UNITED STATES

SECURITIES AND EXCHANGE COMMISSION

WASHINGTON, D.C. 20549

FORM 10-Q


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

For the quarterly period ended

September 30, ~~2021~~2022



Or

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

Commission file number: 001-16209

ARCH CAPITAL GROUP LTD.

(Exact name of registrant as specified in its charter)

Bermuda

98-0374481

(State or other jurisdiction of incorporation or organization)

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

Waterloo House, Ground Floor

100 Pitts Bay Road,

Pembroke

HM 08,

Bermuda

(441)

278-9250

(Address of principal executive offices)

(Registrant’s telephone number, including area code)

Securities registered pursuant to Section 12(b) of the Exchange Act:

Title of each class

Trading Symbol (s)

Name of each exchange on which registered

Common shares, $0.0011 par value per share

ACGL

NASDAQ

Stock Market

Depositary shares, each representing a 1/1000th interest in a 5.45% Series F preferred share

ACGLO

NASDAQ

Stock Market

Depositary shares, each representing a 1/1000th interest in a 4.55% Series G preferred share

ACGLN

NASDAQ

Stock Market

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

Indicate by check mark whether the registrant has submitted electronically every Interactive Data File required to be submitted pursuant to Rule 405 of Regulation S-T (§232.405 of this chapter) during the preceding 12 months (or for such shorter period that the registrant was required to submit such files). Yes ☑No ☐

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

Large Accelerated Filer ☑ Accelerated Filer ☐ Non-accelerated Filer ☐ Smaller reporting company ☐ 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. ☐

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

As of ~~November 1, 2021,~~October 31, 2022, there were ~~386,133,743~~369,873,027 common shares, $0.0011 par value per share, of the registrant outstanding.

Table of Contents

ARCH CAPITAL GROUP LTD.

INDEX TO FORM 10-Q


		Page No.
	PART I
	Financial Information	2
Item 1.	Consolidated Financial Statements	4
Item 2.	Management’s Discussion and Analysis of Financial Condition and Results of Operations	4241
Item 3.	Quantitative and Qualitative Disclosures About Market Risk	6966
Item 4.	Controls and Procedures	6967

	PART II
	Other Information	7067
Item 1.	Legal Proceedings	7067
Item 1A.	Risk Factors	7067
Item 2.	Unregistered Sales of Equity Securities and Use of Proceeds	7168
Item 3.	Defaults Upon Senior Securities	7168
Item 4.	Mine Safety Disclosures	7168
Item 5.	Other Information	7168
Item 6.	Exhibits	7269
	Signatures	7370


ARCH CAPITAL			1			~~2021~~2022 THIRD QUARTER FORM 10-Q

Table of Contents

PART I. FINANCIAL INFORMATION

Cautionary Note Regarding Forward-Looking Statements

The Private Securities Litigation Reform Act of 1995 (“PSLRA”) provides a “safe harbor” for forward-looking statements. This report or any other written or oral statements made by or on behalf of us may include forward-looking statements, which reflect our 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 report 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 our 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 report and in our periodic reports filed with the Securities and Exchange Commission (the “SEC”), and include:

•our ability to successfully implement our business strategy during “soft” as well as “hard” markets;

•acceptance of our business strategy, security and financial condition by rating agencies and regulators, as well as by brokers and our insureds and reinsureds;

•our ability to consummate acquisitions and integrate the business we have acquired or may acquire into our existing operations;

•our ability to maintain or improve our ratings, which may be affected by our 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 we operate;

•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 our access to such markets;

•our ability to successfully enhance, integrate and maintain operating procedures (including information technology) to effectively support our 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 our 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 us and adverse development on claim and/or claim expense liabilities related to business written by our 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 for natural or man-made catastrophic events or severe economic events in our insurance, reinsurance and mortgage businesses could cause large losses and substantial volatility in our results of operations;

•the effect of climate change on our business;

•the effect of contagious disease (including COVID-19) on our business;

•acts of terrorism, political unrest and other hostilities or other unforecasted and unpredictable events;


ARCH CAPITAL			2			~~2021~~2022 THIRD QUARTER FORM 10-Q

Table of Contents

•availability to us of reinsurance to manage our 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 us;

•the timing of loss payments being faster or the receipt of reinsurance recoverables being slower than anticipated by us;

•our investment performance, including legislative or regulatory developments that may adversely affect the fair value of our investments;

•changes in general economic conditions, including sovereign debt concerns or downgrades of U.S. securities by credit rating agencies, which could affect our business, financial condition and results of operations;

•changes in the method for determining the London Inter-bank Offered Rate (“LIBOR”) and the ~~potential~~ replacement of ~~LIBOR;~~LIBOR with alternative benchmark rates;

•the volatility of our shareholders’ equity from foreign currency fluctuations, which could increase due to us not matching portions of our projected liabilities in foreign currencies with investments in the same currencies;

•changes in accounting principles or policies or in our application of such accounting principles or policies;

•changes in the political environment of certain countries in which we operate or underwrite business;

•a disruption caused by cyber-attacks or other technology breaches or failures on us or our business partners and service providers, which could negatively impact our business and/or expose us to litigation;

•statutory or regulatory developments, including as to tax 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 us, our subsidiaries, brokers or customers, including new guidance implementing the Tax Cuts and Jobs Act of ~~2017;~~2017 and the possible implementation of the Organization for Economic Cooperation and Development (“OECD”) Pillar I and Pillar II initiatives; 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 our Annual Report on Form 10-K for the year ended December 31, ~~2020,~~2021, as well as the other factors set forth in our 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 us or persons acting on our 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. We undertake no obligation to publicly update or revise any forward-looking statement, whether as a result of new information, future events or otherwise.


ARCH CAPITAL			3			~~2021~~2022 THIRD QUARTER FORM 10-Q

Table of Contents

ITEM 1. CONSOLIDATED FINANCIAL STATEMENTS


						Page No.

Report of Independent Registered Public Accounting Firm						5

Consolidated Balance Sheets
September 30, ~~2021 (unaudited)~~2022 and December 31, ~~2020~~2021 (unaudited)						6

Consolidated Statements of Income
For the three and nine month periods ended September 30, ~~2021~~2022 and ~~2020~~2021 (unaudited)						7

Consolidated Statements of Comprehensive Income
For the three and nine month periods ended September 30, ~~2021~~2022 and ~~2020~~2021 (unaudited)						8

Consolidated Statements of Changes in Shareholders’ Equity
For the three and nine month periods ended September 30, ~~2021~~2022 and ~~2020~~2021 (unaudited)						9

Consolidated Statements of Cash Flows
For the nine month periods ended September 30, ~~2021~~2022 and ~~2020~~2021 (unaudited)						10

Notes to Consolidated Financial Statements (unaudited)
Note 1 - Basis of Presentation and Recent Accounting Pronouncements						11

Note 2 - A ~~cquisitions~~Share Transactions						11
Note 3 ~~- Share Transactions~~						12
~~Note~~ 4 - Earnings Per Common Share						13
Note 5 4 - Segment Information						14
Note 6 5 - Reserve for Losses and Loss Adjustment Expenses						19
Note 7 6 - Allowance for Expected Credit Losses						2122
Note 8 7 - Investment Information						2324
Note 9 8 - Fair Value						30
Note 10 9 - Derivative Instruments						36
Note 1 1 10 - Commitments and Contingencies						37

Note 1 2 11 - Variable Interest Entities and Noncontrolling Interests						37
Note 1 3 12 - Other Comprehensive Income (Loss)						39

Note 13 - Income Taxes						40
Note 14 - Legal Proceedings						40
Note 15 - Transactions with Related Parties						40

~~Note 1~~4 ~~- Income Taxes~~						41
~~Note 1~~5 ~~- Legal Proceedings~~						41
~~Note 1~~6 ~~- Transactions with Related Parties~~						41
~~Note 1~~7 ~~- Subsequent Event~~						41


ARCH CAPITAL			4			~~2021~~2022 THIRD QUARTER FORM 10-Q

Table of Contents

Report of Independent Registered Public Accounting Firm

To the Board of Directors and Shareholders of Arch Capital Group Ltd.

Results of Review of Interim Financial Statements

We have reviewed the accompanying consolidated balance sheet of Arch Capital Group Ltd. and its subsidiaries (the “Company”) as of September 30, ~~2021,~~2022, and the related consolidated statements of income, comprehensive income, and changes in shareholders’ equity for the three-month and nine-month periods ended September 30, ~~2021~~2022 and ~~2020,~~2021, and the consolidated statements of cash flows for the nine-month periods ended September 30, ~~2021~~2022 and ~~2020,~~2021, including the related notes (collectively referred to as the “interim financial statements”). Based on our reviews, we are not aware of any material modifications that should be made to the accompanying interim financial statements for them to be in conformity with accounting principles generally accepted in the United States of America.

We have previously audited, in accordance with the standards of the Public Company Accounting Oversight Board (United States) (PCAOB), the consolidated balance sheet of the Company as of December 31, ~~2020,~~2021, and the related consolidated statements of income, comprehensive income, changes in shareholders’ equity, and cash flows for the year then ended (not presented herein), and in our report dated February ~~26, 2021,~~25, 2022, we expressed an unqualified opinion on those consolidated financial statements. In our opinion, the information set forth in the accompanying consolidated balance sheet as of December 31, ~~2020,~~2021, is fairly stated, in all material respects, in relation to the consolidated balance sheet from which it has been derived.

Basis for Review Results

These interim financial statements are the responsibility of the Company’s management. We are a public accounting firm registered with the PCAOB and are required to be independent with respect to the Company in accordance with the U.S. federal securities laws and the applicable rules and regulations of the Securities and Exchange Commission and the PCAOB. We conducted our review in accordance with the standards of the PCAOB. A review of interim financial information consists principally of applying analytical procedures and making inquiries of persons responsible for financial and accounting matters. It is substantially less in scope than an audit conducted in accordance with the standards of the PCAOB, the objective of which is the expression of an opinion regarding the financial statements taken as a whole. Accordingly, we do not express such an opinion.

/s/ PricewaterhouseCoopers LLP

New York, NYNew York

November ~~4, 2021~~3, 2022


ARCH CAPITAL			5			~~2021~~2022 THIRD QUARTER FORM 10-Q

Table of Contents

ARCH CAPITAL GROUP LTD. AND SUBSIDIARIES

CONSOLIDATED BALANCE SHEETS

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


		(Unaudited)					(Unaudited)
		September 30, 2021		December 31, 2020			September 30, 2022		December 31, 2021
Assets	Assets					Assets
Investments:	Investments:					Investments:
Fixed maturities available for sale, at fair value (amortized cost: $16,629,621 and $18,143,305; net of allowance for credit losses: $2,111 and $2,397 )		$	16,768,363	$	18,717,825
Short-term investments available for sale, at fair value (amortized cost: $3,070,120 and $1,924,292; net of allowance for credit losses: $0 and $0)		3,069,965		1,924,922
Collateral received under securities lending, at fair value (amortized cost: $— and $301,089)		—		301,096
Fixed maturities available for sale, at fair value (amortized cost: $19,913,055 and $17,973,823; net of allowance for credit losses: $45,993 and $2,883)						Fixed maturities available for sale, at fair value (amortized cost: $19,913,055 and $17,973,823; net of allowance for credit losses: $45,993 and $2,883)	$	18,120,727	$	17,998,109
Short-term investments available for sale, at fair value (amortized cost: $1,941,071 and $1,734,738; net of allowance for credit losses: $0 and $0)						Short-term investments available for sale, at fair value (amortized cost: $1,941,071 and $1,734,738; net of allowance for credit losses: $0 and $0)	1,940,857		1,734,716

Equity securities, at fair value	Equity securities, at fair value	1,790,640		1,444,830		Equity securities, at fair value	809,869		1,804,170

Other investments (portion measured at fair value: $2,043,970 and $3,824,796)		2,043,970		4,324,796
Other investments, at fair value						Other investments, at fair value	1,578,751		1,973,550
Investments accounted for using the equity method	Investments accounted for using the equity method	2,741,293		2,047,889		Investments accounted for using the equity method	3,565,946		3,077,611
Total investments	Total investments	26,414,231		28,761,358		Total investments	26,016,150		26,588,156

Cash	Cash	1,137,721		906,448		Cash	813,583		858,668
Accrued investment income	Accrued investment income	75,832		103,299		Accrued investment income	116,263		85,453
Securities pledged under securities lending, at fair value (amortized cost: $— and $294,493)		—		294,912

