359,606)(2,106,721)(1,453,284)
Financing Activities       
Proceeds from issuance of preferred shares, net— — — — — — 485,821 
Redemption of preferred shares— — — — (450,000)— (450,000)
Purchases of common shares under share repurchase program(10,147)(320,688)(254,988)(362,097)(386,882)(585,823)(872,197)
Proceeds from common shares issued, net1,202 13,195 (17,260)6,137 96 (2,863)281 
Change in cash collateral related to securities lending— — — — (826)— — 
Change in third party investment in non-redeemable noncontrolling interests— — — — — — 15,971 
Dividends paid to redeemable noncontrolling interests— — — — — — (1,907)
Other(2,632)(130,866)48,859 18,474 (49,391)(84,639)(21,752)
Preferred dividends paid(10,184)(10,184)(10,184)(10,184)(17,291)(30,552)(38,096)
Net cash provided by (used for) financing activities(21,761)(448,543)(233,573)(347,670)(904,294)(703,877)(881,879)
Effects of exchange rate changes on foreign currency cash and restricted cash(36,776)(38,866)(3,924)(24)(20,633)(79,566)(34,023)
Increase (decrease) in cash and restricted cash30,093 (87,887)1,347 (234,138)(269,554)(56,447)258,365 
Cash and restricted cash, beginning of period1,228,231 1,316,118 1,314,771 1,548,909 1,818,463 1,314,771 1,290,544 
Cash and restricted cash, end of period$1,258,324 $1,228,231 $1,316,118 $1,314,771 $1,548,909 $1,258,324 $1,548,909 
Income taxes paid (received)$72,930 $119,616 $9,005 $84,371 $61,343 $201,551 $202,439 
Interest paid$416 $63,948 $648 $63,498 $1,104 $65,012 $75,803 
Net cash provided by operating activities, excluding the ‘other’ segment$1,379,749 $902,405 $551,563 $800,004 $1,014,979 $2,833,717 $2,580,697 
7
Arch Capital Group Ltd. and Subsidiaries
Segment Information — Overview


The Company classifies its businesses into three underwriting segments — insurance, reinsurance and mortgage — and two other operating segments — ‘other’ and corporate segment. The Company’s Insurance, Reinsurance and Mortgage segments each have 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 Chief Executive Officer of Arch, the Chief Financial Officer and Treasurer of Arch and the President and Chief Underwriting Officer of Arch. The chief operating decision makers do not assess performance, measure return on equity or make resource allocation decisions on a line of business basis. Management measures segment performance for its three core underwriting segments based on underwriting income or loss. The Company does not manage its assets by underwriting segment and, accordingly, investment income is not allocated to each underwriting segment.

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. 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.

Insurance Segment

The insurance segment consists of the Company’s insurance underwriting units which offer specialty product lines on a worldwide basis. Product lines include:

•    Construction and national accounts: primary and excess casualty coverages to middle and large accounts in the construction industry and a wide range of products for middle and large national accounts, specializing in loss sensitive primary casualty insurance programs (including large deductible, self-insured retention and retrospectively rated programs).
•    Excess and surplus casualty: primary and excess casualty insurance coverages, including middle market energy business, and contract binding, which primarily provides casualty coverage through a network of appointed agents to small and medium risks.
•    Lenders products: collateral protection, debt cancellation and service contract reimbursement products to banks, credit unions, automotive dealerships and original equipment manufacturers and other specialty programs that pertain to automotive lending and leasing.
•    Professional lines: directors’ and officers’ liability, errors and omissions liability, employment practices liability, fiduciary liability, crime, professional indemnity and other financial related coverages for corporate, private equity, venture capital, real estate investment trust, limited partnership, financial institution and not-for-profit clients of all sizes, cyber insurance, and medical professional and general liability insurance coverages for the healthcare industry. The business is predominately written on a claims-made basis.
•    Programs: primarily package policies, underwriting workers’ compensation and umbrella liability business in support of desirable package programs, targeting program managers with unique expertise and niche products offering general liability, commercial automobile, inland marine and property business with minimal catastrophe exposure.
•    Property, energy, marine and aviation: primary and excess general property insurance coverages, including catastrophe-exposed property coverage, for commercial clients. Coverages for marine include hull, war, specie and liability. Aviation and stand alone terrorism are also offered.
•    Travel, accident and health: specialty travel and accident and related insurance products for individual, group travelers, travel agents and suppliers, as well as accident and health, which provides accident, disability and medical plan insurance coverages for employer groups, medical plan members, students and other participant groups.
•    Other: includes alternative market risks (including captive insurance programs), excess workers’ compensation and employer’s liability insurance coverages for qualified self-insured groups, associations and trusts, and contract and commercial surety coverages, including contract bonds (payment and performance bonds) primarily for medium and large contractors and commercial surety bonds for Fortune 1,000 companies and smaller transaction business programs.
8
Arch Capital Group Ltd. and Subsidiaries
Segment Information — Overview

Reinsurance Segment
The reinsurance segment consists of the Company’s reinsurance underwriting units which offer specialty product lines on a worldwide basis. Reinsurance agreements are typically offered on a proportional and/or excess of loss basis and provide coverage to ceding company clients for specific underlying written policies. Product lines include:
•Casualty: provides coverage on third party liability exposures including, among others, executive assurance, professional liability, excess and umbrella liability, excess motor and healthcare business, and workers’ compensation. Business is assumed primarily on a treaty basis, with some facultative coverages also offered.
•Marine and aviation: provides coverage for energy, hull, cargo, specie, liability and transit, and aviation business, including airline and general aviation risks. Business written may also include space business, which includes coverages for satellite assembly, launch and operation for commercial space programs.
•Other specialty: provides coverage for proportional motor reinsurance, whole account multi-line treaties, cyber, trade credit and surety, accident and health, workers’ compensation catastrophe, agriculture and political risk, among others.
•Property catastrophe: provides protection for most types of catastrophic losses, including hurricane, earthquake, flood, tornado, hail and fire, and for other perils on a case-by-case basis. Excess of loss coverages are triggered when aggregate losses and loss adjustment expense from a single occurrence of a covered peril exceed the retention specified in the contract.
•Property excluding property catastrophe: provides coverage for personal lines and/or commercial property exposures and principally covers buildings, structures, equipment and contents. The primary perils in this business include fire, explosion, collapse, riot, vandalism, wind, tornado, flood and earthquake. Business is assumed on either a treaty or facultative basis.
•Other: includes life reinsurance business, casualty clash business and, in limited instances, non-traditional business which is intended to provide insurers with risk management solutions that complement traditional reinsurance.
Mortgage Segment
The mortgage segment includes the Company’s underwriting units which offer mortgage insurance and reinsurance products on a worldwide basis. Underwriting units include:
•U.S. primary mortgage insurance: offers private mortgage insurance through Arch Mortgage Insurance Company and United Guaranty Residential Insurance Company (combined “Arch MI U.S.”), both approved eligible mortgage insurers by Fannie Mae and Freddie Mac. Arch MI U.S. also includes Arch Mortgage Guaranty Company, which is not a government sponsored enterprise (“GSE”) approved entity.
•U.S. credit risk transfer (“CRT”) and other: underwrites CRT transactions, which are predominantly with GSEs, and other U.S. reinsurance transactions.
•International mortgage insurance/reinsurance: underwrites mortgage insurance and reinsurance outside of the U.S.
Corporate Segment
The corporate segment results include net investment income, net realized gains or losses (which includes changes in the allowance for credit losses on financial assets and net impairment losses recognized in earnings), equity in net income or loss of investment funds accounted for using the equity method, other income (loss), corporate expenses, transaction costs and other, amortization of intangible assets, interest expense, net foreign exchange gains or losses, income taxes items, income or loss from operating affiliates and items related to the Company’s non-cumulative preferred shares. Such amounts exclude the results of the ‘other’ segment.
Other Segment
Through June 30, 2021, the ‘other’ segment included the results of Somers. Pursuant to GAAP, Somers was considered a variable interest entity and the Company concluded that it was the primary beneficiary of Somers. As such, the Company consolidated the results of Somers in its consolidated financial statements through June 30, 2021. The portion of Somers’ earnings attributable to third party investors was recorded in the consolidated statements of income as ‘amounts attributable to noncontrolling interests.’ Management measures segment performance for the ‘other’ segment based on net income or loss. In July 2021, the Company announced the completion of the previously disclosed acquisition of Somers by Greysbridge. Based on the governing documents of Greysbridge, the Company has concluded that, while it retains significant influence over Somers, Somers no longer constitutes a variable interest entity. Accordingly, effective July 1, 2021, Arch no longer consolidates the results of Somers in its consolidated financial statements.