Investment in operating affiliates	Investment in operating affiliates	1,111,825		129,291		Investment in operating affiliates	891,212		1,135,655
Premiums receivable (net of allowance for credit losses: $38,715 and $37,781)		2,807,720		2,064,586
Reinsurance recoverable on unpaid and paid losses and loss adjustment expenses (net of allowance for credit losses: $12,831 and $11,636)		5,358,852		4,500,802
Contractholder receivables (net of allowance for credit losses: $3,484 and $8,638)		1,824,990		1,986,924
Premiums receivable (net of allowance for credit losses: $38,229 and $39,958)						Premiums receivable (net of allowance for credit losses: $38,229 and $39,958)	3,579,380		2,633,280
Reinsurance recoverable on unpaid and paid losses and loss adjustment expenses (net of allowance for credit losses: $17,366 and $13,230)						Reinsurance recoverable on unpaid and paid losses and loss adjustment expenses (net of allowance for credit losses: $17,366 and $13,230)	6,356,456		5,880,735
Contractholder receivables (net of allowance for credit losses: $2,360 and $3,437)						Contractholder receivables (net of allowance for credit losses: $2,360 and $3,437)	1,735,730		1,828,691
Ceded unearned premiums	Ceded unearned premiums	1,824,910		1,234,075		Ceded unearned premiums	2,115,539		1,729,455
Deferred acquisition costs	Deferred acquisition costs	893,665		790,708		Deferred acquisition costs	1,122,711		901,841
Receivable for securities sold	Receivable for securities sold	84,019		92,743		Receivable for securities sold	27,042		60,179
Goodwill and intangible assets	Goodwill and intangible assets	963,322		692,863		Goodwill and intangible assets	806,655		944,983

Other assets	Other assets	2,286,649		1,724,288		Other assets	2,756,383		2,453,849
Total assets	Total assets	$	44,783,736	$	43,282,297	Total assets	$	46,337,104	$	45,100,945

Liabilities	Liabilities					Liabilities
Reserve for losses and loss adjustment expenses	Reserve for losses and loss adjustment expenses	$	17,331,047	$	16,513,929	Reserve for losses and loss adjustment expenses	$	19,288,291	$	17,757,156
Unearned premiums	Unearned premiums	6,165,114		4,838,965		Unearned premiums	7,271,279		6,011,942
Reinsurance balances payable	Reinsurance balances payable	1,403,929		683,263		Reinsurance balances payable	1,669,592		1,583,253
Contractholder payables	Contractholder payables	1,828,474		1,995,562		Contractholder payables	1,738,089		1,832,127
Collateral held for insured obligations	Collateral held for insured obligations	254,259		215,581		Collateral held for insured obligations	254,720		242,352
Senior notes	Senior notes	2,724,149		2,861,113		Senior notes	2,725,153		2,724,394
Revolving credit agreement borrowings		—		155,687
Securities lending payable		—		301,089

Payable for securities purchased	Payable for securities purchased	357,531		218,779		Payable for securities purchased	174,769		64,850
Other liabilities	Other liabilities	1,321,470		1,510,888		Other liabilities	1,411,193		1,329,742
Total liabilities	Total liabilities	31,385,973		29,294,856		Total liabilities	34,533,086		31,545,816

Commitments and Contingencies	Commitments and Contingencies	0		0		Commitments and Contingencies
Redeemable noncontrolling interests	Redeemable noncontrolling interests	10,237		58,548		Redeemable noncontrolling interests	8,908		9,233

Shareholders' Equity	Shareholders' Equity					Shareholders' Equity
Non-cumulative preferred shares	Non-cumulative preferred shares	830,000		780,000		Non-cumulative preferred shares	830,000		830,000

Common shares ($0.0011 par, shares issued: 582,908,723 and 579,000,841)		648		643
Common shares ($0.0011 par, shares issued: 587,134,047 and 583,289,850)						Common shares ($0.0011 par, shares issued: 587,134,047 and 583,289,850)	652		648
Additional paid-in capital	Additional paid-in capital	2,061,906		1,977,794		Additional paid-in capital	2,186,599		2,085,075
Retained earnings	Retained earnings	13,842,787		12,362,463		Retained earnings	15,042,561		14,455,868
Accumulated other comprehensive income (loss), net of deferred income tax	Accumulated other comprehensive income (loss), net of deferred income tax	49,184		488,895		Accumulated other comprehensive income (loss), net of deferred income tax	(1,891,827)		(64,600)
Common shares held in treasury, at cost (shares: 195,650,971 and 172,280,199)		(3,396,999)		(2,503,909)
Common shares held in treasury, at cost (shares: 217,812,057 and 204,365,956)						Common shares held in treasury, at cost (shares: 217,812,057 and 204,365,956)	(4,372,875)		(3,761,095)
Total shareholders' equity available to Arch	Total shareholders' equity available to Arch	13,387,526		13,105,886		Total shareholders' equity available to Arch	11,795,110		13,545,896
Non-redeemable noncontrolling interests		—		823,007
Total shareholders' equity		13,387,526		13,928,893

Total liabilities, noncontrolling interests and shareholders' equity	Total liabilities, noncontrolling interests and shareholders' equity	$	44,783,736	$	43,282,297	Total liabilities, noncontrolling interests and shareholders' equity	$	46,337,104	$	45,100,945

See Notes to Consolidated Financial Statements


ARCH CAPITAL			6			~~2021~~2022 THIRD QUARTER FORM 10-Q

Table of Contents

ARCH CAPITAL GROUP LTD. AND SUBSIDIARIES

CONSOLIDATED STATEMENTS OF INCOME

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


		(Unaudited)				(Unaudited)					(Unaudited)				(Unaudited)
		Three Months Ended				Nine Months Ended					Three Months Ended				Nine Months Ended
		September 30,				September 30,					September 30,				September 30,
		2021		2020		2021		2020			2022		2021		2022		2021
Revenues	Revenues									Revenues

Net premiums earned	Net premiums earned	$	1,929,337	$	1,771,092	5,998,668		5,180,890		Net premiums earned	$	2,470,750	$	1,929,337	6,917,158		5,998,668
Net investment income	Net investment income	88,195		128,512		298,664		405,150		Net investment income	128,640		88,195		315,468		298,664
Net realized gains (losses)	Net realized gains (losses)	(25,040)		280,499		320,328		470,127		Net realized gains (losses)	(183,673)		(25,040)		(742,666)		320,328

Other underwriting income	Other underwriting income	7,274		5,413		18,913		18,932		Other underwriting income	3,077		7,274		11,944		18,913
Equity in net income (loss) of investment funds accounted for using the equity method	Equity in net income (loss) of investment funds accounted for using the equity method	105,398		126,735		299,270		57,407		Equity in net income (loss) of investment funds accounted for using the equity method	(18,861)		105,398		75,505		299,270
Other income (loss)	Other income (loss)	(3,960)		—		1,151		65		Other income (loss)	(13,684)		(3,960)		(34,486)		1,151
Total revenues	Total revenues	2,101,204		2,312,251		6,936,994		6,132,571		Total revenues	2,386,249		2,101,204		6,542,923		6,936,994

Expenses	Expenses									Expenses
Losses and loss adjustment expenses	Losses and loss adjustment expenses	1,226,019		1,216,273		3,588,950		3,562,214		Losses and loss adjustment expenses	1,682,696		1,226,019		3,786,187		3,588,950
Acquisition expenses	Acquisition expenses	306,015		247,942		945,639		750,014		Acquisition expenses	447,587		306,015		1,239,065		945,639
Other operating expenses	Other operating expenses	230,832		215,686		736,808		659,479		Other operating expenses	274,747		230,832		842,082		736,808
Corporate expenses	Corporate expenses	19,672		17,937		61,007		56,653		Corporate expenses	17,710		19,672		77,662		61,007
Amortization of intangible assets	Amortization of intangible assets	20,135		16,715		49,823		49,835		Amortization of intangible assets	26,104		20,135		80,478		49,823
Interest expense	Interest expense	33,176		41,343		107,222		105,037		Interest expense	33,063		33,176		98,566		107,222
Net foreign exchange (gains) losses	Net foreign exchange (gains) losses	(36,078)		44,885		(38,366)		11,425		Net foreign exchange (gains) losses	(90,509)		(36,078)		(182,129)		(38,366)
Total expenses	Total expenses	1,799,771		1,800,781		5,451,083		5,194,657		Total expenses	2,391,398		1,799,771		5,941,911		5,451,083

Income (loss) before income taxes and income (loss) from operating affiliates	Income (loss) before income taxes and income (loss) from operating affiliates	301,433		511,470		1,485,911		937,914		Income (loss) before income taxes and income (loss) from operating affiliates	(5,149)		301,433		601,012		1,485,911
Income tax expense		(4,137)		(23,707)		(94,176)		(77,779)
Income tax (expense) benefit										Income tax (expense) benefit	14,900		(4,137)		(19,042)		(94,176)
Income (loss) from operating affiliates	Income (loss) from operating affiliates	124,119		919		224,052		6,262		Income (loss) from operating affiliates	8,507		124,119		37,665		224,052
Net income (loss)	Net income (loss)	$	421,415	$	488,682	$	1,615,787	$	866,397	Net income (loss)	$	18,258	$	421,415	$	619,635	$	1,615,787
Net (income) loss attributable to noncontrolling interests	Net (income) loss attributable to noncontrolling interests	(1,473)		(69,643)		(82,203)		(4,420)		Net (income) loss attributable to noncontrolling interests	(1,157)		(1,473)		(2,390)		(82,203)
Net income (loss) available to Arch	Net income (loss) available to Arch	419,942		419,039		1,533,584		861,977		Net income (loss) available to Arch	17,101		419,942		617,245		1,533,584
Preferred dividends	Preferred dividends	(16,090)		(10,403)		(38,159)		(31,209)		Preferred dividends	(10,184)		(16,090)		(30,552)		(38,159)
Loss on redemption of preferred shares	Loss on redemption of preferred shares	(15,101)		—		(15,101)		—		Loss on redemption of preferred shares	—		(15,101)		—		(15,101)
Net income (loss) available to Arch common shareholders	Net income (loss) available to Arch common shareholders	$	388,751	$	408,636	$	1,480,324	$	830,768	Net income (loss) available to Arch common shareholders	$	6,917	$	388,751	$	586,693	$	1,480,324

Net income per common share and common share equivalent	Net income per common share and common share equivalent									Net income per common share and common share equivalent
Basic	Basic	$	1.00	$	1.01	$	3.74	$	2.06	Basic	$	0.02	$	1.00	$	1.59	$	3.74
Diluted	Diluted	$	0.98	$	1.00	$	3.66	$	2.02	Diluted	$	0.02	$	0.98	$	1.55	$	3.66

Weighted average common shares and common share equivalents outstanding	Weighted average common shares and common share equivalents outstanding									Weighted average common shares and common share equivalents outstanding
Basic	Basic	389,274,220		402,850,485		395,899,591		403,081,266		Basic	365,190,527		389,274,220		369,525,348		395,899,591
Diluted	Diluted	397,903,347		409,194,657		404,260,485		410,314,897		Diluted	373,727,277		397,903,347		378,373,180		404,260,485

See Notes to Consolidated Financial Statements


ARCH CAPITAL			7			~~2021~~2022 THIRD QUARTER FORM 10-Q

Table of Contents

ARCH CAPITAL GROUP LTD. AND SUBSIDIARIES

CONSOLIDATED STATEMENTS OF COMPREHENSIVE INCOME

(U.S. dollars in thousands)


		(Unaudited)				(Unaudited)					(Unaudited)				(Unaudited)
		Three Months Ended				Nine Months Ended					Three Months Ended				Nine Months Ended
		September 30,				September 30,					September 30,				September 30,
		2021		2020		2021		2020			2022		2021		2022		2021
Comprehensive Income	Comprehensive Income									Comprehensive Income
Net income (loss)	Net income (loss)	$	421,415	$	488,682	$	1,615,787	$	866,397	Net income (loss)	$	18,258	$	421,415	$	619,635	$	1,615,787
Other comprehensive income (loss), net of deferred income tax	Other comprehensive income (loss), net of deferred income tax									Other comprehensive income (loss), net of deferred income tax
Unrealized appreciation (decline) in value of available-for-sale investments:	Unrealized appreciation (decline) in value of available-for-sale investments:									Unrealized appreciation (decline) in value of available-for-sale investments:
Unrealized holding gains (losses) arising during period	Unrealized holding gains (losses) arising during period	(95,923)		110,782		(279,102)		546,291		Unrealized holding gains (losses) arising during period	(609,759)		(95,923)		(1,892,119)		(279,102)

Reclassification of net realized (gains) losses, included in net income (loss)	Reclassification of net realized (gains) losses, included in net income (loss)	(62,654)		(79,803)		(120,504)		(368,423)		Reclassification of net realized (gains) losses, included in net income (loss)	46,585		(62,654)		206,573		(120,504)
Foreign currency translation adjustments	Foreign currency translation adjustments	(31,710)		16,709		(54,089)		(5,729)		Foreign currency translation adjustments	(70,388)		(31,710)		(141,681)		(54,089)
Comprehensive income (loss)	Comprehensive income (loss)	231,128		536,370		1,162,092		1,038,536		Comprehensive income (loss)	(615,304)		231,128		(1,207,592)		1,162,092
Net (income) loss attributable to noncontrolling interests	Net (income) loss attributable to noncontrolling interests	(1,473)		(69,643)		(82,203)		(4,420)		Net (income) loss attributable to noncontrolling interests	(1,157)		(1,473)		(2,390)		(82,203)
Other comprehensive (income) loss attributable to noncontrolling interests	Other comprehensive (income) loss attributable to noncontrolling interests	9,423		(10,820)		13,983		2,127		Other comprehensive (income) loss attributable to noncontrolling interests	—		9,423		—		13,983
Comprehensive income (loss) available to Arch	Comprehensive income (loss) available to Arch	$	239,078	$	455,907	$	1,093,872	$	1,036,243	Comprehensive income (loss) available to Arch	$	(616,461)	$	239,078	$	(1,209,982)	$	1,093,872