9
Arch Capital Group Ltd. and Subsidiaries
Segment Information
(U.S. Dollars in thousands)Three Months Ended
September 30, 2022
 InsuranceReinsuranceMortgageSub-total (Core)OtherTotal
Gross premiums written (1)$1,862,026 $1,639,061 $362,409 $3,860,683 $— $3,860,683 
Premiums ceded(493,267)(560,225)(86,230)(1,136,909)— (1,136,909)
Net premiums written1,368,759 1,078,836 276,179 2,723,774 — 2,723,774 
Change in unearned premiums(181,851)(77,062)5,889 (253,024)— (253,024)
Net premiums earned1,186,908 1,001,774 282,068 2,470,750 — 2,470,750 
Other underwriting income (loss)— 452 2,625 3,077 — 3,077 
Losses and loss adjustment expenses(822,663)(927,911)67,878 (1,682,696)— (1,682,696)
Acquisition expenses(232,469)(208,425)(6,693)(447,587)— (447,587)
Other operating expenses(165,499)(62,777)(46,471)(274,747)— (274,747)
Underwriting income (loss)$(33,723)$(196,887)$299,407 68,797 — 68,797 
Net investment income128,640 — 128,640 
Net realized gains (losses)(183,673)— (183,673)
Equity in net income (loss) of investment funds accounted for using the equity method(18,861)— (18,861)
Other income (loss)(13,684)— (13,684)
Corporate expenses (2)(17,634)— (17,634)
Transaction costs and other (2)(76)— (76)
Amortization of intangible assets(26,104)— (26,104)
Interest expense(33,063)— (33,063)
Net foreign exchange gains (losses)90,509 — 90,509 
Income (loss) before income taxes and income (loss) from operating affiliates(5,149)— (5,149)
Income tax (expense) benefit14,900 — 14,900 
Income (loss) from operating affiliates8,507 — 8,507 
Net income (loss)18,258 — 18,258 
Dividends attributable to redeemable noncontrolling interests(1,157)— (1,157)
Net income (loss) available to Arch17,101 — 17,101 
Preferred dividends(10,184)— (10,184)
Net income (loss) available to Arch common shareholders$6,917 $— $6,917 
Underwriting Ratios
Loss ratio69.3 %92.6 %(24.1)%68.1 %— %68.1 %
Acquisition expense ratio19.6 %20.8 %2.4 %18.1 %— %18.1 %
Other operating expense ratio13.9 %6.3 %16.5 %11.1 %— %11.1 %
Combined ratio102.8 %119.7 %(5.2)%97.3 %— %97.3 %
Net premiums written to gross premiums written73.5 %65.8 %76.2 %70.6 %— %70.6 %
Total investable assets$26,682,006 $— $26,682,006 
Total assets46,337,104 — 46,337,104 
Total liabilities34,533,086 — 34,533,086 
(1)    Certain amounts included in the gross premiums written of each segment are related to intersegment transactions and are included in the gross premiums written of each segment. 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.
(2)    Certain expenses have been excluded from ‘corporate expenses’ and reflected in ‘Transaction costs and other.’ See ‘Comments on Regulation G’ for a further discussion of such items.
10
Arch Capital Group Ltd. and Subsidiaries
Segment Information
(U.S. Dollars in thousands)Three Months Ended
September 30, 2021
 InsuranceReinsuranceMortgageSub-total (Core)OtherTotal
Gross premiums written (1)$1,596,619 $1,251,760 $360,934 $3,207,415 $— $3,207,415 
Premiums ceded(442,806)(630,371)(60,207)(1,131,486)— (1,131,486)
Net premiums written1,153,813 621,389 300,727 2,075,929 — 2,075,929 
Change in unearned premiums(215,143)57,313 11,238 (146,592)— (146,592)
Net premiums earned938,670 678,702 311,965 1,929,337 — 1,929,337 
Other underwriting income (loss)— 3,293 3,981 7,274 — 7,274 
Losses and loss adjustment expenses(668,630)(545,846)(11,543)(1,226,019)— (1,226,019)
Acquisition expenses(152,467)(129,450)(24,098)(306,015)— (306,015)
Other operating expenses(138,931)(45,647)(46,254)(230,832)— (230,832)
Underwriting income (loss)$(21,358)$(38,948)$234,051 173,745 — 173,745 
Net investment income88,195 — 88,195 
Net realized gains (losses)(25,040)— (25,040)
Equity in net income (loss) of investment funds accounted for using the equity method105,398 — 105,398 
Other income (loss)(3,960)— (3,960)
Corporate expenses (2)(18,636)— (18,636)
Transaction costs and other (2)(1,036)— (1,036)
Amortization of intangible assets(20,135)— (20,135)
Interest expense(33,176)— (33,176)
Net foreign exchange gains (losses)36,078 — 36,078 
Income (loss) before income taxes and income (loss) from operating affiliates301,433 — 301,433 
Income tax (expense) benefit(4,137)— (4,137)
Income (loss) from operating affiliates124,119 — 124,119 
Net income (loss)421,415 — 421,415 
Dividends attributable to redeemable noncontrolling interests(1,473)— (1,473)
Net income (loss) available to Arch419,942 — 419,942 
Preferred dividends(16,090)— (16,090)
Net income (loss) available to Arch common shareholders$388,751 $— $388,751 
Underwriting Ratios
Loss ratio71.2 %80.4 %3.7 %63.5 %— %63.5 %
Acquisition expense ratio16.2 %19.1 %7.7 %15.9 %— %15.9 %
Other operating expense ratio14.8 %6.7 %14.8 %12.0 %— %12.0 %
Combined ratio102.2 %106.2 %26.2 %91.4 %— %91.4 %
Net premiums written to gross premiums written72.3 %49.6 %83.3 %64.7 %— %64.7 %
Total investable assets$27,278,440 $— $27,278,440 
Total assets44,783,736 — 44,783,736 
Total liabilities31,385,973 — 31,385,973 
 
(1)    Certain amounts included in the gross premiums written of each segment are related to intersegment transactions and are included in the gross premiums written of each segment. 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.
(2)    Certain expenses have been excluded from ‘corporate expenses’ and reflected in ‘Transaction costs and other.’ See ‘Comments on Regulation G’ for a further discussion of such items.
11
Arch Capital Group Ltd. and Subsidiaries
Segment Information
(U.S. Dollars in thousands)Nine Months Ended
September 30, 2022
 InsuranceReinsuranceMortgageSub-total (Core)OtherTotal
Gross premiums written (1)$5,286,798 $5,151,401 $1,099,144 $11,531,185 $— $11,531,185 
Premiums ceded(1,482,886)(1,770,807)(241,097)(3,488,632)— (3,488,632)
Net premiums written3,803,912 3,380,594 858,047 8,042,553 — 8,042,553 
Change in unearned premiums(488,164)(646,421)9,190 (1,125,395)— (1,125,395)
Net premiums earned3,315,748 2,734,173 867,237 6,917,158 — 6,917,158 
Other underwriting income (loss)— 5,814 6,130 11,944 — 11,944 
Losses and loss adjustment expenses(2,053,161)(1,920,189)187,163 (3,786,187)— (3,786,187)
Acquisition expenses(641,807)(569,915)(27,343)(1,239,065)— (1,239,065)
Other operating expenses(493,412)(198,606)(150,064)(842,082)— (842,082)
Underwriting income (loss)$127,368 $51,277 $883,123 1,061,768 — 1,061,768 
Net investment income315,468 — 315,468 
Net realized gains (losses)(742,666)— (742,666)
Equity in net income (loss) of investment funds accounted for using the equity method75,505 — 75,505 
Other income (loss)(34,486)— (34,486)
Corporate expenses (2)(76,928)— (76,928)
Transaction costs and other (2)(734)— (734)
Amortization of intangible assets(80,478)— (80,478)
Interest expense(98,566)— (98,566)
Net foreign exchange gains (losses)182,129 — 182,129 
Income (loss) before income taxes and income (loss) from operating affiliates601,012 — 601,012 
Income tax (expense) benefit(19,042)— (19,042)
Income (loss) from operating affiliates37,665 — 37,665 
Net income (loss)619,635 — 619,635 
Dividends attributable to redeemable noncontrolling interests(2,390)— (2,390)
Net income (loss) available to Arch617,245 — 617,245 
Preferred dividends(30,552)— (30,552)
Net income (loss) available to Arch common shareholders$586,693 $— $586,693 
Underwriting Ratios
Loss ratio61.9 %70.2 %(21.6)%54.7 %— %54.7 %
Acquisition expense ratio19.4 %20.8 %3.2 %17.9 %— %17.9 %
Other operating expense ratio14.9 %7.3 %17.3 %12.2 %— %12.2 %
Combined ratio96.2 %98.3 %(1.1)%84.8 %— %84.8 %
Net premiums written to gross premiums written72.0 %65.6 %78.1 %69.7 %— %69.7 %
 
(1)    Certain amounts included in the gross premiums written of each segment are related to intersegment transactions and are included in the gross premiums written of each segment. 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.
(2)    Certain expenses have been excluded from ‘corporate expenses’ and reflected in ‘Transaction costs and other.’ See ‘Comments on Regulation G’ for a further discussion of such items.
12
Arch Capital Group Ltd. and Subsidiaries
Segment Information
(U.S. Dollars in thousands)Nine Months Ended
September 30, 2021
 InsuranceReinsuranceMortgageSub-total (Core)OtherTotal
Gross premiums written (1)$4,381,372 $4,080,840 $1,143,691 $9,602,213 $457,465 $9,890,912 
Premiums ceded(1,269,165)(1,535,607)(171,923)(2,973,005)(102,763)(2,907,002)
Net premiums written3,112,207 2,545,233 971,768 6,629,208 354,702 6,983,910 
Change in unearned premiums(488,636)(484,607)10,735 (962,508)(22,734)(985,242)
Net premiums earned2,623,571 2,060,626 982,503 5,666,700 331,968 5,998,668 
Other underwriting income (loss)— 3,148 15,026 18,174 739 18,913 
Losses and loss adjustment expenses(1,750,257)(1,494,539)(85,112)(3,329,908)(259,042)(3,588,950)
Acquisition expenses(417,541)(381,060)(84,297)(882,898)(62,741)(945,639)
Other operating expenses(409,386)(150,856)(143,697)(703,939)(32,869)(736,808)
Underwriting income (loss)$46,387 $37,319 $684,423 768,129 (21,945)746,184 
Net investment income256,354 42,310 298,664 
Net realized gains (losses)239,690 80,638 320,328 
Equity in net income (loss) of investment funds accounted for using the equity method299,270 — 299,270 
Other income (loss)1,151 — 1,151 
Corporate expenses (2)(59,279)— (59,279)
Transaction costs and other (2)(793)(935)(1,728)
Amortization of intangible assets(48,925)(898)(49,823)
Interest expense(98,812)(8,410)(107,222)
Net foreign exchange gains (losses)39,691 (1,325)38,366 
Income (loss) before income taxes and income (loss) from operating affiliates1,396,476 89,435 1,485,911 
Income tax (expense) benefit(93,942)(234)(94,176)
Income (loss) from operating affiliates224,052 — 224,052 
Net income (loss)1,526,586 89,201 1,615,787 
Dividends attributable to redeemable noncontrolling interests(1,936)(1,953)(3,889)
Amounts attributable to nonredeemable noncontrolling interests— (78,314)(78,314)
Net income (loss) available to Arch1,524,650 8,934 1,533,584 
Preferred dividends(38,159)— (38,159)
Loss on redemption of preferred shares(15,101)— (15,101)
Net income (loss) available to Arch common shareholders$1,471,390 $8,934 $1,480,324 
Underwriting Ratios
Loss ratio66.7 %72.5 %8.7 %58.8 %78.0 %59.8 %
Acquisition expense ratio15.9 %18.5 %8.6 %15.6 %18.9 %15.8 %
Other operating expense ratio15.6 %7.3 %14.6 %12.4 %9.9 %12.3 %
Combined ratio98.2 %98.3 %31.9 %86.8 %106.8 %87.9 %
Net premiums written to gross premiums written71.0 %62.4 %85.0 %69.0 %77.5 %70.6 %
 
(1)    Certain amounts included in the gross premiums written of each segment are related to intersegment transactions and are included in the gross premiums written of each segment. 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.
(2)    Certain expenses have been excluded from ‘corporate expenses’ and reflected in ‘Transaction costs and other.’ See ‘Comments on Regulation G’ for a further discussion of such items.

13
Arch Capital Group Ltd. and Subsidiaries
Segment Information — Insurance Segment
(U.S. Dollars in thousands)Three Months EndedNine Months Ended
 September 30,June 30,March 31,December 31,September 30,September 30,September 30,
 2022202220222021202120222021
Gross premiums written$1,862,026 $1,705,167 $1,719,605 $1,486,362 $1,596,619 $5,286,798 $4,381,372 
Premiums ceded(493,267)(476,910)(512,709)(450,376)(442,806)(1,482,886)(1,269,165)
Net premiums written1,368,759 1,228,257 1,206,896 1,035,986 1,153,813 3,803,912 3,112,207 
Change in unearned premiums(181,851)(126,113)(180,200)(33,089)(215,143)(488,164)(488,636)
Net premiums earned1,186,908 1,102,144 1,026,696 1,002,897 938,670 3,315,748 2,623,571 
Losses and loss adjustment expenses(822,663)(629,759)(600,739)(594,108)(668,630)(2,053,161)(1,750,257)
Acquisition expenses(232,469)(213,688)(195,650)(188,724)(152,467)(641,807)(417,541)
Other operating expenses(165,499)(161,088)(166,825)(149,520)(138,931)(493,412)(409,386)
Underwriting income (loss)$(33,723)$97,609 $63,482 $70,545 $(21,358)$127,368 $46,387 
Underwriting Ratios
Loss ratio69.3 %57.1 %58.5 %59.2 %71.2 %61.9 %66.7 %
Acquisition expense ratio19.6 %19.4 %19.1 %18.8 %16.2 %19.4 %15.9 %
Other operating expense ratio13.9 %14.6 %16.2 %14.9 %14.8 %14.9 %15.6 %
Combined ratio102.8 %91.1 %93.8 %92.9 %102.2 %96.2 %98.2 %
Catastrophic activity and prior year development:
Current accident year catastrophic events, net of reinsurance and reinstatement premiums13.4 %1.5 %3.1 %2.0 %12.2 %6.2 %7.0 %
Net (favorable) adverse development in prior year loss reserves, net of related adjustments(0.1)%(0.4)%(0.1)%(0.3)%(0.5)%(0.2)%(0.5)%
Combined ratio excluding catastrophic activity and prior year development (1)89.5 %90.0 %90.8 %91.2 %90.5 %90.2 %91.7 %
Net premiums written to gross premiums written73.5 %72.0 %70.2 %69.7 %72.3 %72.0 %71.0 %
 
(1)See ‘Comments on Regulation G’ for further discussion.