See Notes to Consolidated Financial Statements


ARCH CAPITAL			8			~~2021~~2022 THIRD QUARTER FORM 10-Q

Table of Contents

ARCH CAPITAL GROUP LTD. AND SUBSIDIARIES

CONSOLIDATED STATEMENTS OF CHANGES IN SHAREHOLDERS’ EQUITY

(U.S. dollars in thousands)

(Unaudited) (Unaudited)
Three Months Ended Nine Months Ended
September 30, September 30,
2021 2020 2021 2020
Non-cumulative preferred shares
Balance at beginning of period $ 1,280,000 $ 780,000 $ 780,000 $ 780,000
Preferred shares issued — — 500,000 —
Preferred shares redeemed (450,000) — (450,000) —
Balance at beginning and end of period $ 830,000 $ 780,000 $ 830,000 $ 780,000
Common shares
Balance at beginning of period 647 642 643 638
Common shares issued, net 1 — 5 4
Balance at end of period 648 642 648 642
Additional paid-in capital
Balance at beginning of period 2,028,919 1,935,514 1,977,794 1,889,683
Amortization of share-based compensation 14,216 14,662 71,279 55,872
Issue costs on preferred shares — — (14,179) —
Reversal of issue costs on preferred shares redeemed 15,101 — 15,101 —
Other changes 3,670 606 11,911 5,227
Balance at end of period 2,061,906 1,950,782 2,061,906 1,950,782
Retained earnings
Balance at beginning of period 13,454,036 11,420,686 12,362,463 11,021,006
Cumulative effect of an accounting change (1) — — — (22,452)
Balance at beginning of period, as adjusted 13,454,036 11,420,686 12,362,463 10,998,554
Net income (loss) 421,415 488,682 1,615,787 866,397
Net (income) loss attributable to noncontrolling interests (1,473) (69,643) (82,203) (4,420)
Preferred share dividends (16,090) (10,403) (38,159) (31,209)
Loss on redemption of preferred shares (15,101) — (15,101) —
Balance at end of period 13,842,787 11,829,322 13,842,787 11,829,322
Accumulated other comprehensive income (loss), net of deferred income tax
Balance at beginning of period 230,048 349,488 488,895 212,091
Unrealized appreciation (decline) in value of available-for-sale investments, net of deferred income tax:
Balance at beginning of period 264,702 418,487 501,295 258,486
Unrealized holding gains (losses) during period, net of reclassification adjustment (158,577) 30,979 (399,606) 177,868
Unrealized holding gains (losses) during period attributable to noncontrolling interests 10,752 (11,179) 15,188 1,933
Balance at end of period 116,877 438,287 116,877 438,287
Foreign currency translation adjustments, net of deferred income tax:
Balance at beginning of period (34,654) (68,999) (12,400) (46,395)
Foreign currency translation adjustments (31,710) 16,709 (54,089) (5,729)
Foreign currency translation adjustments attributable to noncontrolling interests (1,329) 360 (1,204) 194
Balance at end of period (67,693) (51,930) (67,693) (51,930)
Balance at end of period 49,184 386,357 49,184 386,357
Common shares held in treasury, at cost
Balance at beginning of period (3,007,578) (2,494,505) (2,503,909) (2,406,047)
Shares repurchased for treasury (389,421) (601) (893,090) (89,059)
Balance at end of period (3,396,999) (2,495,106) (3,396,999) (2,495,106)
Total shareholders’ equity available to Arch 13,387,526 12,451,997 13,387,526 12,451,997
Non-redeemable noncontrolling interests — 757,920 — 757,920
Total shareholders’ equity $ 13,387,526 $ 13,209,917 $ 13,387,526 $ 13,209,917

~~(1) Adoption of~~ ~~ASU 2016-13, “Financial Instruments - Credit Losses (Topic 326)”.~~


	(Unaudited)				(Unaudited)
	Three Months Ended				Nine Months Ended
	September 30,				September 30,
	2022		2021		2022		2021
Non-cumulative preferred shares
Balance at beginning of period	$	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







Common shares
Balance at beginning of period	652		647		648		643
Common shares issued, net	—		1		4		5
Balance at end of period	652		648		652		648

Additional paid-in capital
Balance at beginning of period	2,170,661		2,028,919		2,085,075		1,977,794



Amortization of share-based compensation	13,518		14,216		80,023		71,279
Issue costs on preferred shares	—		—		—		(14,179)
Reversal of issue costs on preferred shares redeemed	—		15,101		—		15,101

Other changes	2,420		3,670		21,501		11,911
Balance at end of period	2,186,599		2,061,906		2,186,599		2,061,906

Retained earnings
Balance at beginning of period	15,035,644		13,454,036		14,455,868		12,362,463


Net income (loss)	18,258		421,415		619,635		1,615,787
Net (income) loss attributable to noncontrolling interests	(1,157)		(1,473)		(2,390)		(82,203)
Preferred share dividends	(10,184)		(16,090)		(30,552)		(38,159)
Loss on redemption of preferred shares	—		(15,101)		—		(15,101)
Balance at end of period	15,042,561		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)		230,048		(64,600)		488,895
Unrealized appreciation (decline) in value of available-for-sale investments, net of deferred income tax:
Balance at beginning of period	(1,108,886)		264,702		13,486		501,295


Unrealized holding gains (losses) during period, net of reclassification adjustment	(563,174)		(158,577)		(1,685,546)		(399,606)
Unrealized holding gains (losses) during period attributable to noncontrolling interests	—		10,752		—		15,188

Balance at end of period	(1,672,060)		116,877		(1,672,060)		116,877
Foreign currency translation adjustments, net of deferred income tax:
Balance at beginning of period	(149,379)		(34,654)		(78,086)		(12,400)
Foreign currency translation adjustments	(70,388)		(31,710)		(141,681)		(54,089)
Foreign currency translation adjustments attributable to noncontrolling interests	—		(1,329)		—		(1,204)
Balance at end of period	(219,767)		(67,693)		(219,767)		(67,693)
Balance at end of period	(1,891,827)		49,184		(1,891,827)		49,184

Common shares held in treasury, at cost
Balance at beginning of period	(4,361,126)		(3,007,578)		(3,761,095)		(2,503,909)
Shares repurchased for treasury	(11,749)		(389,421)		(611,780)		(893,090)
Balance at end of period	(4,372,875)		(3,396,999)		(4,372,875)		(3,396,999)



Total shareholders’ equity	$	11,795,110	$	13,387,526	$	11,795,110	$	13,387,526

See Notes to Consolidated Financial Statements


ARCH CAPITAL			9			~~2021~~2022 THIRD QUARTER FORM 10-Q

Table of Contents

ARCH CAPITAL GROUP LTD. AND SUBSIDIARIES

CONSOLIDATED STATEMENTS OF CASH FLOWS

(U.S. dollars in thousands)


		(Unaudited)					(Unaudited)
		Nine Months Ended					Nine Months Ended
		September 30,					September 30,
		2021		2020			2022		2021
Operating Activities	Operating Activities					Operating Activities
Net income (loss)	Net income (loss)	$	1,615,787	$	866,397	Net income (loss)	$	619,635	$	1,615,787
Adjustments to reconcile net income (loss) to net cash provided by operating activities:	Adjustments to reconcile net income (loss) to net cash provided by operating activities:					Adjustments to reconcile net income (loss) to net cash provided by operating activities:
Net realized (gains) losses	Net realized (gains) losses	(367,313)		(477,683)		Net realized (gains) losses	742,680		(367,313)

Equity in net (income) or loss of investment funds accounted for using the equity method and other income or loss	Equity in net (income) or loss of investment funds accounted for using the equity method and other income or loss	(372,650)		30,306		Equity in net (income) or loss of investment funds accounted for using the equity method and other income or loss	106,405		(372,650)
Amortization of intangible assets	Amortization of intangible assets	49,823		49,835		Amortization of intangible assets	80,478		49,823
Share-based compensation	Share-based compensation	72,303		56,433		Share-based compensation	80,029		72,303
Changes in:	Changes in:					Changes in:
Reserve for losses and loss adjustment expenses, net of unpaid losses and loss adjustment expenses recoverable	Reserve for losses and loss adjustment expenses, net of unpaid losses and loss adjustment expenses recoverable	1,548,211		1,668,069		Reserve for losses and loss adjustment expenses, net of unpaid losses and loss adjustment expenses recoverable	1,553,084		1,548,211
Unearned premiums, net of ceded unearned premiums	Unearned premiums, net of ceded unearned premiums	985,242		498,811		Unearned premiums, net of ceded unearned premiums	1,125,395		985,242
Premiums receivable	Premiums receivable	(847,098)		(461,766)		Premiums receivable	(1,095,741)		(847,098)
Deferred acquisition costs	Deferred acquisition costs	(247,966)		(107,238)		Deferred acquisition costs	(242,377)		(247,966)
Reinsurance balances payable	Reinsurance balances payable	618,571		205,620		Reinsurance balances payable	128,418		618,571
Other items, net	Other items, net	(427,359)		2,666		Other items, net	(264,289)		(427,359)
Net cash provided by (used for) operating activities		2,627,551		2,331,450
Net cash provided by operating activities						Net cash provided by operating activities	2,833,717		2,627,551
Investing Activities	Investing Activities					Investing Activities
Purchases of fixed maturity investments	Purchases of fixed maturity investments	(29,870,023)		(34,050,883)		Purchases of fixed maturity investments	(13,065,302)		(29,870,023)
Purchases of equity securities	Purchases of equity securities	(978,951)		(1,355,848)		Purchases of equity securities	(786,733)		(978,951)
Purchases of other investments	Purchases of other investments	(1,350,056)		(841,886)		Purchases of other investments	(1,270,099)		(1,350,056)
Proceeds from sales of fixed maturity investments	Proceeds from sales of fixed maturity investments	30,067,792		32,544,867		Proceeds from sales of fixed maturity investments	9,990,418		30,067,792
Proceeds from sales of equity securities	Proceeds from sales of equity securities	695,633		731,793		Proceeds from sales of equity securities	1,539,808		695,633
Proceeds from sales, redemptions and maturities of other investments	Proceeds from sales, redemptions and maturities of other investments	1,487,919		791,807		Proceeds from sales, redemptions and maturities of other investments	1,075,679		1,487,919
Proceeds from redemptions and maturities of fixed maturity investments	Proceeds from redemptions and maturities of fixed maturity investments	1,234,412		645,292		Proceeds from redemptions and maturities of fixed maturity investments	577,864		1,234,412
Net settlements of derivative instruments	Net settlements of derivative instruments	(67,830)		163,290		Net settlements of derivative instruments	(106,347)		(67,830)

Net (purchases) sales of short-term investments	Net (purchases) sales of short-term investments	(1,172,798)		(1,159,351)		Net (purchases) sales of short-term investments	(151,980)		(1,172,798)
Change in cash collateral related to securities lending		—		81,210

Purchase of operating affiliate	Purchase of operating affiliate	(753,916)		—		Purchase of operating affiliate	—		(753,916)
Impact of the deconsolidation of the variable interest entity	Impact of the deconsolidation of the variable interest entity	(349,202)		—		Impact of the deconsolidation of the variable interest entity	—		(349,202)
Purchases of fixed assets	Purchases of fixed assets	(34,407)		(26,717)		Purchases of fixed assets	(38,383)		(34,407)
Other	Other	(361,857)		(131,992)		Other	128,354		(361,857)
Net cash provided by (used for) investing activities		(1,453,284)		(2,608,418)
Net cash used for investing activities						Net cash used for investing activities	(2,106,721)		(1,453,284)
Financing Activities	Financing Activities					Financing Activities
Proceeds from issuance of preferred shares, net	Proceeds from issuance of preferred shares, net	485,821		—		Proceeds from issuance of preferred shares, net	—		485,821
Redemption of preferred shares	Redemption of preferred shares	(450,000)		—		Redemption of preferred shares	—		(450,000)
Purchases of common shares under share repurchase program	Purchases of common shares under share repurchase program	(872,197)		(75,486)		Purchases of common shares under share repurchase program	(585,823)		(872,197)
Proceeds from common shares issued, net	Proceeds from common shares issued, net	281		(9,656)		Proceeds from common shares issued, net	(2,863)		281
Proceeds from borrowings		—		1,018,793
Repayments of borrowings		—		(304,000)
Change in cash collateral related to securities lending		—		(81,210)