14
Arch Capital Group Ltd. and Subsidiaries
Segment Information — Insurance Segment
(U.S. Dollars in thousands)Three Months EndedNine Months Ended
 September 30,June 30,March 31,December 31,September 30,September 30,September 30,
 2022202220222021202120222021
Net premiums written
Professional Lines$412,173 30.1 %$349,402 28.4 %$347,841 28.8 %$373,752 36.1 %$310,185 26.9 %$1,109,416 29.2 %$803,392 25.8 %
Property, energy, marine and aviation241,357 17.6 %245,724 20.0 %200,661 16.6 %158,120 15.3 %205,021 17.8 %687,742 18.1 %564,462 18.1 %
Programs189,263 13.8 %163,339 13.3 %129,401 10.7 %92,002 8.9 %196,048 17.0 %482,003 12.7 %503,822 16.2 %
Excess and surplus casualty110,917 8.1 %120,509 9.8 %100,289 8.3 %101,199 9.8 %98,320 8.5 %331,715 8.7 %258,259 8.3 %
Travel, accident and health107,434 7.8 %105,970 8.6 %165,332 13.7 %79,176 7.6 %62,837 5.4 %378,736 10.0 %226,214 7.3 %
Construction and national accounts98,381 7.2 %100,656 8.2 %135,683 11.2 %98,468 9.5 %102,294 8.9 %334,720 8.8 %333,484 10.7 %
Lenders products41,889 3.1 %36,042 2.9 %25,232 2.1 %32,833 3.2 %38,905 3.4 %103,163 2.7 %114,151 3.7 %
Other167,345 12.2 %106,615 8.7 %102,457 8.5 %100,436 9.7 %140,203 12.2 %376,417 9.9 %308,423 9.9 %
Total$1,368,759 100.0 %$1,228,257 100.0 %$1,206,896 100.0 %$1,035,986 100.0 %$1,153,813 100.0 %$3,803,912 100.0 %$3,112,207 100.0 %
Underwriting location
United States$915,833 66.9 %$842,851 68.6 %$794,662 65.8 %$680,840 65.7 %$797,395 69.1 %$2,553,346 67.1 %$2,132,199 68.5 %
Europe380,063 27.8 %316,363 25.8 %357,897 29.7 %292,591 28.2 %301,877 26.2 %1,054,323 27.7 %832,601 26.8 %
Other72,863 5.3 %69,043 5.6 %54,337 4.5 %62,555 6.0 %54,541 4.7 %196,243 5.2 %147,407 4.7 %
Total$1,368,759 100.0 %$1,228,257 100.0 %$1,206,896 100.0 %$1,035,986 100.0 %$1,153,813 100.0 %$3,803,912 100.0 %$3,112,207 100.0 %
Net premiums earned
Professional Lines$341,833 28.8 %$314,115 28.5 %$289,813 28.2 %$280,041 27.9 %$249,007 26.5 %$945,761 28.5 %$662,776 25.3 %
Property, energy, marine and aviation202,483 17.1 %180,663 16.4 %174,335 17.0 %179,566 17.9 %178,167 19.0 %557,481 16.8 %488,326 18.6 %
Programs150,453 12.7 %148,681 13.5 %139,809 13.6 %137,754 13.7 %137,299 14.6 %438,943 13.2 %369,113 14.1 %
Excess and surplus casualty100,175 8.4 %98,369 8.9 %90,761 8.8 %85,713 8.5 %84,048 9.0 %289,305 8.7 %232,314 8.9 %
Travel, accident and health133,445 11.2 %130,185 11.8 %104,630 10.2 %87,212 8.7 %56,102 6.0 %368,260 11.1 %168,378 6.4 %
Construction and national accounts109,905 9.3 %98,831 9.0 %97,468 9.5 %98,510 9.8 %104,261 11.1 %306,204 9.2 %317,597 12.1 %
Lenders products33,253 2.8 %27,594 2.5 %30,588 3.0 %34,451 3.4 %33,030 3.5 %91,435 2.8 %119,507 4.6 %
Other115,361 9.7 %103,706 9.4 %99,292 9.7 %99,650 9.9 %96,756 10.3 %318,359 9.6 %265,560 10.1 %
Total$1,186,908 100.0 %$1,102,144 100.0 %$1,026,696 100.0 %$1,002,897 100.0 %$938,670 100.0 %$3,315,748 100.0 %$2,623,571 100.0 %

15
Arch Capital Group Ltd. and Subsidiaries
Segment Information — Reinsurance Segment
(U.S. Dollars in thousands)Three Months EndedNine Months Ended
 September 30,June 30,March 31,December 31,September 30,September 30,September 30,
 2022202220222021202120222021
Gross premiums written$1,639,061 $1,793,398 $1,718,942 $1,013,090 $1,251,760 $5,151,401 $4,080,840 
Premiums ceded(560,225)(630,764)(579,818)(303,949)(630,371)(1,770,807)(1,535,607)
Net premiums written1,078,836 1,162,634 1,139,124 709,141 621,389 3,380,594 2,545,233 
Change in unearned premiums(77,062)(234,635)(334,724)70,676 57,313 (646,421)(484,607)
Net premiums earned1,001,774 927,999 804,400 779,817 678,702 2,734,173 2,060,626 
Other underwriting income (loss)452 4,526 836 521 3,293 5,814 3,148 
Losses and loss adjustment expenses(927,911)(537,578)(454,700)(430,180)(545,846)(1,920,189)(1,494,539)
Acquisition expenses(208,425)(189,494)(171,996)(155,694)(129,450)(569,915)(381,060)
Other operating expenses(62,777)(66,053)(69,776)(61,954)(45,647)(198,606)(150,856)
Underwriting income (loss)$(196,887)$139,400 $108,764 $132,510 $(38,948)$51,277 $37,319 
Underwriting Ratios
Loss ratio92.6 %57.9 %56.5 %55.2 %80.4 %70.2 %72.5 %
Acquisition expense ratio20.8 %20.4 %21.4 %20.0 %19.1 %20.8 %18.5 %
Other operating expense ratio6.3 %7.1 %8.7 %7.9 %6.7 %7.3 %7.3 %
Combined ratio119.7 %85.4 %86.6 %83.1 %106.2 %98.3 %98.3 %
Catastrophic activity and prior year development:
Current accident year catastrophic events, net of reinsurance and reinstatement premiums39.1 %7.1 %6.7 %6.7 %32.6 %18.7 %18.7 %
Net (favorable) adverse development in prior year loss reserves, net of related adjustments(4.9)%(4.5)%(2.8)%(6.4)%(9.6)%(4.2)%(5.3)%
Combined ratio excluding catastrophic activity and prior year development (1)85.5 %82.8 %82.7 %82.8 %83.2 %83.8 %84.9 %
Net premiums written to gross premiums written65.8 %64.8 %66.3 %70.0 %49.6 %65.6 %62.4 %
 
(1)See ‘Comments on Regulation G’ for further discussion.



16
Arch Capital Group Ltd. and Subsidiaries
Segment Information — Reinsurance Segment
(U.S. Dollars in thousands)Three Months EndedNine Months Ended
 September 30,June 30,March 31,December 31,September 30,September 30,September 30,
 2022202220222021202120222021
Net premiums written
Other Specialty$381,004 35.3 %$434,710 37.4 %$363,834 31.9 %$207,812 29.3 %$167,006 26.9 %$1,179,548 34.9 %$747,662 29.4 %
Property excluding property catastrophe341,809 31.7 %299,042 25.7 %295,419 25.9 %225,127 31.7 %237,025 38.1 %936,270 27.7 %778,959 30.6 %
Casualty230,308 21.3 %212,724 18.3 %266,455 23.4 %176,952 25.0 %187,066 30.1 %709,487 21.0 %631,212 24.8 %
Property catastrophe77,606 7.2 %154,451 13.3 %128,971 11.3 %35,536 5.0 %(7,125)(1.1)%361,028 10.7 %197,724 7.8 %
Marine and aviation28,633 2.7 %35,129 3.0 %51,817 4.5 %40,708 5.7 %19,159 3.1 %115,579 3.4 %131,045 5.1 %
Other19,476 1.8 %26,578 2.3 %32,628 2.9 %23,006 3.2 %18,258 2.9 %78,682 2.3 %58,631 2.3 %
Total$1,078,836 100.0 %$1,162,634 100.0 %$1,139,124 100.0 %$709,141 100.0 %$621,389 100.0 %$3,380,594 100.0 %$2,545,233 100.0 %
Underwriting location
Bermuda$520,594 48.3 %$589,169 50.7 %$541,312 47.5 %$340,108 48.0 %$221,336 35.6 %$1,651,075 48.8 %$1,217,186 47.8 %
United States312,179 28.9 %286,925 24.7 %270,667 23.8 %201,079 28.4 %207,815 33.4 %869,771 25.7 %627,425 24.7 %
Europe and other246,063 22.8 %286,540 24.6 %327,145 28.7 %167,954 23.7 %192,238 30.9 %859,748 25.4 %700,622 27.5 %
Total$1,078,836 100.0 %$1,162,634 100.0 %$1,139,124 100.0 %$709,141 100.0 %$621,389 100.0 %$3,380,594 100.0 %$2,545,233 100.0 %
Net premiums earned
Other Specialty$330,142 33.0 %$284,321 30.6 %$231,618 28.8 %$247,437 31.7 %$195,649 28.8 %$846,081 30.9 %$571,364 27.7 %
Property excluding property catastrophe282,488 28.2 %266,545 28.7 %232,529 28.9 %235,731 30.2 %210,280 31.0 %781,562 28.6 %600,842 29.2 %
Casualty221,636 22.1 %214,714 23.1 %197,858 24.6 %174,180 22.3 %159,697 23.5 %634,208 23.2 %492,574 23.9 %
Property catastrophe117,820 11.8 %94,679 10.2 %77,076 9.6 %55,453 7.1 %61,107 9.0 %289,575 10.6 %225,285 10.9 %
Marine and aviation25,182 2.5 %41,768 4.5 %42,192 5.2 %40,256 5.2 %29,818 4.4 %109,142 4.0 %112,699 5.5 %
Other24,506 2.4 %25,972 2.8 %23,127 2.9 %26,760 3.4 %22,151 3.3 %73,605 2.7 %57,862 2.8 %
Total$1,001,774 100.0 %$927,999 100.0 %$804,400 100.0 %$779,817 100.0 %$678,702 100.0 %$2,734,173 100.0 %$2,060,626 100.0 %
                    