Third party investment in non-redeemable noncontrolling interests	Third party investment in non-redeemable noncontrolling interests	15,971		(2,867)		Third party investment in non-redeemable noncontrolling interests	—		15,971

Dividends paid to redeemable noncontrolling interests	Dividends paid to redeemable noncontrolling interests	(1,907)		(3,541)		Dividends paid to redeemable noncontrolling interests	—		(1,907)
Other	Other	(21,752)		55,266		Other	(84,639)		(21,752)
Preferred dividends paid	Preferred dividends paid	(38,096)		(31,209)		Preferred dividends paid	(30,552)		(38,096)
Net cash provided by (used for) financing activities		(881,879)		566,090
Net cash used for financing activities						Net cash used for financing activities	(703,877)		(881,879)

Effects of exchange rate changes on foreign currency cash and restricted cash	Effects of exchange rate changes on foreign currency cash and restricted cash	(34,023)		(5,847)		Effects of exchange rate changes on foreign currency cash and restricted cash	(79,566)		(34,023)

Increase (decrease) in cash and restricted cash	Increase (decrease) in cash and restricted cash	258,365		283,275		Increase (decrease) in cash and restricted cash	(56,447)		258,365
Cash and restricted cash, beginning of year	Cash and restricted cash, beginning of year	1,290,544		903,698		Cash and restricted cash, beginning of year	1,314,771		1,290,544
Cash and restricted cash, end of period	Cash and restricted cash, end of period	$	1,548,909	$	1,186,973	Cash and restricted cash, end of period	$	1,258,324	$	1,548,909

See Notes to Consolidated Financial Statements


ARCH CAPITAL			10			~~2021~~2022 THIRD QUARTER FORM 10-Q

Table of Contents

ARCH CAPITAL GROUP LTD. AND SUBSIDIARIES

NOTES TO CONSOLIDATED FINANCIAL STATEMENTS (UNAUDITED)

1. Basis of Presentation and Recent Accounting Pronouncements

General

Arch Capital Group Ltd. (“Arch Capital”) is a public listed Bermuda exempted company which provides insurance, reinsurance and mortgage insurance on a worldwide basis through its wholly-owned subsidiaries. As used herein, the “Company” means Arch Capital and its subsidiaries. The Company’s consolidated financial statements through June 30, 2021 included the results of Somers Group Holdings Ltd. (formerly Watford Holdings Ltd.) and its wholly owned subsidiaries (“~~Watford”~~Somers”) ~~through June 30, 2021.~~. Effective July 1, 2021, ~~Watford~~Somers is wholly owned by Greysbridge Holdings Ltd., (“Greysbridge”) and Greysbridge is owned 40% by the Company, 30% by certain investment funds managed by Kelso & Company (“Kelso”) and 30% by certain investment funds managed by Warburg Pincus LLC (“Warburg”). Based on the governing documents of Greysbridge, the Company concluded that, while it retains significant influence over ~~Watford, Watford~~Somers, Somers no longer constitutes a variable interest entity. Accordingly, effective July 1, 2021, Arch no longer consolidates the results of ~~Watford~~Somers in its consolidated financial statements and footnotes. See note 1211.

Basis of Presentation

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

Certain information and footnote disclosures normally included in financial statements prepared in accordance with GAAP have been condensed or omitted; however, management believes that the disclosures are adequate to make the information presented not misleading. This report should be read in conjunction with the Company’s Annual Report on Form 10-K for the year ended December 31, ~~2020~~2021

(“~~2020~~2021 Form 10-K”), including the Company’s audited consolidated financial statements and related notes.

The Company has reclassified the presentation of certain prior year information to conform to the current presentation, including the correct 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’.presentation. Such reclassifications had no effect on the Company’s net income, comprehensive income, shareholders’ equity or cash flows. ~~Management views the impact of the prior period misclassification as not material to the financial statements on a quantitative and qualitative basis. See~~ ~~note 8~~. Tabular amounts are in U.S. Dollars in thousands, except share amounts, unless otherwise noted.

Recent Accounting Pronouncements

~~Recently Issued Accounting Standards Adopted~~Inflation Reduction Act of 2022

On August 16, 2022, the U.S. government enacted the Inflation Reduction Act of 2022, which among other things implements a 15% minimum tax on book income of certain large corporations, a 1% excise tax on net stock repurchases and several tax incentives to promote clean energy. The effective date of these provisions is January 1, 2023. Based on its current analysis of the provisions, the Company adopted ASU 2019-12, “Simplifying the Accounting for Income Taxes.” This ASU eliminates certain exceptions for recognizing deferred taxes for investments, performing intraperiod tax allocations and calculating income taxes in interim periods. The ASU also clarifies the accounting for transactionsdoes not expect that ~~result in a step-up in the tax basis of goodwill. The adoption of~~ this ~~guidance did not~~legislation will have a material effect on the Company’s consolidated financial statements.

Recently Issued Accounting Standards Adopted

For information regarding additional accounting standards that the Company has not yet adopted, see note ~~3(r)~~3(s), “Significant Accounting Policies—Recent Accounting Pronouncements,” of the notes to consolidated financial statements in the Company’s ~~2020~~2021 Form 10-K.

2. ~~Acquisitions~~

~~Westpac Lenders Mortgage Insurance Limited (“WLMI”)~~

On August 31, 2021, the Company completed the acquisition of WLMI, an Australian Prudential Regulation Authority authorized captive lenders mortgage insurance (“LMI”) provider to the Westpac Banking Corporation (“Westpac”). As part of the acquisition, WLMI will retain its existing risk in force and remain Westpac’s exclusive provider of LMI on new mortgage originations for a period of 10 years. Upon completion of this transaction, the Company renamed WLMI to Arch Lenders Mortgage Indemnity Limited (“ALMI”). ~~ALMI will become the Company’s primary provider of LMI to the Australian market.~~


~~ARCH CAPITAL~~			11			~~2021 THIRD QUARTER FORM 10-Q~~

~~Table of Contents~~

~~ARCH CAPITAL GROUP LTD. AND SUBSIDIARIES~~

~~NOTES TO CONSOLIDATED FINANCIAL STATEMENTS (UNAUDITED)~~

~~Somerset Bridge Group Limited, Southern Rock Holdings Limited and affiliates (“Somerset”)~~

On August 6, 2021, the Company completed the acquisition of Somerset. The acquisition includes Somerset’s motor insurance managing general agent, distribution capabilities through direct and aggregator channels, affiliated insurer and fully integrated claims operation.

~~In connection with the acquisitions noted above, the Company increased its goodwill and intangible assets by $337.4 million.~~

3. Share Transactions

Share Repurchases

The board of directors of Arch Capital has authorized the investment in Arch Capital’s common shares through a share repurchase program. Since the inception of the share repurchase program, Arch Capital has repurchased ~~412.0~~433.6 million common shares for an aggregate purchase price of ~~$4.92~~$5.87 billion. For the nine months ended September 30, ~~2021,~~2022, Arch Capital repurchased ~~22.8~~12.9 million shares under the share repurchase program with an aggregate purchase price of ~~$872.2~~$585.8 million. ~~Arch Capital repurchased 2.6 million shares under the share repurchase program with an aggregate purchase price of $75.5 million during the nine months ended September 30, 2020.~~ At September 30, ~~2021, $44.3~~2022, $596.4 million of share repurchases were available under the program, which may be effected from time to time in open market or privately negotiated transactions. The timing and amount of the repurchase transactions under this program will depend on a variety of factors, including market conditions and corporate and regulatory considerations. ~~See~~


ARCH CAPITAL			11			2022 THIRD QUARTER FORM 10-Q

~~note 17~~Table of Contents.

ARCH CAPITAL GROUP LTD. AND SUBSIDIARIES

NOTES TO CONSOLIDATED FINANCIAL STATEMENTS (UNAUDITED)

The 2022 Long-Term Incentive and Share Award Plan (the“2022 Plan”)

The 2022 Plan became effective as of May 4, 2022 following approval by shareholders of the Company. The 2022 Plan provides for the issuance of stock options, stock appreciation rights, restricted shares, restricted share units payable in common shares or cash, dividend equivalents, performance shares and performance units and other share-based awards to Arch Capital’s eligible employees and directors. The number of common shares reserved for grants under the 2022 Plan, subject to anti-dilution adjustments in the event of certain changes in Arch Capital’s capital structure, is 9,000,000; provided, that no more than 6,000,000 common shares may be issued as incentive stock options under Section 422 of the Code. The 2022 Plan will terminate as to future awards on February 25, 2032. At September 30, 2022, 9,000,000 shares are available for future issuance.

Series G Preferred Shares

In June 2021, Arch Capital completed a $500 million underwritten public offering of 20.0 million depositary shares (the “Depositary Shares”), each of which represents a 1/1,000th interest in a share of its ~~4.550%~~4.55% Non-Cumulative Preferred Shares, Series G $0.01 par value and $25,000 liquidation preference per share (equivalent to $25 liquidation preference per Depositary Share) (the “Series G Preferred Shares”). Each Depositary Share, evidenced by a depositary receipt, entitles the holder, through the depositary, to a proportional fractional interest in all rights and preferences of the Series G Preferred Shares represented thereby (including any dividend, liquidation, redemption and voting rights).

Holders of Series G Preferred Shares will be entitled to receive dividend payments only when, as and if declared by

the Company’s board of directors or a duly authorized committee of the board. Any such dividends will be payable from, and including, the date of original issue on a ~~non-cumulative~~noncumulative basis, quarterly in arrears on the last day of March, June, September and December of each year, at an annual rate of ~~4.550%~~4.55%. Dividends on the Series G Preferred Shares are not cumulative. The Company will be restricted from paying dividends on or repurchasing its common shares unless certain dividend payments are made on the Series G

Preferred Shares. The Company may not declare or pay a dividend on the Series G Preferred Shares under certain circumstances, including if the Company is or, after giving effect to such payment, would be in breach of applicable individual or group solvency and liquidity requirements or applicable individual or group enhanced capital requirements ~~("ECR"~~(“ECR”). The Series G Preferred Shares may not be redeemed at any time if the ECR would be breached immediately before or after giving effect to such redemption, unless the Company replaces the capital represented by preference shares to be redeemed with capital having equal or better capital treatment.

Except in specified circumstances relating to certain tax or corporate events, the Series G Preferred Shares are not redeemable prior to June 11, 2026. On and after that date, the Series G Preferred Shares will be redeemable at the Company’s option, in whole or in part, at a redemption price of $25,000 per share of the Series G Preferred Shares (equivalent to $25 per depositary share), plus any declared and unpaid dividends, without accumulation of any undeclared dividends to, but excluding, the redemption date.

The Depositary Shares will be redeemed if and to the extent the related Series G Preferred Shares are redeemed by the Company. Neither the Depositary Shares nor the Series G Preferred Shares have a stated maturity, nor will they be subject to any sinking fund or mandatory redemption. The Series G Preferred Shares are not convertible into any other securities. The Series G Preferred Shares do not have voting rights, except under limited circumstances.

The net proceeds from the Series G Preferred Shares offering of approximately $485.8 million were ~~primarily~~ used to redeem the Company’s issued and outstanding 5.25% Series E Non-Cumulative Preferred Shares in September 2021. The preferred shares were redeemed at a redemption price equal to $25 per depositary share, plus all declared and unpaid dividends to (but excluding) the redemption date. In accordance with GAAP, following the redemption, original issuance costs related to such shares have been removed from additional paid-in capital and recorded as a “loss on redemption of preferred shares.” Such adjustment had no impact on total shareholders’ equity or cash flows.