17
Arch Capital Group Ltd. and Subsidiaries
Segment Information — Mortgage Segment
(U.S. Dollars in thousands)Three Months EndedNine Months Ended
 September 30,June 30,March 31,December 31,September 30,September 30,September 30,
2022202220222021202120222021
Gross premiums written$362,409 $371,896 $364,839 $364,134 $360,934 $1,099,144 $1,143,691 
Premiums ceded(86,230)(78,148)(76,719)(74,834)(60,207)(241,097)(171,923)
Net premiums written276,179 293,748 288,120 289,300 300,727 858,047 971,768 
Change in unearned premiums5,889 1,884 1,417 11,616 11,238 9,190 10,735 
Net premiums earned282,068 295,632 289,537 300,916 311,965 867,237 982,503 
Other underwriting income (1)2,625 (1,556)5,061 2,639 3,981 6,130 15,026 
Losses and loss adjustment expenses67,878 64,681 54,604 28,435 (11,543)187,163 (85,112)
Acquisition expenses(6,693)(10,137)(10,513)(13,121)(24,098)(27,343)(84,297)
Other operating expenses(46,471)(50,251)(53,342)(50,313)(46,254)(150,064)(143,697)
Underwriting income$299,407 $298,369 $285,347 $268,556 $234,051 $883,123 $684,423 
Underwriting Ratios
Loss ratio(24.1)%(21.9)%(18.9)%(9.4)%3.7 %(21.6)%8.7 %
Acquisition expense ratio2.4 %3.4 %3.6 %4.4 %7.7 %3.2 %8.6 %
Other operating expense ratio16.5 %17.0 %18.4 %16.7 %14.8 %17.3 %14.6 %
Combined ratio(5.2)%(1.5)%3.1 %11.7 %26.2 %(1.1)%31.9 %
Net (favorable) adverse development in prior year loss reserves, net of related adjustments(45.1)%(40.7)%(36.5)%(24.2)%(15.5)%(40.7)%(10.6)%
Combined ratio excluding prior year development (2)39.9 %39.2 %39.6 %35.9 %41.7 %39.6 %42.5 %
Net premiums written to gross premiums written76.2 %79.0 %79.0 %79.4 %83.3 %78.1 %85.0 %
Net premiums written by underwriting location
United States$188,290 $201,166 $201,150 $210,988 $221,315 $590,606 $703,489 
Other87,889 92,582 86,970 78,312 79,412 267,441 268,279 
Total$276,179 $293,748 $288,120 $289,300 $300,727 $858,047 $971,768 
United States %68.2 %68.5 %69.8 %72.9 %73.6 %68.8 %72.4 %
Other %31.8 %31.5 %30.2 %27.1 %26.4 %31.2 %27.6 %

(1)     Primarily related to income earned on various risk-sharing products offered to government sponsored enterprises and mortgage lenders.
(2)    See ‘Comments on Regulation G’ for further discussion.
18
Arch Capital Group Ltd. and Subsidiaries
Segment Information — Mortgage Segment
(U.S. Dollars in millions)September 30, 2022June 30, 2022March 31, 2022December 31, 2021September 30, 2021
Insurance In Force (IIF) (1)
U.S. primary mortgage insurance$294,857 58.8 %$291,952 59.8 %$283,484 59.7 %$280,945 61.0 %$280,379 61.3 %
U.S. credit risk transfer (CRT) and other (2)143,897 28.7 %129,203 26.5 %122,189 25.8 %110,018 23.9 %108,203 23.6 %
International mortgage insurance/reinsurance (3)63,068 12.6 %67,082 13.7 %68,800 14.5 %69,655 15.1 %69,127 15.1 %
Total$501,822 100.0 %$488,237 100.0 %$474,473 100.0 %$460,618 100.0 %$457,709 100.0 %
Risk In Force (RIF) (4)
U.S. primary mortgage insurance$75,343 85.1 %$74,258 85.0 %$71,699 84.3 %$70,619 84.3 %$70,320 84.8 %
U.S. credit risk transfer and other (2)6,473 7.3 %6,037 6.9 %5,670 6.7 %5,120 6.1 %4,817 5.8 %
International mortgage insurance/reinsurance (3)6,727 7.6 %7,103 8.1 %7,709 9.1 %7,983 9.5 %7,803 9.4 %
Total$88,543 100.0 %$87,398 100.0 %$85,078 100.0 %$83,722 100.0 %$82,940 100.0 %
Supplemental disclosures for U.S. primary mortgage insurance:
Total RIF by credit quality (FICO score):
>=740$46,538 61.8 %$45,612 61.4 %$43,509 60.7 %$42,451 60.1 %$41,927 59.6 %
680-73924,671 32.7 %24,409 32.9 %23,827 33.2 %23,646 33.5 %23,732 33.7 %
620-6793,850 5.1 %3,942 5.3 %4,052 5.7 %4,196 5.9 %4,323 6.1 %
<620284 0.4 %295 0.4 %311 0.4 %326 0.5 %338 0.5 %
Total$75,343 100.0 %$74,258 100.0 %$71,699 100.0 %$70,619 100.0 %$70,320 100.0 %
Weighted average FICO score748 747 747 746 745 
Total RIF by Loan-To-Value (LTV):
95.01% and above$7,334 9.7 %$7,400 10.0 %$7,421 10.4 %$7,538 10.7 %$7,708 11.0 %
90.01% to 95.00%43,049 57.1 %41,951 56.5 %39,882 55.6 %38,829 55.0 %38,378 54.6 %
85.01% to 90.00%20,876 27.7 %20,718 27.9 %20,183 28.1 %20,006 28.3 %19,980 28.4 %
85.00% and below4,084 5.4 %4,189 5.6 %4,213 5.9 %4,246 6.0 %4,254 6.0 %
Total$75,343 100.0 %$74,258 100.0 %$71,699 100.0 %$70,619 100.0 %$70,320 100.0 %
Weighted average LTV92.9 %92.8 %92.8 %92.8 %92.8 %
Total RIF by State:
California$6,219 8.3 %$6,077 8.2 %$5,781 8.1 %$5,559 7.9 %$5,451 7.8 %
Texas6,080 8.1 %5,971 8.0 %5,733 8.0 %5,594 7.9 %5,590 7.9 %
Florida3,275 4.3 %3,301 4.4 %3,272 4.6 %3,303 4.7 %3,344 4.8 %
Georgia3,150 4.2 %3,109 4.2 %2,978 4.2 %2,902 4.1 %2,908 4.1 %
North Carolina3,139 4.2 %3,075 4.1 %2,964 4.1 %2,921 4.1 %2,921 4.2 %
Illinois3,087 4.1 %3,054 4.1 %2,955 4.1 %2,933 4.2 %2,920 4.2 %
Minnesota2,996 4.0 %2,980 4.0 %2,913 4.1 %2,916 4.1 %2,936 4.2 %
Massachusetts2,771 3.7 %2,684 3.6 %2,566 3.6 %2,537 3.6 %2,519 3.6 %
Virginia2,647 3.5 %2,634 3.5 %2,504 3.5 %2,446 3.5 %2,412 3.4 %
Michigan2,587 3.4 %2,558 3.4 %2,509 3.5 %2,492 3.5 %2,500 3.6 %
Other39,392 52.3 %38,815 52.3 %37,524 52.3 %37,016 52.4 %36,819 52.4 %
Total$75,343 100.0 %$74,258 100.0 %$71,699 100.0 %$70,619 100.0 %$70,320 100.0 %
Weighted average coverage (end of period RIF divided by IIF)25.6 %25.4 %25.3 %25.1 %25.1 %
U.S. mortgage insurance total RIF, net of reinsurance (5)$56,890 $56,529 $54,792 $54,574 $54,847 
Analysts’ persistency (6)75.4 %71.3 %66.9 %62.4 %57.7 %
Risk-to-capital ratio -- Arch MI U.S. (7)7.6:1 7.8:1 7.8:1 8.0:1 8.6:1
PMIER sufficiency ratio -- Arch MI U.S. (8)237 %219 %205 %197 %195 %

(1) The aggregate dollar amount of each insured mortgage loan’s current principal balance.(5) Total RIF for the U.S. mortgage insurance operations (see note 4) after external reinsurance.
(2) Includes all CRT transactions, which are predominantly with GSEs, and other U.S. reinsurance transactions.
(6) Represents the % of IIF at the beginning of a 12-mo. period that remained in force at the end of the period.
(3) International mortgage insurance and reinsurance with risk primarily located in Australia and to lesser extent Europe and Asia.
(7) Represents current (non-delinquent) RIF, net of reinsurance, divided by statutory capital (estimate for September 30, 2022).
(4) The aggregate dollar amount of each insured mortgage loan’s current principal balance multiplied by the insurance coverage percentage specified in the policy for insurance policies issued and after contract limits and/or loss ratio caps for risk-sharing or reinsurance transactions
(8) Calculated as available assets divided by required assets as defined within PMIERs (estimate for September 30, 2022). There was approximately $2.18 billion of excess available assets at September 30, 2022.
19
Arch Capital Group Ltd. and Subsidiaries
Segment Information — Mortgage Segment
(U.S. Dollars in millions, except policy/loan/claim count)Three Months Ended
September 30, 2022June 30, 2022March 31, 2022December 31, 2021September 30, 2021
Supplemental disclosures for U.S. primary mortgage insurance:
Total new insurance written (NIW) (1)$17,425 $23,499 $20,015 $22,544 $27,841 
Total NIW by credit quality (FICO score):
>=740$11,615 66.7 %$16,121 68.6 %$13,152 65.7 %$14,349 63.6 %$17,514 62.9 %
680-7395,322 30.5 %6,800 28.9 %6,254 31.2 %7,238 32.1 %9,012 32.4 %
620-679485 2.8 %576 2.5 %606 3.0 %957 4.2 %1,315 4.7 %
<6203 — %2 — %3 — %— — %— — %
  Total$17,425 100.0 %$23,499 100.0 %$20,015 100.0 %$22,544 100.0 %$27,841 100.0 %
Total NIW by LTV:
95.01% and above$973 5.6 %$1,195 5.1 %$1,096 5.5 %$1,475 6.5 %$1,554 5.6 %
90.01% to 95.00%9,916 56.9 %13,290 56.6 %10,778 53.8 %11,382 50.5 %14,240 51.1 %
85.01% to 90.00%4,839 27.8 %6,591 28.0 %5,733 28.6 %6,677 29.6 %8,394 30.1 %
85.00% and below1,697 9.7 %2,423 10.3 %2,408 12.0 %3,010 13.4 %3,653 13.1 %
  Total$17,425 100.0 %$23,499 100.0 %$20,015 100.0 %$22,544 100.0 %$27,841 100.0 %
Total NIW monthly vs. single:
Monthly$16,911 97.1 %$22,872 97.3 %$19,201 95.9 %$21,623 95.9 %$26,515 95.2 %
Single514 2.9 %627 2.7 %814 4.1 %921 4.1 %1,326 4.8 %
  Total$17,425 100.0 %$23,499 100.0 %$20,015 100.0 %$22,544 100.0 %$27,841 100.0 %
Total NIW purchase vs. refinance:
Purchase$17,159 98.5 %$23,059 98.1 %$19,157 95.7 %$21,174 93.9 %$25,711 92.3 %
Refinance266 1.5 %440 1.9 %858 4.3 %1,370 6.1 %2,130 7.7 %
  Total$17,425 100.0 %$23,499 100.0 %$20,015 100.0 %$22,544 100.0 %$27,841 100.0 %
Ending number of policies in force (PIF) (2)1,168,735 1,168,147 1,159,020 1,171,835 1,188,768 
Rollforward of insured loans in default:
Beginning delinquent number of loans20,692 24,270 27,645 31,770 37,319 
Plus: new notices9,515 7,978 8,835 9,071 8,068 
Less: cures(9,832)(11,363)(12,030)(13,038)(13,410)
Less: paid claims(161)(193)(180)(158)(207)
Ending delinquent number of loans (2)20,214 20,692 24,270 27,645 31,770 
Ending percentage of loans in default (2)1.73 %1.77 %2.09 %2.36 %2.67 %
Losses:
Number of claims paid161 193 180 158 207 
Total paid claims (in thousands)$5,223 $5,626 $6,016 $8,131 $7,551 
Average per claim (in thousands)$32.4 $29.2 $33.4 $51.5 $36.5 
Severity (3)72.3 %72.3 %78.1 %83.0 %78.7 %
Average case reserve per default (in thousands)$27.7 $30.3 $28.4 $26.7 $23.5 
(1)    The original principal balance of all loans that received coverage during the period.    
(2)    Includes first lien primary and pool policies.    
(3)    Represents total paid claims divided by RIF of loans for which claims were paid.