ARCH CAPITAL			12			~~2021~~2022 THIRD QUARTER FORM 10-Q

Table of Contents

ARCH CAPITAL GROUP LTD. AND SUBSIDIARIES

NOTES TO CONSOLIDATED FINANCIAL STATEMENTS (UNAUDITED)

4.3. Earnings Per Common Share

The following table sets forth the computation of basic and diluted earnings per common share:


		Three Months Ended				Nine Months Ended					Three Months Ended				Nine Months Ended
		September 30,				September 30,					September 30,				September 30,
		2021		2020		2021		2020			2022		2021		2022		2021
Numerator:	Numerator:									Numerator:
Net income (loss)	Net income (loss)	$	421,415	$	488,682	$	1,615,787	$	866,397	Net income (loss)	$	18,258	$	421,415	$	619,635	$	1,615,787
Amounts attributable to noncontrolling interests	Amounts attributable to noncontrolling interests	(1,473)		(69,643)		(82,203)		(4,420)		Amounts attributable to noncontrolling interests	(1,157)		(1,473)		(2,390)		(82,203)
Net income (loss) available to Arch	Net income (loss) available to Arch	419,942		419,039		1,533,584		861,977		Net income (loss) available to Arch	17,101		419,942		617,245		1,533,584
Preferred dividends	Preferred dividends	(16,090)		(10,403)		(38,159)		(31,209)		Preferred dividends	(10,184)		(16,090)		(30,552)		(38,159)
Loss on redemption of preferred shares	Loss on redemption of preferred shares	(15,101)		—		(15,101)		—		Loss on redemption of preferred shares	—		(15,101)		—		(15,101)
Net income (loss) available to Arch common shareholders	Net income (loss) available to Arch common shareholders	$	388,751	$	408,636	$	1,480,324	$	830,768	Net income (loss) available to Arch common shareholders	$	6,917	$	388,751	$	586,693	$	1,480,324

Denominator:	Denominator:									Denominator:

Weighted average common shares and common share equivalents outstanding — basic	Weighted average common shares and common share equivalents outstanding — basic	389,274,220		402,850,485		395,899,591		403,081,266		Weighted average common shares and common share equivalents outstanding — basic	365,190,527		389,274,220		369,525,348		395,899,591
Effect of dilutive common share equivalents:	Effect of dilutive common share equivalents:									Effect of dilutive common share equivalents:
Nonvested restricted shares	Nonvested restricted shares	2,131,915		1,580,791		1,877,930		1,690,447		Nonvested restricted shares	2,351,039		2,131,915		2,171,158		1,877,930
Stock options (1)	Stock options (1)	6,497,212		4,763,381		6,482,964		5,543,184		Stock options (1)	6,185,711		6,497,212		6,676,674		6,482,964
Weighted average common shares and common share equivalents outstanding — diluted	Weighted average common shares and common share equivalents outstanding — diluted	397,903,347		409,194,657		404,260,485		410,314,897		Weighted average common shares and common share equivalents outstanding — diluted	373,727,277		397,903,347		378,373,180		404,260,485

Earnings per common share:	Earnings per common share:									Earnings per common share:
Basic	Basic	$	1.00	$	1.01	$	3.74	$	2.06	Basic	$	0.02	$	1.00	$	1.59	$	3.74
Diluted	Diluted	$	0.98	$	1.00	$	3.66	$	2.02	Diluted	$	0.02	$	0.98	$	1.55	$	3.66

(1) Certain stock options were not included in the computation of diluted earnings per share where the exercise price of the stock options exceeded the average market price and would have been anti-dilutive or where, when applying the treasury stock method to in-the-money options, the sum of the proceeds, including unrecognized compensation, exceeded the average market price and would have been anti-dilutive. For the ~~2021~~2022 third quarter and ~~2020~~2021 third quarter, the number of stock options excluded were ~~1,948,006~~774,481 and ~~4,713,241,~~1,948,006, respectively. For the nine months ended September 30, ~~2021~~2022 and ~~2020 period,~~2021, the number of stock options excluded were ~~2,397,507~~785,682 and ~~2,361,413,~~2,397,507, respectively.


ARCH CAPITAL			13			~~2021~~2022 THIRD QUARTER FORM 10-Q

Table of Contents

ARCH CAPITAL GROUP LTD. AND SUBSIDIARIES

NOTES TO CONSOLIDATED FINANCIAL STATEMENTS (UNAUDITED)

5.4. Segment Information

The Company classifies its businesses into 3three underwriting segments — insurance, reinsurance and mortgage — and 2two other operating segments — ~~‘other’~~corporate and ~~corporate (non-underwriting).~~‘other.’ The Company determined its reportable 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.

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 Capital, the Chief Financial Officer and Treasurer of Arch Capital and the President and Chief Underwriting Officer of Arch Capital. 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 3three underwriting segments based on underwriting income or loss. The Company does not manage its assets by underwriting segment, with the exception of goodwill and intangible assets, and accordingly, investment income is not allocated to each underwriting 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; excess and surplus casualty; lenders products; professional lines; programs; property, energy, marine and aviation; travel, accident and health; and other (consisting of alternative markets, excess workers' compensation and surety business).

The reinsurance segment consists of the Company’s reinsurance underwriting units which offer specialty product lines on a worldwide basis. Product lines include: casualty; marine and aviation; other specialty; property catastrophe; property excluding property catastrophe (losses on a single risk, both excess of loss and pro rata); and other (consisting of life reinsurance, casualty clash and other).

The mortgage segment includes the Company’s U.S. primary mortgage insurance business, investment and services related to U.S. credit-risk transfer (“CRT”) which are predominately with government sponsored enterprises (“GSE’s”) and international mortgage insurance and reinsurance operations. Arch Mortgage Insurance Company and United Guaranty Residential Insurance Company (combined “Arch MI U.S.”) are approved as eligible mortgage insurers by Federal National Mortgage Association (“Fannie Mae”) and Federal Home Loan Mortgage Corporation (“Freddie Mac”), each a GSE. Arch MI U.S. also includes Arch Mortgage Guaranty Company, which is not a GSE-approved entity.

The corporate ~~(non-underwriting)~~ segment results include net investment income, ~~other income (loss), corporate expenses, transaction costs and other, interest expense, items related to the Company’s non-cumulative preferred shares,~~ 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~~investments 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, income or loss from operating affiliates and ~~income taxes.~~items related to the Company’s non-cumulative preferred shares. Such amounts exclude the results of the ‘other’ segment.

Through June 30, 2021, the ‘other’ segment included the results of ~~Watford.~~Somers. In July 2021, the Company announced the completion of the previously disclosed acquisition of ~~Watford~~Somers by Greysbridge. Based on the governing documents of Greysbridge, the Company has concluded that, while it retains significant influence over ~~Watford, Watford~~Somers, Somers no longer constitutes a variable interest entity. Accordingly, effective July 1, 2021, Arch no longer consolidates the results of ~~Watford~~Somers in its consolidated financial statements. See note 1211.


ARCH CAPITAL			14			~~2021~~2022 THIRD QUARTER FORM 10-Q

Table of Contents

ARCH CAPITAL GROUP LTD. AND SUBSIDIARIES

NOTES TO CONSOLIDATED FINANCIAL STATEMENTS (UNAUDITED)

The following tables summarize the Company’s underwriting income or loss by segment, together with a reconciliation of underwriting income or loss to net income available to Arch common shareholders:


		Three Months Ended																			Three Months Ended
		September 30, 2021																			September 30, 2022
		Insurance			Reinsurance			Mortgage			Sub-Total			Other			Total				Insurance			Reinsurance			Mortgage			Sub-Total			Other			Total

Gross premiums written (1)	Gross premiums written (1)	$	1,596,619		$	1,251,760		$	360,934		$	3,207,415		$	—		$	3,207,415		Gross premiums written (1)	$	1,862,026		$	1,639,061		$	362,409		$	3,860,683		$	—		$	3,860,683
Premiums ceded	Premiums ceded	(442,806)			(630,371)			(60,207)			(1,131,486)			—			(1,131,486)			Premiums ceded	(493,267)			(560,225)			(86,230)			(1,136,909)			—			(1,136,909)
Net premiums written	Net premiums written	1,153,813			621,389			300,727			2,075,929			—			2,075,929			Net premiums written	1,368,759			1,078,836			276,179			2,723,774			—			2,723,774
Change in unearned premiums	Change in unearned premiums	(215,143)			57,313			11,238			(146,592)			—			(146,592)			Change in unearned premiums	(181,851)			(77,062)			5,889			(253,024)			—			(253,024)
Net premiums earned	Net premiums earned	938,670			678,702			311,965			1,929,337			—			1,929,337			Net premiums earned	1,186,908			1,001,774			282,068			2,470,750			—			2,470,750
Other underwriting income (loss)	Other underwriting income (loss)	—			3,293			3,981			7,274			—			7,274			Other underwriting income (loss)	—			452			2,625			3,077			—			3,077
Losses and loss adjustment expenses	Losses and loss adjustment expenses	(668,630)			(545,846)			(11,543)			(1,226,019)			—			(1,226,019)			Losses and loss adjustment expenses	(822,663)			(927,911)			67,878			(1,682,696)			—			(1,682,696)
Acquisition expenses	Acquisition expenses	(152,467)			(129,450)			(24,098)			(306,015)			—			(306,015)			Acquisition expenses	(232,469)			(208,425)			(6,693)			(447,587)			—			(447,587)
Other operating expenses	Other operating expenses	(138,931)			(45,647)			(46,254)			(230,832)			—			(230,832)			Other operating expenses	(165,499)			(62,777)			(46,471)			(274,747)			—			(274,747)
Underwriting income (loss)	Underwriting income (loss)	$	(21,358)		$	(38,948)		$	234,051		173,745			—			173,745			Underwriting income (loss)	$	(33,723)		$	(196,887)		$	299,407		68,797			—			68,797

Net investment income	Net investment income										88,195			—			88,195			Net investment income										128,640			—			128,640
Net realized gains (losses)	Net realized gains (losses)										(25,040)			—			(25,040)			Net realized gains (losses)										(183,673)			—			(183,673)

Equity in net income (loss) of investment funds accounted for using the equity method	Equity in net income (loss) of investment funds accounted for using the equity method										105,398			—			105,398			Equity in net income (loss) of investment funds accounted for using the equity method										(18,861)			—			(18,861)
Other income (loss)	Other income (loss)										(3,960)			—			(3,960)			Other income (loss)										(13,684)			—			(13,684)
Corporate expenses (2)	Corporate expenses (2)										(18,636)			—			(18,636)			Corporate expenses (2)										(17,634)			—			(17,634)
Transaction costs and other (2)	Transaction costs and other (2)										(1,036)			—			(1,036)			Transaction costs and other (2)										(76)			—			(76)
Amortization of intangible assets	Amortization of intangible assets										(20,135)			—			(20,135)			Amortization of intangible assets										(26,104)			—			(26,104)
Interest expense	Interest expense										(33,176)			—			(33,176)			Interest expense										(33,063)			—			(33,063)
Net foreign exchange gains (losses)	Net foreign exchange gains (losses)										36,078			—			36,078			Net foreign exchange gains (losses)										90,509			—			90,509
Income (loss) before income taxes and income (loss) from operating affiliates	Income (loss) before income taxes and income (loss) from operating affiliates										301,433			—			301,433			Income (loss) before income taxes and income (loss) from operating affiliates										(5,149)			—			(5,149)
Income tax (expense) benefit	Income tax (expense) benefit										(4,137)			—			(4,137)			Income tax (expense) benefit										14,900			—			14,900
Income (loss) from operating affiliates	Income (loss) from operating affiliates										124,119			—			124,119			Income (loss) from operating affiliates										8,507			—			8,507
Net income (loss)	Net income (loss)										421,415			—			421,415			Net income (loss)										18,258			—			18,258
Amounts attributable to redeemable noncontrolling interests	Amounts attributable to redeemable noncontrolling interests										(1,473)			—			(1,473)			Amounts attributable to redeemable noncontrolling interests										(1,157)			—			(1,157)
Amounts attributable to nonredeemable noncontrolling interests											—			—			—

Net income (loss) available to Arch	Net income (loss) available to Arch										419,942			—			419,942			Net income (loss) available to Arch										17,101			—			17,101
Preferred dividends	Preferred dividends										(16,090)			—			(16,090)			Preferred dividends										(10,184)			—			(10,184)
Loss on redemption of preferred shares											(15,101)			—			(15,101)

Net income (loss) available to Arch common shareholders	Net income (loss) available to Arch common shareholders										$	388,751		$	—		$	388,751		Net income (loss) available to Arch common shareholders										$	6,917		$	—		$	6,917

Underwriting Ratios	Underwriting Ratios																			Underwriting Ratios
Loss ratio	Loss ratio	71.2		%	80.4		%	3.7		%	63.5		%	—		%	63.5		%	Loss ratio	69.3		%	92.6		%	(24.1)		%	68.1		%	—		%	68.1		%
Acquisition expense ratio	Acquisition expense ratio	16.2		%	19.1		%	7.7		%	15.9		%	—		%	15.9		%	Acquisition expense ratio	19.6		%	20.8		%	2.4		%	18.1		%	—		%	18.1		%
Other operating expense ratio	Other operating expense ratio	14.8		%	6.7		%	14.8		%	12.0		%	—		%	12.0		%	Other operating expense ratio	13.9		%	6.3		%	16.5		%	11.1		%	—		%	11.1		%
Combined ratio	Combined ratio	102.2		%	106.2		%	26.2		%	91.4		%	—		%	91.4		%	Combined ratio	102.8		%	119.7		%	(5.2)		%	97.3		%	—		%	97.3		%

Goodwill and intangible assets	Goodwill and intangible assets	$	261,103		$	176,128		$	526,091		$	963,322		$	—		$	963,322		Goodwill and intangible assets	$	224,525		$	140,800		$	441,330		$	806,655		$	—		$	806,655

(1) Certain amounts included in the gross premiums written of each segment are related to intersegment transactions. Accordingly, the sum of gross premiums written for each segment does not agree to the total gross premiums written as shown in the table above due to the elimination of intersegment transactions in the total.

(2) Certain expenses have been excluded from ‘corporate expenses’ and reflected in ‘transaction costs and other.’


ARCH CAPITAL			15			~~2021~~2022 THIRD QUARTER FORM 10-Q

Table of Contents

ARCH CAPITAL GROUP LTD. AND SUBSIDIARIES

NOTES TO CONSOLIDATED FINANCIAL STATEMENTS (UNAUDITED)


		Three Months Ended																			Three Months Ended
		September 30, 2020																			September 30, 2021
		Insurance			Reinsurance			Mortgage			Sub-Total			Other			Total				Insurance			Reinsurance			Mortgage			Sub-Total			Other			Total

Gross premiums written (1)	Gross premiums written (1)	$	1,206,328		$	1,004,590		$	346,248		$	2,556,914		$	197,480		$	2,681,032		Gross premiums written (1)	$	1,596,619		$	1,251,760		$	360,934		$	3,207,415		$	—		$	3,207,415
Premiums ceded	Premiums ceded	(382,167)			(400,388)			(47,783)			(830,086)			(50,164)			(806,888)			Premiums ceded	(442,806)			(630,371)			(60,207)			(1,131,486)			—			(1,131,486)
Net premiums written	Net premiums written	824,161			604,202			298,465			1,726,828			147,316			1,874,144			Net premiums written	1,153,813			621,389			300,727			2,075,929			—			2,075,929
Change in unearned premiums	Change in unearned premiums	(105,007)			(49,704)			52,944			(101,767)			(1,285)			(103,052)			Change in unearned premiums	(215,143)			57,313			11,238			(146,592)			—			(146,592)
Net premiums earned	Net premiums earned	719,154			554,498			351,409			1,625,061			146,031			1,771,092			Net premiums earned	938,670			678,702			311,965			1,929,337			—			1,929,337
Other underwriting income (loss)	Other underwriting income (loss)	(31)			298			4,600			4,867			546			5,413			Other underwriting income (loss)	—			3,293			3,981			7,274			—			7,274
Losses and loss adjustment expenses	Losses and loss adjustment expenses	(525,321)			(422,084)			(153,055)			(1,100,460)			(115,813)			(1,216,273)			Losses and loss adjustment expenses	(668,630)			(545,846)			(11,543)			(1,226,019)			—			(1,226,019)
Acquisition expenses	Acquisition expenses	(102,420)			(85,388)			(35,716)			(223,524)			(24,418)			(247,942)			Acquisition expenses	(152,467)			(129,450)			(24,098)			(306,015)			—			(306,015)
Other operating expenses	Other operating expenses	(122,541)			(41,818)			(36,708)			(201,067)			(14,619)			(215,686)			Other operating expenses	(138,931)			(45,647)			(46,254)			(230,832)			—			(230,832)
Underwriting income (loss)	Underwriting income (loss)	$	(31,159)		$	5,506		$	130,530		104,877			(8,273)			96,604			Underwriting income (loss)	$	(21,358)		$	(38,948)		$	234,051		173,745			—			173,745

Net investment income	Net investment income										99,857			28,655			128,512			Net investment income										88,195			—			88,195
Net realized gains (losses)	Net realized gains (losses)										210,984			69,515			280,499			Net realized gains (losses)										(25,040)			—			(25,040)

Equity in net income (loss) of investment funds accounted for using the equity method	Equity in net income (loss) of investment funds accounted for using the equity method										126,735			—			126,735			Equity in net income (loss) of investment funds accounted for using the equity method										105,398			—			105,398
Other income (loss)	Other income (loss)										—			—			—			Other income (loss)										(3,960)			—			(3,960)
Corporate expenses (2)	Corporate expenses (2)										(16,263)			—			(16,263)			Corporate expenses (2)										(18,636)			—			(18,636)
Transaction costs and other (2)	Transaction costs and other (2)										(1,674)			—			(1,674)			Transaction costs and other (2)										(1,036)			—			(1,036)
Amortization of intangible assets	Amortization of intangible assets										(16,715)			—			(16,715)			Amortization of intangible assets										(20,135)			—			(20,135)
Interest expense	Interest expense										(36,224)			(5,119)			(41,343)			Interest expense										(33,176)			—			(33,176)
Net foreign exchange gains (losses)	Net foreign exchange gains (losses)										(38,681)			(6,204)			(44,885)			Net foreign exchange gains (losses)										36,078			—			36,078
Income (loss) before income taxes and income (loss) from operating affiliates	Income (loss) before income taxes and income (loss) from operating affiliates										432,896			78,574			511,470			Income (loss) before income taxes and income (loss) from operating affiliates										301,433			—			301,433
Income tax (expense) benefit	Income tax (expense) benefit										(23,638)			(69)			(23,707)			Income tax (expense) benefit										(4,137)			—			(4,137)
Income (loss) from operating affiliates	Income (loss) from operating affiliates										919			—			919			Income (loss) from operating affiliates										124,119			—			124,119
Net income (loss)	Net income (loss)										410,177			78,505			488,682			Net income (loss)										421,415			—			421,415
Amounts attributable to redeemable noncontrolling interests	Amounts attributable to redeemable noncontrolling interests										(882)			(993)			(1,875)			Amounts attributable to redeemable noncontrolling interests										(1,473)			—			(1,473)
Amounts attributable to nonredeemable noncontrolling interests											—			(67,768)			(67,768)

Net income (loss) available to Arch	Net income (loss) available to Arch										409,295			9,744			419,039			Net income (loss) available to Arch										419,942			—			419,942
Preferred dividends	Preferred dividends										(10,403)			—			(10,403)			Preferred dividends										(16,090)			—			(16,090)

Loss on redemption of preferred shares																				Loss on redemption of preferred shares										(15,101)			—			(15,101)
Net income (loss) available to Arch common shareholders	Net income (loss) available to Arch common shareholders										$	398,892		$	9,744		$	408,636		Net income (loss) available to Arch common shareholders										$	388,751		$	—		$	388,751

Underwriting Ratios	Underwriting Ratios																			Underwriting Ratios
Loss ratio	Loss ratio	73.0		%	76.1		%	43.6		%	67.7		%	79.3		%	68.7		%	Loss ratio	71.2		%	80.4		%	3.7		%	63.5		%	—		%	63.5		%
Acquisition expense ratio	Acquisition expense ratio	14.2		%	15.4		%	10.2		%	13.8		%	16.7		%	14.0		%	Acquisition expense ratio	16.2		%	19.1		%	7.7		%	15.9		%	—		%	15.9		%
Other operating expense ratio	Other operating expense ratio	17.0		%	7.5		%	10.4		%	12.4		%	10.0		%	12.2		%	Other operating expense ratio	14.8		%	6.7		%	14.8		%	12.0		%	—		%	12.0		%
Combined ratio	Combined ratio	104.2		%	99.0		%	64.2		%	93.9		%	106.0		%	94.9		%	Combined ratio	102.2		%	106.2		%	26.2		%	91.4		%	—		%	91.4		%

Goodwill and intangible assets	Goodwill and intangible assets	$	282,146		$	20,319		$	403,662		$	706,127		$	7,650		$	713,777		Goodwill and intangible assets	$	261,103		$	176,128		$	526,091		$	963,322		$	—		$	963,322

(2) Certain expenses have been excluded from ‘corporate expenses’ and reflected in ‘transaction costs and other.’


ARCH CAPITAL			16			2022 THIRD QUARTER FORM 10-Q

Table of Contents

ARCH CAPITAL GROUP LTD. AND SUBSIDIARIES

NOTES TO CONSOLIDATED FINANCIAL STATEMENTS (UNAUDITED)


	Nine Months Ended
	September 30, 2022
	Insurance			Reinsurance			Mortgage			Sub-Total			Other			Total

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 written	3,803,912			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 earned	3,315,748			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 income										315,468			—			315,468
Net realized gains (losses)										(742,666)			—			(742,666)

Equity in net income (loss) of investment funds accounted for using the equity method										75,505			—			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 affiliates										601,012			—			601,012
Income tax (expense) benefit										(19,042)			—			(19,042)
Income (loss) from operating affiliates										37,665			—			37,665
Net income (loss)										619,635			—			619,635
Amounts attributable to redeemable noncontrolling interests										(2,390)			—			(2,390)

Net income (loss) available to Arch										617,245			—			617,245
Preferred dividends										(30,552)			—			(30,552)

Net income (loss) available to Arch common shareholders										$	586,693		$	—		$	586,693

Underwriting Ratios
Loss ratio	61.9		%	70.2		%	(21.6)		%	54.7		%	—		%	54.7		%
Acquisition expense ratio	19.4		%	20.8		%	3.2		%	17.9		%	—		%	17.9		%
Other operating expense ratio	14.9		%	7.3		%	17.3		%	12.2		%	—		%	12.2		%
Combined ratio	96.2		%	98.3		%	(1.1)		%	84.8		%	—		%	84.8		%

(2) Certain expenses have been excluded from ‘corporate expenses’ and reflected in ‘transaction costs and other.’


ARCH CAPITAL			1617			~~2021~~2022 THIRD QUARTER FORM 10-Q

Table of Contents

ARCH CAPITAL GROUP LTD. AND SUBSIDIARIES

NOTES TO CONSOLIDATED FINANCIAL STATEMENTS (UNAUDITED)


	Nine Months Ended
	September 30, 2021
	Insurance			Reinsurance			Mortgage			Sub-Total			Other			Total

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 written	3,112,207			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 earned	2,623,571			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 income										256,354			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 method										299,270			—			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 affiliates										1,396,476			89,435			1,485,911
Income tax (expense) benefit										(93,942)			(234)			(94,176)
Income (loss) from operating affiliates										224,052			—			224,052
Net income (loss)										1,526,586			89,201			1,615,787
Amounts 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 Arch										1,524,650			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 ratio	66.7		%	72.5		%	8.7		%	58.8		%	78.0		%	59.8		%
Acquisition expense ratio	15.9		%	18.5		%	8.6		%	15.6		%	18.9		%	15.8		%
Other operating expense ratio	15.6		%	7.3		%	14.6		%	12.4		%	9.9		%	12.3		%
Combined ratio	98.2		%	98.3		%	31.9		%	86.8		%	106.8		%	87.9		%

(2) Certain expenses have been excluded from ‘corporate expenses’ and reflected in ‘transaction costs and other.’


~~ARCH CAPITAL~~			17			~~2021 THIRD QUARTER FORM 10-Q~~

~~Table of Contents~~

~~ARCH CAPITAL GROUP LTD. AND SUBSIDIARIES~~

~~NOTES TO CONSOLIDATED FINANCIAL STATEMENTS (UNAUDITED)~~

Nine Months Ended
September 30, 2020
Insurance Reinsurance Mortgage Sub-Total Other Total
Gross premiums written (1) $ 3,444,335 $ 2,934,174 $ 1,084,337 $ 7,461,860 $ 590,309 $ 7,831,554
Premiums ceded (1,119,165) (967,698) (136,154) (2,222,031) (150,437) (2,151,853)
Net premiums written 2,325,170 1,966,476 948,183 5,239,829 439,872 5,679,701
Change in unearned premiums (202,188) (388,321) 113,965 (476,544) (22,267) (498,811)
Net premiums earned 2,122,982 1,578,155 1,062,148 4,763,285 417,605 5,180,890
Other underwriting income (loss) (31) 1,767 15,649 17,385 1,547 18,932
Losses and loss adjustment expenses (1,550,632) (1,235,586) (444,721) (3,230,939) (331,275) (3,562,214)
Acquisition expenses (317,428) (255,516) (108,304) (681,248) (68,766) (750,014)
Other operating expenses (370,947) (125,831) (120,178) (616,956) (42,523) (659,479)
Underwriting income (loss) $ (116,056) $ (37,011) $ 404,594 $ 251,527 $ (23,412) $ 228,115
Net investment income 313,916 91,234 405,150
Net realized gains (losses) 523,964 (53,837) 470,127
Equity in net income (loss) of investment funds accounted for using the equity method 57,407 — 57,407
Other income (loss) 65 — 65
Corporate expenses (2) (51,407) — (51,407)
Transaction costs and other (2) (5,246) — (5,246)
Amortization of intangible assets (49,835) — (49,835)
Interest expense (86,599) (18,438) (105,037)
Net foreign exchange gains (losses) (17,812) 6,387 (11,425)
Income (loss) before income taxes and income (loss) from operating affiliates 935,980 1,934 937,914
Income tax (expense) benefit (78,112) 333 (77,779)
Income (loss) from operating affiliates 6,262 — 6,262
Net income (loss) 864,130 2,267 866,397
Amounts attributable to redeemable noncontrolling interests (1,873) (3,125) (4,998)
Amounts attributable to nonredeemable noncontrolling interests — 578 578
Net income (loss) available to Arch 862,257 (280) 861,977
Preferred dividends (31,209) — (31,209)
Net income (loss) available to Arch common shareholders $ 831,048 $ (280) $ 830,768
Underwriting Ratios
Loss ratio 73.0 % 78.3 % 41.9 % 67.8 % 79.3 % 68.8 %
Acquisition expense ratio 15.0 % 16.2 % 10.2 % 14.3 % 16.5 % 14.5 %
Other operating expense ratio 17.5 % 8.0 % 11.3 % 13.0 % 10.2 % 12.7 %
Combined ratio 105.5 % 102.5 % 63.4 % 95.1 % 106.0 % 96.0 %