20
Arch Capital Group Ltd. and Subsidiaries
Segment Information — Mortgage Segment
Supplemental disclosures for U.S. primary mortgage insurance:
(U.S. Dollars in millions)September 30, 2022December 31, 2021
Loss Reserves, Net (1)Primary IIF (2)Primary RIF (3)Delinquency RateLoss Reserves, Net (1)Primary IIF (2)Primary RIF (3)Delinquency Rate
% of TotalTotal% of TotalTotal% of Total% of TotalTotal% of TotalTotal% of Total
Policy year:
2012 and prior34.9 %$10,362 3.5 %$2,509 3.3 %8.22 %27.9 %$13,030 4.6 %$2,960 4.2 %8.48 %
20132.4 %3,196 1.1 %855 1.1 %2.12 %2.6 %4,206 1.5 %1,148 1.6 %2.63 %
20141.9 %3,903 1.3 %1,071 1.4 %2.61 %1.9 %4,822 1.7 %1,328 1.9 %3.14 %
20152.6 %6,607 2.2 %1,780 2.4 %2.11 %3.0 %8,703 3.1 %2,340 3.3 %2.67 %
20166.3 %11,021 3.7 %2,953 3.9 %2.47 %7.6 %14,344 5.1 %3,841 5.4 %3.29 %
20179.8 %10,017 3.4 %2,654 3.5 %3.27 %10.9 %13,128 4.7 %3,436 4.9 %4.09 %
201812.8 %10,744 3.6 %2,742 3.6 %3.95 %15.2 %14,046 5.0 %3,562 5.0 %5.28 %
201911.2 %19,961 6.8 %5,038 6.7 %2.24 %15.2 %25,841 9.2 %6,467 9.2 %3.13 %
202011.3 %68,974 23.4 %17,294 23.0 %0.87 %12.5 %82,502 29.4 %20,341 28.8 %0.97 %
20216.4 %91,486 31.0 %23,152 30.7 %0.66 %3.2 %100,323 35.7 %25,196 35.7 %0.29 %
20220.5 %58,586 19.9 %15,295 20.3 %0.17 %
Total100.0 %$294,857 100.0 %$75,343 100.0 %1.73 %100.0 %$280,945 100.0 %$70,619 100.0 %2.36 %

(1)    Total reserves for losses and loss adjustment expenses, net of recoverables, was $545.6 million at September 30, 2022, compared to $710.7 million at December 31, 2021.
(2)    The aggregate dollar amount of each insured mortgage loan’s current principal balance.
(3)    The aggregate dollar amount of each insured mortgage loan’s current principal balance multiplied by the insurance coverage percentage specified in the policy for insurance policies issued and after contract limits and/or loss ratio caps for risk-sharing transactions.
21
Arch Capital Group Ltd. and Subsidiaries
Segment Information - Consolidated Excluding the 'Other' Segment (Sub-Total (Core))

(U.S. Dollars in thousands)Three Months EndedNine Months Ended
 September 30,June 30,March 31,December 31,September 30,September 30,September 30,
 2022202220222021202120222021
Gross premiums written$3,860,683 $3,869,727 $3,800,775 $2,861,575 $3,207,415 $11,531,185 $9,602,213 
Premiums ceded(1,136,909)(1,185,088)(1,166,635)(827,148)(1,131,486)(3,488,632)(2,973,005)
Net premiums written2,723,774 2,684,639 2,634,140 2,034,427 2,075,929 8,042,553 6,629,208 
Change in unearned premiums(253,024)(358,864)(513,507)49,203 (146,592)(1,125,395)(962,508)
Net premiums earned2,470,750 2,325,775 2,120,633 2,083,630 1,929,337 6,917,158 5,666,700 
Other underwriting income (loss)3,077 2,970 5,897 3,160 7,274 11,944 18,174 
Losses and loss adjustment expenses(1,682,696)(1,102,656)(1,000,835)(995,853)(1,226,019)(3,786,187)(3,329,908)
Acquisition expenses(447,587)(413,319)(378,159)(357,539)(306,015)(1,239,065)(882,898)
Other operating expenses(274,747)(277,392)(289,943)(261,787)(230,832)(842,082)(703,939)
Underwriting income (loss)$68,797 $535,378 $457,593 $471,611 $173,745 $1,061,768 $768,129 
Underwriting Ratios
Loss ratio68.1 %47.4 %47.2 %47.8 %63.5 %54.7 %58.8 %
Acquisition expense ratio18.1 %17.8 %17.8 %17.2 %15.9 %17.9 %15.6 %
Other operating expense ratio11.1 %11.9 %13.7 %12.6 %12.0 %12.2 %12.4 %
Combined ratio97.3 %77.1 %78.7 %77.6 %91.4 %84.8 %86.8 %
Catastrophic activity and prior year development:
Current accident year catastrophic events, net of reinsurance and reinstatement premiums22.3 %3.5 %4.0 %3.5 %17.4 %10.4 %10.1 %
Net (favorable) adverse development in prior year loss reserves, net of related adjustments(7.2)%(7.2)%(6.1)%(6.0)%(6.1)%(6.9)%(4.0)%
Combined ratio excluding catastrophic activity and prior year development (1)82.2 %80.8 %80.8 %80.1 %80.1 %81.3 %80.7 %
Components of losses and loss adjustment expenses incurred (1)
Paid losses and loss adjustment expenses$765,542 $745,134 $727,011 $783,806 $626,291 $2,237,687 $1,882,967 
Change in unpaid losses and loss adjustment expenses917,154 357,522 273,824 212,047 599,728 1,548,500 1,446,941 
Total losses and loss adjustment expenses$1,682,696 $1,102,656 $1,000,835 $995,853 $1,226,019 $3,786,187 $3,329,908 
Net premiums written to gross premiums written70.6 %69.4 %69.3 %71.1 %64.7 %69.7 %69.0 %
 
(1)See ‘Comments on Regulation G’ for further discussion.


22
Arch Capital Group Ltd. and Subsidiaries
Segment Information — Selected Information on Losses and Loss Adjustment Expenses

(U.S. Dollars in thousands)Three Months EndedNine Months Ended
 September 30,June 30,March 31,December 31,September 30,September 30,September 30,
 2022202220222021202120222021
Estimated net (favorable) adverse development in prior year loss reserves, net of related adjustments (1)
Net impact on underwriting results:
Insurance$(1,171)$(4,469)$(1,406)$(2,990)$(4,439)$(7,046)$(12,553)
Reinsurance(49,516)(41,907)(22,383)(49,762)(65,439)(113,806)(108,513)
Mortgage(127,290)(120,201)(105,619)(72,865)(48,416)(353,110)(103,791)
Total $(177,977)$(166,577)$(129,408)$(125,617)$(118,294)$(473,962)$(224,857)
Impact on losses and loss adjustment expenses:
Insurance$(5,411)$(6,711)$(7,271)$(3,115)$(5,066)$(19,393)$(13,121)
Reinsurance(49,194)(46,422)(32,473)(59,219)(72,319)(128,089)(119,604)
Mortgage(126,218)(118,093)(102,068)(70,419)(45,124)(346,379)(99,139)
Total$(180,823)$(171,226)$(141,812)$(132,753)$(122,509)$(493,861)$(231,864)
Impact on acquisition expenses:
Insurance$4,240 $2,242 $5,865 $125 $627 $12,347 $568 
Reinsurance(322)4,515 10,090 9,457 6,880 14,283 11,091 
Mortgage(1,072)(2,108)(3,551)(2,446)(3,292)(6,731)(4,652)
Total$2,846 $4,649 $12,404 $7,136 $4,215 $19,899 $7,007 
Impact on combined ratio:
Insurance(0.1)%(0.4)%(0.1)%(0.3)%(0.5)%(0.2)%(0.5)%
Reinsurance(4.9)%(4.5)%(2.8)%(6.4)%(9.6)%(4.2)%(5.3)%
Mortgage(45.1)%(40.7)%(36.5)%(24.2)%(15.5)%(40.7)%(10.6)%
Total (7.2)%(7.2)%(6.1)%(6.0)%(6.1)%(6.9)%(4.0)%
Impact on loss ratio:
Insurance(0.5)%(0.6)%(0.7)%(0.3)%(0.5)%(0.6)%(0.5)%
Reinsurance(4.9)%(5.0)%(4.0)%(7.6)%(10.7)%(4.7)%(5.8)%
Mortgage(44.7)%(39.9)%(35.3)%(23.4)%(14.5)%(39.9)%(10.1)%
Total(7.3)%(7.4)%(6.7)%(6.4)%(6.3)%(7.1)%(4.1)%
Impact on acquisition expense ratio:
Insurance0.4 %0.2 %0.6 %0.0 %0.0 %0.4 %0.0 %
Reinsurance0.0 %0.5 %1.2 %1.2 %1.1 %0.5 %0.5 %
Mortgage(0.4)%(0.8)%(1.2)%(0.8)%(1.0)%(0.8)%(0.5)%
Total 0.1 %0.2 %0.6 %0.4 %0.2 %0.2 %0.1 %
Estimated net losses incurred from current accident year catastrophic events (2)
Insurance$158,973 $16,360 $31,855 $20,312 $114,433 $207,188 $184,308 
Reinsurance391,843 66,021 53,977 51,966 221,431 511,841 386,277 
Total$550,816 $82,381 $85,832 $72,278 $335,864 $719,029 $570,585 
Impact on combined ratio:
Insurance13.4 %1.5 %3.1 %2.0 %12.2 %6.2 %7.0 %
Reinsurance39.1 %7.1 %6.7 %6.7 %32.6 %18.7 %18.7 %
Total22.3 %3.5 %4.0 %3.5 %17.4 %10.4 %10.1 %
(1)Presented on a ‘core’ basis which excludes amounts related to the ‘other’ segment (i.e., results of Somers). See ‘Comments on Regulation G’ for a further discussion of the presentation of ‘core’ results.
(2)Equals estimated losses from catastrophic events occurring in the current accident year (e.g. natural catastrophes, man-made events, pandemic events), net of reinsurance and reinstatement premiums. As regards the natural catastrophe estimates included within, amounts shown for the insurance segment are for named catastrophic events only, while amounts shown for the reinsurance segment include (i) named events with over $5 million of losses incurred by its Bermuda and Europe operations and (ii) all catastrophe losses incurred by its U.S. operations. Amounts not applicable for the mortgage segment.
23
Arch Capital Group Ltd. and Subsidiaries
Investment Information — Investable Asset Summary and Investment Portfolio Metrics
The following table summarizes the Company’s investable assets and portfolio metrics:
(U.S. Dollars in thousands)September 30,June 30,March 31,December 31,September 30,
20222022202220212021
Investable assets:
Fixed maturities available for sale, at fair value$18,120,727 67.9 %$17,585,029 66.6 %$17,648,853 66.0 %$17,998,109 65.6 %$16,768,363 61.5 %
Fixed maturities—fair value option (1)530,303 2.0 %525,451 2.0 %426,187 1.6 %416,698 1.5 %414,007 1.5 %
Total fixed maturities18,651,030 69.9 %18,110,480 68.6 %18,075,040 67.6 %18,414,807 67.1 %17,182,370 63.0 %
Equity securities, at fair value809,869 3.0 %772,689 2.9 %1,002,572 3.7 %1,804,170 6.6 %1,790,640 6.6 %
Equity securities—fair value option (1)13,905 0.1 %14,489 0.1 %21,300 0.1 %26,493 0.1 %24,523 0.1 %
Total equity securities823,774 3.1 %787,178 3.0 %1,023,872 3.8 %1,830,663 6.7 %1,815,163 6.7 %
Other investments—fair value option (1)1,005,929 3.8 %1,054,771 4.0 %1,226,808 4.6 %1,432,553 5.2 %1,489,759 5.5 %
Investments accounted for using the equity method (2)3,565,946 13.4 %3,496,341 13.2 %3,325,543 12.4 %3,077,611 11.2 %2,741,293 10.0 %
Short-term investments available for sale, at fair value1,940,857 7.3 %2,227,874 8.4 %2,332,624 8.7 %1,734,716 6.3 %3,069,965 11.3 %
Short-term investments—fair value option (1)28,614 0.1 %39,657 0.2 %12,371 0.0 %97,806 0.4 %115,681 0.4 %
Total short-term investments1,969,471 7.4 %2,267,531 8.6 %2,344,995 8.8 %1,832,522 6.7 %3,185,646 11.7 %
Cash813,583 3.0 %813,548 3.1 %812,917 3.0 %858,668 3.1 %1,137,721 4.2 %
Securities transactions entered into but not settled at the balance sheet date(147,727)(0.6)%(134,777)(0.5)%(59,819)(0.2)%(4,671)0.0 %(273,512)(1.0)%
Total investable assets held by the Company$26,682,006 100.0 %$26,395,072 100.0 %$26,749,356 100.0 %$27,442,153 100.0 %$27,278,440 100.0 %
Average effective duration (in years)2.84 2.94 2.93 2.70 2.68  
Average S&P/Moody’s credit ratings (3) AA/Aa2  AA-/Aa3  AA-/Aa3  AA-/Aa3  AA-/Aa3  
(1)     Included in “other investments” on the balance sheet.
(2)    Changes in the carrying value of investment funds accounted for using the equity method are recorded as “equity in net income (loss) of investment funds accounted for using the equity method” rather than as                 an unrealized gain or loss component of accumulated other comprehensive income.
(3)    Average credit ratings on the Company’s investment portfolio on securities with ratings assigned by Standard & Poor’s (“S&P”) and Moody’s Investors Service (“Moody’s”).
24
Arch Capital Group Ltd. and Subsidiaries
Investment Information — Composition of Net Investment Income, Yield and Total Return

The following table summarizes the Company’s net investment income, yield and total return (1):
(U.S. Dollars in thousands, except share data)Three Months EndedNine Months Ended
 September 30,June 30,March 31,December 31,September 30,September 30,September 30,
 2022202220222021202120222021
Composition of net investment income (1):       
Fixed maturities$123,568 $105,342 $82,053 $74,846 $75,964 $310,963 $232,690 
Equity securities (dividends)4,261 6,121 6,238 18,295 9,867 16,620 23,799 
Short-term investments9,304 4,120 2,575 3,325 1,858 15,999 3,474 
Other (2)8,644 7,984 12,076 12,712 19,114 28,704 55,699 
Gross investment income145,777 123,567 102,942 109,178 106,803 372,286 315,662 
Investment expenses(17,137)(17,175)(22,506)(18,724)(18,608)(56,818)(59,308)
Net investment income$128,640 $106,392 $80,436 $90,454 $88,195 $315,468 $256,354 
Per share$0.34 $0.28 $0.21 $0.23 $0.22 $0.83 $0.63 
Equity in net income (loss) of investment funds accounted for using the equity method(18,861)58,061 36,305 67,132 105,398 75,505 299,270 
Per share$(0.05)$0.15 $0.09 $0.17 $0.26 $0.20 $0.74 
Investment income yield, at amortized cost (1) (3):
Pre-tax2.06 %1.76 %1.34 %1.46 %1.41 %1.72 %1.40 %
After-tax1.77 %1.49 %1.13 %1.27 %1.24 %1.46 %1.23 %
Total return on investments (1) (4)(3.01)%(3.02)%(3.07)%0.39 %0.01 %(8.83)%1.50 %

(1)Presented on a ‘core’ basis which excludes amounts related to the ‘other’ segment (i.e., results of Somers). See ‘Comments on Regulation G’ for a further discussion of the presentation of ‘core’ results.
(2)Amounts include dividends and other distributions on investment funds, term loan investments, funds held balances, cash balances and other.
(3)Presented on an annualized basis and excluding the impact of investments for which returns are not included within investment income, such as investments accounted for using the equity method and certain equities.
(4)Total return on investments includes investment income, equity in net income or loss of investment funds accounted for using the equity method, net realized gains and losses (excluding changes in allowance for credit losses on non-investment related financial assets) and the change in unrealized gains or losses and is calculated on a pre-tax basis and before investment expenses. See ‘Comments on Regulation G’ for a further discussion of the presentation of total return on investments.

25
Arch Capital Group Ltd. and Subsidiaries
Investment Information — Composition of Fixed Maturities
 
The following table summarizes the Company’s fixed maturities:
(U.S. Dollars in thousands)
Fair
Value		Gross
Unrealized
Gains		Gross
Unrealized
Losses		Net
Unrealized
Gains (Losses)		Allowance
for Credit Losses		Amortized
Cost		Fair Value /
Amortized Cost		Fair Value
% of Total
At September 30, 2022
Corporates$7,620,446 $51,777 $(895,365)$(843,588)$(35,657)$8,499,691 89.7 %40.9 %
U.S. government and government agencies5,126,407 36,074 (400,784)(364,710)— 5,491,117 93.4 %27.5 %
Municipal bonds407,724 5,437 (37,692)(32,255)(99)440,078 92.6 %2.2 %
Non-U.S. government securities2,077,202 9,315 (287,583)(278,268)(1,720)2,357,190 88.1 %11.1 %
Asset-backed securities1,591,642 1,076 (105,037)(103,961)(6,936)1,702,539 93.5 %8.5 %
Commercial mortgage-backed securities1,064,238 3,079 (50,010)(46,931)(1,583)1,112,752 95.6 %5.7 %
Residential mortgage-backed securities763,371 7,561 (84,183)(76,622)2 839,991 90.9 %4.1 %
Total$18,651,030 $114,319 $(1,860,654)$(1,746,335)$(45,993)$20,443,358 91.2 %100.0 %
At December 31, 2021
Corporates$6,941,879 $104,170 $(69,194)$34,976 $(2,037)$6,908,940 100.5 %37.7 %
U.S. government and government agencies4,772,764 10,076 (45,967)(35,891)— 4,808,655 99.3 %25.9 %
Municipal bonds404,666 18,724 (1,409)17,315 (2)387,353 104.5 %2.2 %
Non-U.S. government securities2,144,079 54,048 (34,749)19,299 (82)2,124,862 100.9 %11.6 %
Asset-backed securities2,696,458 6,540 (11,108)(4,568)(708)2,701,734 99.8 %14.6 %
Commercial mortgage-backed securities1,046,484 1,740 (3,117)(1,377)(6)1,047,867 99.9 %5.7 %
Residential mortgage-backed securities408,477 2,825 (5,410)(2,585)(48)411,110 99.4 %2.2 %
Total$18,414,807 $198,123 $(170,954)$27,169 $(2,883)$18,390,521 100.1 %100.0 %



26
Arch Capital Group Ltd. and Subsidiaries
Investment Information — Credit Quality Distribution and Maturity Profile

The following table summarizes the credit quality distribution and maturity profile of the Company’s fixed maturities:
(U.S. Dollars in thousands)September 30,June 30,March 31,December 31,September 30,
20222022202220212021
Credit quality distribution of total fixed maturities (1):
U.S. government and government agencies (2)$5,746,853 30.8 %$4,892,483 27.0 %$4,981,102 27.6 %$5,063,191 27.5 %$4,830,467 28.1 %
AAA3,344,746 17.9 %3,352,551 18.5 %3,171,975 17.5 %3,783,386 20.5 %3,257,679 19.0 %
AA2,030,730 10.9 %2,064,313 11.4 %2,222,236 12.3 %2,459,413 13.4 %2,217,452 12.9 %
A3,382,545 18.1 %3,464,240 19.1 %3,227,560 17.9 %2,943,594 16.0 %2,773,104 16.1 %
BBB3,001,304 16.1 %3,114,961 17.2 %3,181,195 17.6 %2,936,398 15.9 %2,807,788 16.3 %
BB532,162 2.9 %551,876 3.0 %564,762 3.1 %501,588 2.7 %522,357 3.0 %
B357,543 1.9 %367,275 2.0 %364,181 2.0 %371,747 2.0 %348,036 2.0 %
Lower than B12,417 0.1 %4,742 — %7,057 — %43,756 0.2 %43,751 0.3 %
Not rated242,730 1.3 %298,039 1.6 %354,972 2.0 %311,734 1.7 %381,736 2.2 %
Total fixed maturities, at fair value$18,651,030 100.0 %$18,110,480 100.0 %$18,075,040 100.0 %$18,414,807 100.0 %$17,182,370 100.0 %
Maturity profile of total fixed maturities:
Due in one year or less$602,340 3.2 %$434,779 2.4 %$323,999 1.8 %$318,572 1.7 %$430,048 2.5 %
Due after one year through five years10,285,415 55.1 %9,661,066 53.3 %9,756,481 54.0 %8,536,801 46.4 %8,035,751 46.8 %
Due after five years through ten years4,031,643 21.6 %4,261,397 23.5 %4,296,537 23.8 %4,807,858 26.1 %4,601,049 26.8 %
Due after 10 years312,381 1.7 %422,104 2.3 %535,301 3.0 %600,157 3.3 %437,895 2.5 %
15,231,779 81.7 %14,779,346 81.6 %14,912,318 82.5 %14,263,388 77.5 %13,504,743 78.6 %
Residential mortgage-backed securities763,371 4.1 %698,168 3.9 %416,138 2.3 %408,477 2.2 %405,797 2.4 %
Commercial mortgage-backed securities1,064,238 5.7 %1,023,088 5.6 %1,066,365 5.9 %1,046,484 5.7 %579,424 3.4 %
Asset-backed securities1,591,642 8.5 %1,609,878 8.9 %1,680,219 9.3 %2,696,458 14.6 %2,692,406 15.7 %
Total fixed maturities, at fair value$18,651,030 100.0 %$18,110,480 100.0 %$18,075,040 100.0 %$18,414,807 100.0 %$17,182,370 100.0 %

(1)     For individual fixed maturities, S&P ratings are used. In the absence of an S&P rating, ratings from Moody’s are used, followed by ratings from Fitch Ratings.
(2)     Includes U.S. government-sponsored agency mortgage backed securities and agency commercial mortgage backed securities.