~~(2) Certain expenses have been excluded from ‘corporate expenses’ and reflected in ‘transaction costs and other.’~~


ARCH CAPITAL			18			~~2021~~2022 THIRD QUARTER FORM 10-Q

Table of Contents

ARCH CAPITAL GROUP LTD. AND SUBSIDIARIES

NOTES TO CONSOLIDATED FINANCIAL STATEMENTS (UNAUDITED)

6.5. Reserve for Losses and Loss Adjustment Expenses

The following table represents an analysis of losses and loss adjustment expenses and a reconciliation of the beginning and ending reserve for losses and loss adjustment expenses:


		Three Months Ended				Nine Months Ended					Three Months Ended				Nine Months Ended
		September 30,				September 30,					September 30,				September 30,
		2021		2020		2021		2020			2022		2021		2022		2021
Reserve for losses and loss adjustment expenses at beginning of period	Reserve for losses and loss adjustment expenses at beginning of period	$	17,196,648	$	15,044,874	$	16,513,929	$	13,891,842	Reserve for losses and loss adjustment expenses at beginning of period	$	18,194,324	$	17,196,648	$	17,757,156	$	16,513,929
Unpaid losses and loss adjustment expenses recoverable	Unpaid losses and loss adjustment expenses recoverable	4,146,020		4,156,157		4,314,855		4,082,650		Unpaid losses and loss adjustment expenses recoverable	5,686,348		4,146,020		5,599,231		4,314,855
Net reserve for losses and loss adjustment expenses at beginning of period	Net reserve for losses and loss adjustment expenses at beginning of period	13,050,628		10,888,717		12,199,074		9,809,192		Net reserve for losses and loss adjustment expenses at beginning of period	12,507,976		13,050,628		12,157,925		12,199,074

Net incurred losses and loss adjustment expenses relating to losses occurring in:	Net incurred losses and loss adjustment expenses relating to losses occurring in:									Net incurred losses and loss adjustment expenses relating to losses occurring in:
Current year	Current year	1,348,528		1,264,315		3,812,381		3,673,346		Current year	1,863,519		1,348,528		4,280,048		3,812,381
Prior years	Prior years	(122,509)		(48,042)		(223,431)		(111,132)		Prior years	(180,823)		(122,509)		(493,861)		(223,431)
Total net incurred losses and loss adjustment expenses	Total net incurred losses and loss adjustment expenses	1,226,019		1,216,273		3,588,950		3,562,214		Total net incurred losses and loss adjustment expenses	1,682,696		1,226,019		3,786,187		3,588,950

Net losses and loss adjustment expense reserves of acquired business ~~(2)~~(1)	Net losses and loss adjustment expense reserves of acquired business ~~(2)~~(1)	104,307		—		104,307		$	—	Net losses and loss adjustment expense reserves of acquired business ~~(2)~~(1)	—		104,307		—		104,307

Retroactive reinsurance transactions ~~(1)~~(2)	Retroactive reinsurance transactions ~~(1)~~(2)	—		—		(183,893)		60,635		Retroactive reinsurance transactions ~~(1)~~(2)	—		—		—		(183,893)

Impact of deconsolidation of Watford (3)		(1,460,611)		—		(1,460,611)		—
Impact of deconsolidation of Somers (3)										Impact of deconsolidation of Somers (3)	—		(1,460,611)		—		(1,460,611)

Net foreign exchange (gains) losses		(78,152)		114,122		10,818		22,706
Net foreign exchange (gains) losses and other										Net foreign exchange (gains) losses and other	(243,387)		(78,152)		(524,682)		10,818

Net paid losses and loss adjustment expenses relating to losses occurring in:	Net paid losses and loss adjustment expenses relating to losses occurring in:									Net paid losses and loss adjustment expenses relating to losses occurring in:
Current year	Current year	(208,923)		(189,961)		(432,348)		(359,395)		Current year	(226,575)		(208,923)		(463,847)		(432,348)
Prior years	Prior years	(417,368)		(512,263)		(1,610,397)		(1,578,464)		Prior years	(538,967)		(417,368)		(1,773,840)		(1,610,397)
Total net paid losses and loss adjustment expenses	Total net paid losses and loss adjustment expenses	(626,291)		(702,224)		(2,042,745)		(1,937,859)		Total net paid losses and loss adjustment expenses	(765,542)		(626,291)		(2,237,687)		(2,042,745)

Net reserve for losses and loss adjustment expenses at end of period	Net reserve for losses and loss adjustment expenses at end of period	12,215,900		11,516,888		12,215,900		11,516,888		Net reserve for losses and loss adjustment expenses at end of period	13,181,743		12,215,900		13,181,743		12,215,900
Unpaid losses and loss adjustment expenses recoverable	Unpaid losses and loss adjustment expenses recoverable	5,115,147		4,383,638		5,115,147		4,383,638		Unpaid losses and loss adjustment expenses recoverable	6,106,548		5,115,147		6,106,548		5,115,147
Reserve for losses and loss adjustment expenses at end of period	Reserve for losses and loss adjustment expenses at end of period	$	17,331,047	$	15,900,526	$	17,331,047	$	15,900,526	Reserve for losses and loss adjustment expenses at end of period	$	19,288,291	$	17,331,047	$	19,288,291	$	17,331,047

(1) Represents activity related to the Company’s acquisitions in the 2021 period of the Westpac Lenders Mortgage Insurance Limited and Somerset Bridge Group Limited, Southern Rock Holdings Limited and affiliates.

(2) During the 2021 first quarter, the Company entered into a reinsurance to close and other related agreements with Premia Managing Agency Limited (“Premia”), in connection with the 2018 and prior years of account related to the acquisition of Barbican Group Holdings Limited (“Barbican”). ~~During the 2020 first quarter, the Company entered into a reinsurance to close agreement of the 2017 and prior years of account previously covered by a third party arrangement.~~

~~(2) Represents activity related to the Company’s acquisitions in the 2021 period. See~~ ~~note 2~~.

(3) See note 121 1.

Development on Prior Year Loss Reserves

2022 Third Quarter

During the 2022 third quarter, the Company recorded net favorable development on prior year loss reserves of $180.8 million, which consisted of $5.4 million from the insurance segment, $49.2 million from the reinsurance segment and $126.2 million from the mortgage segment.

The insurance segment’s net favorable development of $5.4 million, or 0.5 loss ratio points, for the 2022 third quarter consisted of $15.9 million of net favorable development in short-tailed lines and $10.5 million of net adverse development in medium-tailed and long-tailed lines. Net favorable development in short-tailed lines reflected $8.9 million of favorable development in property (excluding marine), primarily from 2020 and 2021 accident years (i.e.,

the year in which a loss occurred) and $5.7 million of favorable development in lenders products, primarily from the 2021 accident year. Net adverse development in medium-tailed lines included $11.3 million of adverse development in professional liability business, primarily from the 2013 to 2016 and 2020 accident years, partially offset by favorable development in marine business of $5.9 million, across most accident years. Net adverse development in long-tailed lines reflected $12.3 million related to casualty business, primarily from the 2014 and 2020 accident years, partially offset by favorable development in construction, executive assurance and other lines of business.

The reinsurance segment’s net favorable development of $49.2 million, or 4.9 loss ratio points, for the 2022 third quarter consisted of $58.1 million of net favorable development in short-tailed and medium-tailed lines and


ARCH CAPITAL			19			2022 THIRD QUARTER FORM 10-Q

Table of Contents

ARCH CAPITAL GROUP LTD. AND SUBSIDIARIES

NOTES TO CONSOLIDATED FINANCIAL STATEMENTS (UNAUDITED)

$8.9 million of net adverse development in long-tailed lines. Net favorable development in short-tailed lines reflected $35.8 million of favorable development related to property other than property catastrophe business, primarily from 2015 to 2021 underwriting years (i.e., all premiums and losses attributable to contracts having an inception or renewal date within the given twelve-month period) and $12.7 million of favorable development related to property catastrophe business, primarily from the 2014 to 2017 underwriting years. Net favorable development in medium-tailed lines included $7.9 million in marine and aviation lines, across most underwriting years. Net adverse development in long-tailed lines reflected $9.5 million related to casualty business, primarily from the 2014 to 2017 underwriting years.

The mortgage segment’s net favorable development was $126.2 million, or 44.7 loss ratio points, for the 2022 third quarter, with the largest contributor being reserve releases associated with the U.S. first lien portfolio from the 2020 and 2021 accident years. The Company’s credit risk transfer, international, second lien and student loan businesses also contributed to the favorable development.

2021 Third Quarter

During the 2021 third quarter, the Company recorded net favorable development on prior year loss reserves of $122.5 million, which consisted of $5.1 million from the insurance segment, $72.3 million from the reinsurance segment and $45.1 million from the mortgage segment.

The insurance segment’s net favorable development of $5.1 million, or 0.5 loss ratio points, for the 2021 third quarter consisted of $49.0 million of net favorable development in short-tailed and long-tailed lines and $43.9 million of net adverse development in medium-tailed lines. Net favorable development in short-tailed lines reflected $5.4 million of

favorable development in lenders products, primarily from the 2020 accident year, (~~i.e., the year in which a loss occurred),~~ $5.4 million of favorable development from property (excluding marine), primarily from the 2020 accident year, and $5.1 million of favorable development in travel and accident, across most accident years. Net favorable development in long-tailed lines reflected $26.3 million of favorable development related to construction and national accounts, across most accident years, and $6.7 million of favorable development related to other business, including alternative markets, primarily from the 2015 to 2018 accident years. Net adverse development in medium-tailed lines included $37.0 million of adverse development in contract binding business, across most accident years, partially offset by favorable development in marine and programs, primarily from more recent accident years.


~~ARCH CAPITAL~~			19			~~2021 THIRD QUARTER FORM 10-Q~~

~~Table of Contents~~

~~ARCH CAPITAL GROUP LTD. AND SUBSIDIARIES~~

~~NOTES TO CONSOLIDATED FINANCIAL STATEMENTS (UNAUDITED)~~

The reinsurance segment’s net favorable development of $72.3 million, or 10.7 loss ratio points, for the 2021 third quarter consisted of $65.4 million of net favorable

development in short-tailed lines and $6.9 million in medium-tailed and long-tailed lines. Net favorable development in short-tailed lines reflected $46.1 million of favorable development related to property catastrophe and property other than property catastrophe business, primarily from the 2017 to 2020 underwriting years ~~(i.e., all premiums and losses attributable to contracts having an inception or renewal date within the given twelve-month period)~~ and $18.9 million of favorable development related to other specialty, primarily from the 2012 to 2017 underwriting years. Net favorable development in medium-tailed and long-tailed lines included $4.7 million of favorable development in casualty, primarily from the 2013 and 2014 underwriting years.

The mortgage segment’s net favorable development was $45.1 million, or 14.5 loss ratio points, for the 2021 third quarter, about half of which came from U.S. primary mortgage insurance, from better than expected cure activity in pre-pandemic delinquencies and recoveries on second lien and student loans, and the other half from our CRT portfolio and international mortgage insurance.

~~2020 Third Quarter~~Nine Months Ended September 30, 2022

During the ~~2020 third quarter,~~nine months ended September 30, 2022, the Company recorded net favorable development on prior year loss reserves of ~~$48.0~~$493.9 million, which consisted of ~~$2.3~~$19.4 million from the insurance segment, ~~$42.0~~$128.1 million from the reinsurance segment and ~~$4.5~~$346.4 million from the mortgage ~~segment, partially offset by $0.7 million unfavorable from the ‘other’~~ segment.

The insurance segment’s net favorable development of ~~$2.3~~$19.4 million, or ~~0.3~~0.6 loss ratio points, for the ~~2020 third quarter~~2022 period consisted of ~~$12.9~~$49.1 million of net favorable development in short-tailed and ~~long-tailed lines and $10.6~~$29.7 million of net adverse development in ~~medium-tailed~~medium and long-tailed lines. Net favorable development ~~of $11.8 million~~ in short-tailed lines reflected ~~$8.0 million of favorable development from property (excluding marine), primarily from the 2015 to 2018 accident years and $3.4~~$36.5 million of favorable development in lenders products, primarily from the 2021 accident year, and $14.3 million of favorable development related to travel and accident business, primarily from the 2019 to 2021 accident ~~year.~~years. Net ~~favorable~~adverse development in medium-tailed lines included $24.9 million of ~~$1.1~~adverse development in professional liability business, primarily from the 2013 to 2015 and 2018 to 2020 accident years, and $5.5 million of adverse development in ~~long-tailed lines reflected $8.7~~contract binding business, across most accident years, partially offset by $11.4 million of favorable development in ~~construction and national accounts,~~marine business, across most accident years. Net adverse development in long-tailed lines reflected $18.0 million of adverse development related to casualty business, primarily from the ~~2018~~2020 and 2021 accident ~~year, and $4.2~~years, partially offset by $17.4 million of favorable development ~~related to~~in other business, including alternative markets and excess workers’ compensation, primarily from the ~~2013 to 2017 accident years, partially offset by $11.7 million of adverse development in executive assurance~~2019 and ~~casualty, primarily from the 2015 and 2019 accident year. Net adverse development in medium-tailed lines included $7.1 million of adverse development in program business, primarily from~~

~~2015 to 2018 accident years and $3.7 million of adverse development in contract binding, across all~~prior accident years.