27
Arch Capital Group Ltd. and Subsidiaries
Investment Information — Analysis of Corporate Exposures

The following table summarizes the Company’s corporate bonds by sector:
(U.S. Dollars in thousands)September 30,June 30,March 31,December 31,September 30,
20222022202220212021
Sector:
Industrials$2,926,134 38.4 %$2,928,443 37.5 %$2,990,553 39.1 %$3,082,440 44.4 %$3,227,049 47.6 %
Financials4,094,264 53.7 %4,191,142 53.7 %4,054,531 53.0 %3,397,199 48.9 %3,132,330 46.2 %
Utilities483,490 6.3 %559,150 7.2 %460,793 6.0 %363,468 5.2 %381,737 5.6 %
Covered bonds3,848 0.1 %1,720 0.0 %1,870 0.0 %4,511 0.1 %2,661 0.0 %
All other (1)112,710 1.5 %130,807 1.7 %145,934 1.9 %94,261 1.4 %34,166 0.5 %
Total$7,620,446 100.0 %$7,811,262 100.0 %$7,653,681 100.0 %$6,941,879 100.0 %$6,777,943 100.0 %
Credit quality distribution (2):
AAA$162,906 2.1 %$160,327 2.1 %$144,047 1.9 %$122,008 1.8 %$114,395 1.7 %
AA823,931 10.8 %784,206 10.0 %835,869 10.9 %1,006,360 14.5 %946,277 14.0 %
A2,945,719 38.7 %2,973,180 38.1 %2,691,615 35.2 %2,414,764 34.8 %2,293,741 33.8 %
BBB2,834,413 37.2 %2,931,983 37.5 %2,968,760 38.8 %2,453,904 35.3 %2,530,014 37.3 %
BB516,986 6.8 %522,904 6.7 %550,960 7.2 %463,072 6.7 %477,833 7.0 %
B351,360 4.6 %353,134 4.5 %360,902 4.7 %355,993 5.1 %329,581 4.9 %
Lower than B11,390 0.1 %4,260 0.1 %6,210 0.1 %30,878 0.4 %30,365 0.4 %
Not rated(26,259)(0.3)%81,268 1.0 %95,318 1.2 %94,900 1.4 %55,737 0.8 %
Total$7,620,446 100.0 %$7,811,262 100.0 %$7,653,681 100.0 %$6,941,879 100.0 %$6,777,943 100.0 %

(1)    Includes sovereign securities, supranational securities and other.
(2)    For individual fixed maturities, S&P ratings are used. In the absence of an S&P rating, ratings from Moody’s are used, followed by ratings from Fitch Ratings.

The following table summarizes the Company’s top ten exposures to fixed income corporate issuers by fair value at September 30, 2022:
(U.S. Dollars in thousands)Fair
Value		% of Asset Class% of Investable AssetsCredit Quality (1)
Issuer:
Bank of America Corporation$430,809 5.7 %1.6 %A-/A2
JPMorgan Chase & Co.297,868 3.9 %1.1 %A-/A1
Morgan Stanley268,742 3.5 %1.0 %A-/A1
Citigroup Inc.260,312 3.4 %1.0 %BBB+/A3
The Goldman Sachs Group, Inc.243,516 3.2 %0.9 %BBB+/A2
Wells Fargo & Company237,947 3.1 %0.9 %BBB+/A1
Blackstone Inc.165,585 2.2 %0.6 %BBB/Baa3
Blue Owl Capital Inc.157,904 2.1 %0.6 %BBB-/Baa3
UBS Group AG125,810 1.7 %0.5 %A/Aa3
Dai-ichi Life Holdings, Inc.106,357 1.4 %0.4 %AA-/A1
Total$2,294,850 30.1 %8.6 %
 
(1)    Average credit ratings assigned by S&P and Moody’s, respectively.

28
Arch Capital Group Ltd. and Subsidiaries
Investment Information — Structured Securities

The following table provides the composition of the Company’s structured securities:
(U.S. Dollars in thousands)AgenciesAAAAAABBBNon-Investment GradeTotal
At September 30, 2022      
Residential mortgage-backed securities$602,423 $113,613 $29,575 $— $— $17,760 $763,371 
Commercial mortgage-backed securities18,022 693,681 154,401 22,601 86,644 88,889 1,064,238 
Asset-backed securities— 904,469 150,542 310,567 45,094 180,970 1,591,642 
Total$620,445 $1,711,763 $334,518 $333,168 $131,738 $287,619 $3,419,251 
At December 31, 2021
Residential mortgage-backed securities$268,229 $86,344 $40,502 $2,444 $6 $10,952 $408,477 
Commercial mortgage-backed securities22,198 710,692 141,065 6,990 67,555 97,984 1,046,484 
Asset-backed securities— 1,548,239 230,922 397,242 367,504 152,551 2,696,458 
Total$290,427 $2,345,275 $412,489 $406,676 $435,065 $261,487 $4,151,419 
29
Arch Capital Group Ltd. and Subsidiaries
Comments on Regulation G
Throughout this financial supplement, the Company presents its operations in the way it believes will be the most meaningful and useful to investors, analysts, rating agencies and others who use the Company’s financial information in evaluating the performance of the Company. This presentation includes the use of after-tax operating income available to Arch common shareholders, which is defined as net income available to Arch common shareholders, excluding net realized gains or losses (which includes changes in the allowance for credit losses on financial assets and net impairment losses recognized in earnings), equity in net income or loss of investment funds accounted for using the equity method, net foreign exchange gains or losses, transaction costs and other and loss on redemption of preferred shares, net of income taxes, and the use of annualized operating return on average common equity. The presentation of after-tax operating income available to Arch common shareholders and annualized operating return on average common equity are non-GAAP financial measures as defined in Regulation G. The reconciliation of such measures to net income available to Arch common shareholders and annualized net income return on average common equity (the most directly comparable GAAP financial measures) in accordance with Regulation G is included on the following page.
The Company believes that net realized gains or losses, equity in net income or loss of investment funds accounted for using the equity method, net foreign exchange gains or losses, transaction costs and other and loss on redemption of preferred shares in any particular period are not indicative of the performance of, or trends in, the Company’s business performance. Although net realized gains or losses, equity in net income or loss of investment funds accounted for using the equity method and net foreign exchange gains or losses are an integral part of the Company’s operations, the decision to realize investment gains or losses, the recognition of the change in the carrying value of investments accounted for using the fair value option in net realized gains or losses, the recognition of equity in net income or loss of investment funds accounted for using the equity method and the recognition of foreign exchange gains or losses are independent of the insurance underwriting process and result, in large part, from general economic and financial market conditions. Furthermore, certain users of the Company’s financial information believe that, for many companies, the timing of the realization of investment gains or losses is largely opportunistic. In addition, changes in the allowance for credit losses and net impairment losses recognized in earnings on the Company’s investments represent other-than-temporary declines in expected recovery values on securities without actual realization. The use of the equity method on certain of the Company’s investments in certain funds that invest in fixed maturity securities is driven by the ownership structure of such funds (either limited partnerships or limited liability companies). In applying the equity method, these investments are initially recorded at cost and are subsequently adjusted based on the Company’s proportionate share of the net income or loss of the funds (which include changes in the fair value of the underlying securities in the funds). This method of accounting is different from the way the Company accounts for its other fixed maturity securities and the timing of the recognition of equity in net income or loss of investment funds accounted for using the equity method may differ from gains or losses in the future upon sale or maturity of such investments. Transaction costs and other include advisory, financing, legal, severance, incentive compensation and other transaction costs related to acquisitions. The Company believes that transaction costs and other, due to their non-recurring nature, are not indicative of the performance of, or trends in, the Company’s business performance. The loss on redemption of preferred shares related to the redemption of the Company's Series E preferred shares in September 2021 had no impact on shareholders' equity or cash flows. Due to these reasons, the Company excludes net realized gains or losses, equity in net income or loss of investment funds accounted for using the equity method, net foreign exchange gains or losses, transaction costs and other and loss on redemption of preferred shares from the calculation of after-tax operating income or loss available to Arch common shareholders.
The Company believes that showing net income available to Arch common shareholders exclusive of the items referred to above reflects the underlying fundamentals of the Company’s business since the Company evaluates the performance of and manages its business to produce an underwriting profit. In addition to presenting net income available to Arch common shareholders, the Company believes that this presentation enables investors and other users of the Company’s financial information to analyze the Company’s performance in a manner similar to how the Company’s management analyzes performance. The Company also believes that this measure follows industry practice and, therefore, allows the users of the Company’s financial information to compare the Company’s performance with its industry peer group. The Company believes that the equity analysts and certain rating agencies which follow the Company and the insurance industry as a whole generally exclude these items from their analyses for the same reasons.
In addition, through June 30, 2021, the Company’s presentation included the use of information prepared on a ‘core’ basis, which excluded amounts related to the ‘other’ segment (i.e., results of Somers). Information provided on a ‘core’ basis represent non-GAAP financial measures as defined in Regulation G. Pursuant to GAAP, Somers was considered a variable interest entity and the Company concluded that it was the primary beneficiary of Somers through June 30, 2021. As such, the Company consolidated the results of Somers in its consolidated financial statements. The Company’s presentation of information on a ‘core’ basis enabled investors and other users of the Company’s financial information to analyze the Company’s performance in a manner similar to how the Company’s management analyzed performance. See ‘Segment Information’ for a further discussion of segment results and a reconciliation of core and consolidated results. In the 2020 fourth quarter, Arch, Somers, and Greysbridge Ltd., a wholly-owned subsidiary of Arch, entered into an Agreement and Plan of Merger (as amended, the “Merger Agreement”). Arch assigned its rights under the Merger Agreement to Greysbridge Holdings Ltd. (“Greysbridge”). The merger and the related Greysbridge equity financing closed on July 1, 2021. Effective July 1, 2021, Somers is wholly owned by Greysbridge, and Greysbridge is owned 40% by Arch and 30% by certain funds managed by Kelso & Company and 30% by certain funds managed by Warburg Pincus LLC. Based on the governing documents of Greysbridge, we concluded that, while we retain significant influence over Greysbridge, Greysbridge does not constitute a variable interest entity. Accordingly, effective July 1, 2021, we no longer consolidate the results of Somers in our consolidated financial statements and footnotes.
The Company’s segment information includes the presentation of consolidated underwriting income or loss and a subtotal of underwriting income or loss on a ‘core’ basis (for periods prior to July 1, 2021). Such measures represent the pre-tax profitability of the Company’s underwriting operations and include net premiums earned plus other underwriting income, less losses and loss adjustment expenses, acquisition expenses and other operating expenses. Other operating expenses include those operating expenses that are incremental and/or directly attributable to the Company’s individual underwriting operations. Underwriting income or loss does not incorporate items included in the Company’s corporate segment. While these measures are presented in the Segment Information footnote to the Company’s Consolidated Financial Statements, they are considered non-GAAP financial measures when presented elsewhere on a consolidated basis. The reconciliations of underwriting income or loss to income before income taxes (the most directly comparable GAAP financial measure) on a consolidated basis and a ‘core’ basis (for periods prior to July 1, 2021), in accordance with Regulation G, is shown on pages 10 to 13.
In addition, the Company’s segment information includes the use of a combined ratio excluding catastrophic activity and prior year development, for the insurance and reinsurance segments, and a combined ratio excluding prior year development, for the mortgage segment. These ratios are non-GAAP financial measures as defined in Regulation G. The reconciliation of such measures to the combined ratio (the most directly comparable GAAP financial measure) in accordance with Regulation G are shown on the individual segment pages. The Company’s management utilizes the adjusted combined ratios excluding current accident year catastrophic events and favorable or adverse development in prior year loss reserves in its analysis of the underwriting performance of each of its underwriting segments.
Total return on investments includes investment income, equity in net income or loss of investment funds accounted for using the equity method, net realized gains and losses (excluding changes in the allowance for credit losses on non-investment related financial assets) and the change in unrealized gains and losses generated by Arch’s investment portfolio. Total return is calculated on a pre-tax basis and before investment expenses, excludes amounts reflected in the ‘other’ segment, and reflects the effect of financial market conditions along with foreign currency fluctuations. Management uses total return on investments as a key measure of the return generated to Arch common shareholders, and compares the return generated by the Company’s investment portfolio against benchmark returns during the periods presented.
30
Arch Capital Group Ltd. and Subsidiaries
Operating Income Reconciliation and Annualized Operating Return on Average Common Equity
The following table summarizes the Company’s consolidated financial data, including a reconciliation of net income (loss) available to Arch common shareholders to after-tax operating income (loss) available to Arch common shareholders and related diluted per share results. Each line item reflects the impact of the Company’s ownership of Somers’ outstanding common equity through June 30, 2021:
(U.S. Dollars in thousands, except share data)Three Months EndedNine Months Ended
 September 30,June 30,March 31,December 31,September 30,September 30,September 30,
 2022202220222021202120222021
Net income available to Arch common shareholders$6,917 $394,160 $185,616 $613,081 $388,751 $586,693 $1,480,324 
Net realized (gains) losses183,674 266,579 292,414 (59,517)25,040 742,667 (247,949)
Equity in net (income) loss of investment funds accounted for using the equity method18,861 (58,061)(36,305)(67,132)(105,398)(75,505)(299,270)
Net foreign exchange (gains) losses(90,537)(87,797)(3,855)(3,221)(36,078)(182,189)(39,522)
Transaction costs and other76 261 397 310 1,036 734 889 
Loss on redemption of preferred shares— — — — 15,101 — 15,101 
Income tax expense (benefit) (1)(13,019)(8,646)(16,268)9,736 6,236 (37,933)32,100 
After-tax operating income available to Arch common shareholders$105,972 $506,496 $421,999 $493,257 $294,688 $1,034,467 $941,673 
Diluted per common share results:
Net income available to Arch common shareholders$0.02 $1.04 $0.48 $1.58 $0.98 $1.55 $3.66 
Net realized (gains) losses0.48 0.70 0.76 (0.16)0.05 1.96 (0.61)
Equity in net (income) loss of investment funds accounted for using the equity method0.05 (0.15)(0.09)(0.17)(0.26)(0.20)(0.74)
Net foreign exchange (gains) losses(0.24)(0.23)(0.01)(0.01)(0.09)(0.48)(0.10)
Transaction costs and other0.00 0.00 0.00 0.00 0.00 0.00 0.00 
Loss on redemption of preferred shares— — — — 0.04 — 0.04 
Income tax expense (benefit) (1)(0.03)(0.02)(0.04)0.03 0.02 (0.10)0.08 
After-tax operating income available to Arch common shareholders$0.28 $1.34 $1.10 $1.27 $0.74 $2.73 $2.33 
Weighted average common shares and common share equivalents outstanding - diluted373,727,277 377,952,988 384,194,363 388,869,378 397,903,347 378,373,180 404,260,485 
Beginning common shareholders’ equity$11,587,566 $12,089,589 $12,715,896 $12,557,526 $12,706,072 $12,715,896 $12,325,886 
Ending common shareholders’ equity10,965,110 11,587,566 12,089,589 12,715,896 12,557,526 10,965,110 12,557,526 
Average common shareholders’ equity$11,276,338 $11,838,578 $12,402,743 $12,636,711 $12,631,799 $11,840,503 $12,441,706 
Annualized net income return on average common equity0.2 %13.3 %6.0 %19.4 %12.3 %6.6 %15.9 %
Annualized operating return on average common equity3.8 %17.1 %13.6 %15.6 %9.3 %11.6 %10.1 %

(1)Income tax expense on net realized gains or losses (which includes changes in the allowance for credit losses on financial assets and 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 and transaction costs and other reflects the relative mix reported by jurisdiction and the varying tax rates in each jurisdiction.


31
Arch Capital Group Ltd. and Subsidiaries
Operating Income and Effective Tax Rate Calculations
The following table provides a reconciliation of income (loss) before income taxes to after-tax operating income (loss) available to Arch common shareholders and an analysis of the effective tax rate on pre-tax operating income (loss) available to Arch common shareholders:
(U.S. Dollars in thousands)Three Months EndedNine Months Ended
September 30,June 30,March 31,December 31,September 30,September 30,September 30,
 2022202220222021202120222021
Arch Operating Income Components (1):
Income (loss) before income taxes and income (loss) from operating affiliates$(5,149)$421,628 $184,533 $617,440 $301,433 $601,012 $1,396,476 
Net realized (gains) losses183,673 266,579 292,414 (59,517)25,040 742,666 (239,690)
Equity in net (income) loss of investment funds accounted for using the equity method18,861 (58,061)(36,305)(67,132)(105,398)(75,505)(299,270)
Net foreign exchange (gains) losses(90,509)(87,775)(3,845)(3,163)(36,078)(182,129)(39,691)
Transaction costs and other(1,108)658 (170)(171)(437)(620)(1,065)
Income (loss) from operating affiliates
8,507 4,640 24,518 40,641 124,119 37,665 224,052 
Pre-tax operating income114,275 547,669 461,145 528,098 308,679 1,123,089 1,040,812 
Arch share of ‘other’ segment operating income (loss) (2)— — — — — — 931 
Pre-tax operating income available to Arch (b)114,275 547,669 461,145 528,098 308,679 1,123,089 1,041,743 
Income tax (expense) benefit (a)1,881 (30,989)(28,962)(24,657)2,099 (58,070)(61,911)
After-tax operating income available to Arch116,156 516,680 432,183 503,441 310,778 1,065,019 979,832 
Preferred dividends(10,184)(10,184)(10,184)(10,184)(16,090)(30,552)(38,159)
After-tax operating income available to Arch common shareholders$105,972 $506,496 $421,999 $493,257 $294,688 $1,034,467 $941,673 
Effective tax rate on pre-tax operating income (loss) available to Arch (a)/(b)(1.6)%5.7 %6.3 %4.7 %(0.7)%5.2 %5.9 %

(1)    Line items are presented on a ‘core’ basis, excluding amounts related to the ‘other’ segment (i.e., results of Somers). See ‘Comments on Regulation G’ for a further discussion of the presentation of ‘core’ results.
(2)    Balances in the ‘other’ segment and a calculation of Arch’s share of the ‘other’ segment operating income (loss) is as follows:
(U.S. Dollars in thousands)Three Months EndedNine Months Ended
September 30,June 30,March 31,December 31,September 30,September 30,September 30,
 2022202220222021202120222021
Balances in ‘other’ segment:
Underwriting income (loss)$— $— $— $— $— $— $(21,945)
Net investment income— — — — — — 42,310 
Interest expense— — — — — — (8,410)
Amortization of intangible assets— — — — — — (898)
Preferred dividends— — — — — — (1,953)
Pre-tax operating income (loss) available to common shareholders— — — — — — 9,104 
Arch ownership (4)n/an/an/an/a— %n/an/a
Arch share of ‘Other’ segment operating income (loss) (3)$— $— $— $— $— $— $931 

(3) Excludes amounts attributable to net realized gains or losses and net foreign exchange gains or losses in the ‘other’ segment (see ‘Segment Information’).
(4) Effective July 1, 2021, Somers is wholly owned by Greysbridge and Greysbridge is owned 40% by the Company, accordingly, the Company no longer consolidates the results of Somers in its consolidated financial statements. See ‘Comments on Regulation G’ for a further discussion of the presentation of ‘core’ results.
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Arch Capital Group Ltd. and Subsidiaries
Capital Structure and Share Repurchase Activity
The following table provides an analysis of the Company’s capital structure (1):
(U.S. Dollars in thousands, except share data)September 30,June 30,March 31,December 31,September 30,
20222022202220212021
Debt:
Arch senior notes, due May 1, 2034 ($300,000 principal, 7.35%)$300,000 $300,000 $300,000 $300,000 $300,000 
Arch-U.S. senior notes, due Nov. 1, 2043 ($500,000 principal, 5.144%) (2)500,000 500,000 500,000 500,000 500,000 
Arch Finance senior notes, due December 15, 2026 ($500,000 principal, 4.011%) (3)500,000 500,000 500,000 500,000 500,000 
Arch Finance senior notes, due December 15, 2046 ($450,000 principal, 5.031%) (3)450,000 450,000 450,000 450,000 450,000 
Arch senior notes, due June 30, 2050 ($1,000,000 principal, 3.635%)1,000,000 1,000,000 1,000,000 1,000,000 1,000,000 
Deferred debt costs on senior notes(24,847)(25,104)(25,358)(25,606)(25,851)
Revolving credit agreement borrowings, due December 17, 2024 (variable)— — — — — 
Total debt$2,725,153 $2,724,896 $2,724,642 $2,724,394 $2,724,149 
Shareholders’ equity available to Arch:
Series F non-cumulative preferred shares (5.45%)330,000 330,000 330,000 330,000 330,000 
Series G non-cumulative preferred shares (4.55%)500,000 500,000 500,000 500,000 500,000 
Common shareholders’ equity (a)10,965,110 11,587,566 12,089,589 12,715,896 12,557,526 
Total shareholders’ equity available to Arch$11,795,110 $12,417,566 $12,919,589 $13,545,896 $13,387,526 
Total capital available to Arch$14,520,263 $15,142,462 $15,644,231 $16,270,290 $16,111,675 
Common shares outstanding, net of treasury shares (b)369,321,990 369,346,815 375,730,891 378,923,894 387,257,752 
Book value per common share (4) (a)/(b)$29.69 $31.37 $32.18 $33.56 $32.43 
Leverage ratios:
Senior notes/total capital available to Arch18.8 %18.0 %17.4 %16.7 %16.9 %
Revolving credit agreement borrowings/total capital available to Arch— %— %— %— %— %
Debt/total capital available to Arch18.8 %18.0 %17.4 %16.7 %16.9 %
Preferred/total capital available to Arch5.7 %5.5 %5.3 %5.1 %5.2 %
Debt and preferred/total capital available to Arch24.5 %23.5 %22.7 %21.8 %22.1 %
(1)    Presented on a ‘core’ basis which excludes amounts related to the ‘other’ segment (i.e., results of Somers). See ‘Comments on Regulation G’ for a further discussion of the presentation of ‘core’ results.
(2)    Issued by Arch Capital Group (U.S.) Inc. (“Arch-U.S.”), a wholly owned subsidiary of Arch, and fully and unconditionally guaranteed by Arch.
(3)    Issued by Arch Capital Finance LLC (“Arch Finance”), a wholly owned subsidiary of Arch U.S. MI Holdings Inc., and fully and unconditionally guaranteed by Arch.
(4)    Excludes the effects of stock options, restricted and performance stock units outstanding.

The following table provides the impact of share repurchases under the Company’s share repurchase program:
(U.S. Dollars in thousands except share data)Three Months EndedCumulative
 September 30,June 30,March 31,December 31,September 30,September 30,
 202220222022202120212022
Effect of share repurchases:
Aggregate cost of shares repurchased$10,147 $320,688 $254,988 $362,097 $386,882 $5,871,883 
Shares repurchased236,194 7,090,447 5,564,764 8,668,100 9,704,956 433,570,317 
Average price per share repurchased$42.96 $45.23 $45.82 $41.77 $39.86 $13.54 
Remaining share repurchase authorization (1)$596,411 
(1)    Repurchases under the share repurchase authorization may be effected from time to time in open market or privately negotiated transactions through December 31, 2022.
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