The reinsurance segment’s net favorable development of ~~$42.0~~$128.1 million, or ~~7.6~~4.7 loss ratio points, for the ~~2020 third quarter~~2022 period consisted of ~~$45.6~~$147.8 million of net favorable development ~~in short-tailed~~from short and medium-tailed lines, ~~and~~partially offset by


ARCH CAPITAL			20			2022 THIRD QUARTER FORM 10-Q

Table of Contents

ARCH CAPITAL GROUP LTD. AND SUBSIDIARIES

NOTES TO CONSOLIDATED FINANCIAL STATEMENTS (UNAUDITED)

$19.7 million of net adverse development ~~of $3.6 million~~ from long-tailed lines. Net favorable development in short-tailed lines reflected ~~$27.6~~$83.2 million of favorable development ~~related to property catastrophe and~~from property other than property catastrophe business, primarily from the ~~2016~~2015 to ~~2019~~2021 underwriting years, ~~and $7.8~~$22.4 million of favorable development from ~~other specialty,~~property catastrophe, primarily from the ~~2016~~2018 to ~~2019~~2020 underwriting ~~years.~~years, and $19.8 million from other specialty business, primarily from the 2021 underwriting year. Net favorable development ~~of $9.4 million~~ in medium-tailed lines ~~reflected favorable development~~included $22.7 million in marine and aviation lines, across most underwriting years. ~~Adverse~~Net adverse development ~~of $3.6 million~~ in long-tailed lines primarily reflected ~~an increase~~$19.3 million in casualty reserves, ~~from casualty,~~ primarily from the ~~2012 to 2019~~2021 underwriting ~~years.~~year.

The mortgage segment’s net favorable development was ~~$4.5~~$346.4 million, or ~~1.3~~39.9 loss ratio points, for the 2022 period, with the largest contributor being reserve releases associated with the U.S. first lien portfolio from the 2020 ~~third quarter, primarily driven by subrogation recoveries on~~and 2021 accident years. The Company’s credit risk transfer, international, second lien and student loan ~~business.~~businesses also contributed to the favorable development.

Nine Months Ended September 30, 2021

During the nine months ended September 30, 2021, the Company recorded net favorable development on prior year loss reserves of $223.4 million, which consisted of $13.1 million from the insurance segment, $119.6 million from the reinsurance segment, ~~and~~ $99.1 million from the mortgage segment, partially offset by $8.4 million of adverse development from the ‘other’ segment (activity for the six months ended June 30, 2021 prior to deconsolidation of ~~Watford)~~Somers).

The insurance segment’s net favorable development of $13.1 million, or 0.5 loss ratio points, for the 2021 period consisted of $102.5 million of net favorable development in short-tailed and long-tailed lines, partially offset by $89.4 million of net adverse development in medium-tailed lines. Net favorable development of $65.3 million in short-tailed lines reflected $27.0 million of favorable development from property (excluding marine), primarily from the 2019 and 2020 accident years, $24.0 million of favorable development in lenders products, primarily from the 2020 accident year, and $14.4 million of favorable development in travel and accident, primarily from the 2017 to 2020 accident years. Net favorable development of $37.1 million in long-tailed lines included favorable development primarily related to construction, national accounts and alternative markets, primarily from the 2016 to 2019 accident years. Net adverse development in medium-tailed lines reflected $57.1 million of adverse development in contract binding business, primarily from the 2014 to 2019 accident years, $26.2 million of adverse development in professional liability business,


~~ARCH CAPITAL~~			20			~~2021 THIRD QUARTER FORM 10-Q~~

~~Table of Contents~~

~~ARCH CAPITAL GROUP LTD. AND SUBSIDIARIES~~

~~NOTES TO CONSOLIDATED FINANCIAL STATEMENTS (UNAUDITED)~~

primarily from the 2019 and 2020 accident years, and ~~$6.9~~

$6.9 million of adverse development in programs business, primarily from the 2019 accident year.

The reinsurance segment’s net favorable development of $119.6 million, or 5.8 loss ratio points, for the 2021 period consisted of $139.7 million of net favorable development from short-tailed and medium-tailed lines, partially offset by $20.1 million of net adverse development from long-tailed lines. Net favorable development of $132.6 million in short-tailed lines reflected $97.1 million of favorable development from other specialty lines, primarily from the 2016 to 2019 underwriting years, and $71.7 million of favorable development from property other than property catastrophe business, primarily from the 2017 to 2020 underwriting years. Such amounts were partially offset by adverse development of $36.3 million from property catastrophe, primarily from the 2020 underwriting year. Adverse development in long-tailed lines reflected an increase in reserves from casualty, primarily from the 2018 underwriting year.

The mortgage segment’s net favorable development was $99.1 million, or 10.1 loss ratio points, for the 2021 period, which included reserve releases associated with various vintage credit risk transfer contracts that were called by the GSEs, favorable development on U.S. and international business and subrogation recoveries on second lien and student loan business.

~~Nine Months Ended September 30, 2020~~

During the nine months ended September 30, 2020, the Company recorded net favorable development on prior year loss reserves of $111.1 million, which consisted of $5.9 million from the insurance segment, $93.8 million from the reinsurance segment, $10.8 million from the mortgage segment and $0.6 million from the ‘other’ segment.

The insurance segment’s net favorable development of $5.9 million, or 0.3 loss ratio points, for the 2020 period consisted of $41.6 million of net favorable development in short-tailed and long-tailed lines, partially offset by $35.7 million of net adverse development in medium-tailed lines. Net favorable development of $27.2 million in short-tailed lines reflected $17.5 million of favorable development from property (excluding marine), primarily from the 2015 to 2018 accident years, $6.2 million of favorable development on travel and accident, primarily from 2019 accident year, and $3.5 million of favorable development in lenders products, primarily from the 2018 and 2019 accident years. Net favorable development of $14.4 million in long-tailed lines included $11.7 million of favorable development related to other business, including alternative markets and excess workers’ compensation, primarily from the 2013 to 2017 accident years. Net adverse development in medium-tailed lines reflected $23.0 million of adverse development in contract binding business, across all accident years, and $13.5 million of adverse development


ARCH CAPITAL			21			2022 THIRD QUARTER FORM 10-Q

Table of Contents

ARCH CAPITAL GROUP LTD. AND SUBSIDIARIES

NOTES TO CONSOLIDATED FINANCIAL STATEMENTS (UNAUDITED)

~~in program business, primarily from the 2016 to 2018 accident years.~~

The reinsurance segment’s net favorable development of $93.8 million, or 5.9 loss ratio points, for the 2020 period consisted of $113.0 million of net favorable development from short-tailed and medium-tailed lines, partially offset by $19.2 million of net adverse development from long-tailed lines. Net favorable development of $101.8 million in short-tailed lines reflected $52.1 million related to property catastrophe and property other than property catastrophe business, primarily from the 2016 to 2019 underwriting years, and $47.1 million from other specialty lines, across most underwriting years. Adverse development in long-tailed lines of $19.2 million reflected an increase in reserves from casualty, primarily from the 2012 to 2015 underwriting years.

The mortgage segment’s net favorable development was $10.8 million, or 1.0 loss ratio points, for the 2020 period, primarily driven by subrogation recoveries on second lien and student loan business.

7.6. Allowance for Expected Credit Losses

Premiums Receivable

The following table provides a roll forward of the allowance for expected credit losses of the Company’s premium receivables:


							Premium Receivables, Net of Allowance		Allowance for Expected Credit Losses
Three Months Ended September 30, 2022						Three Months Ended September 30, 2022
Balance at beginning of period						Balance at beginning of period	$	3,634,182	$	38,170
Change for provision of expected credit losses (1)						Change for provision of expected credit losses (1)			59
Balance at end of period						Balance at end of period	$	3,579,380	$	38,229
		Premium Receivables, Net of Allowance		Allowance for Expected Credit Losses
Three Months Ended September 30, 2021	Three Months Ended September 30, 2021					Three Months Ended September 30, 2021
Balance at beginning of period	Balance at beginning of period	$	2,866,578	$	35,979	Balance at beginning of period	$	2,866,578	$	35,979

Change for provision of expected credit losses (1)	Change for provision of expected credit losses (1)			2,736		Change for provision of expected credit losses (1)			2,736

Balance at end of period	Balance at end of period	$	2,807,720	$	38,715	Balance at end of period	$	2,807,720	$	38,715

Three Months Ended September 30, 2020
Nine Months Ended September 30, 2022						Nine Months Ended September 30, 2022
Balance at beginning of period	Balance at beginning of period	$	2,203,753	$	36,054	Balance at beginning of period	$	2,633,280	$	39,958

Change for provision of expected credit losses (1)	Change for provision of expected credit losses (1)			1,046		Change for provision of expected credit losses (1)			(1,729)
Balance at end of period	Balance at end of period	$	2,225,311	$	37,100	Balance at end of period	$	3,579,380	$	38,229

Nine Months Ended September 30, 2021	Nine Months Ended September 30, 2021					Nine Months Ended September 30, 2021
Balance at beginning of period	Balance at beginning of period	$	2,064,586	$	37,781	Balance at beginning of period	$	2,064,586	$	37,781

Change for provision of expected credit losses (1)	Change for provision of expected credit losses (1)			934		Change for provision of expected credit losses (1)			934

Balance at end of period	Balance at end of period	$	2,807,720	$	38,715	Balance at end of period	$	2,807,720	$	38,715

Nine Months Ended September 30, 2020
Balance at beginning of period		$	1,778,717	$	21,003
Cumulative effect of accounting change (2)				6,539
Change for provision of expected credit losses (1)				9,558

Balance at end of period		$	2,225,311	$	37,100

(1)Amounts deemed uncollectible are written-off in operating expenses. For the ~~2021~~2022 third quarter and ~~2020~~2021 third quarter, amounts written off were ~~$1.2~~$1.9 million and ~~nil,~~$1.2 million, respectively. For the nine months ended September 30, ~~2021~~2022 and ~~2020~~2021 period, amounts written off were ~~were $2.4~~$6.6 million and ~~$2.3~~$2.4 million, respectively.

~~(2)~~
~~Adoption~~

Reinsurance Recoverables

The following table provides a roll forward of the allowance for expected credit losses of the Company’s reinsurance recoverables:


	Reinsurance Recoverables, Net of Allowance		Allowance for Expected Credit Losses
Three Months Ended September 30, 2022
Balance at beginning of period	$	5,938,511	$	14,740
Change for provision of expected credit losses			2,626
Balance at end of period	$	6,356,456	$	17,366

Three Months Ended September 30, 2021
Balance at beginning of period	$	4,314,515	$	11,029
Change for provision of expected credit losses			1,802
Balance at end of period	$	5,358,852	$	12,831

Nine Months Ended September 30, 2022
Balance at beginning of period	$	5,880,735	$	13,230
Change for provision of expected credit losses			4,136
Balance at end of period	$	6,356,456	$	17,366

Nine Months Ended September 30, 2021
Balance at beginning of period	$	4,500,802	$	11,636
Change for provision of expected credit losses			1,195
Balance at end of period	$	5,358,852	$	12,831

~~ASU 2016-13, “Financial Instruments - Credit Losses (Topic 326)”.~~


ARCH CAPITAL			2122			~~2021~~2022 THIRD QUARTER FORM 10-Q

Table of Contents

ARCH CAPITAL GROUP LTD. AND SUBSIDIARIES

NOTES TO CONSOLIDATED FINANCIAL STATEMENTS (UNAUDITED)

~~Reinsurance Recoverables~~

~~The following table provides a roll forward of the allowance for expected credit losses of the Company’s reinsurance recoverables:~~

Reinsurance Recoverables, Net of Allowance Allowance for Expected Credit Losses
Three Months Ended September 30, 2021
Balance at beginning of period $ 4,314,515 $ 11,029
Change for provision of expected credit losses 1,802
Balance at end of period $ 5,358,852 $ 12,831
Three Months Ended September 30, 2020
Balance at beginning of period $ 4,363,507 $ 13,595
Change for provision of expected credit losses 399
Balance at end of period $ 4,621,937 $ 13,994
Nine Months Ended September 30, 2021
Balance at beginning of period $ 4,500,802 $ 11,636
Change for provision of expected credit losses 1,195
Balance at end of period $ 5,358,852 $ 12,831
Nine Months Ended September 30, 2020
Balance at beginning of period $ 4,346,816 $ 1,364
Cumulative effect of accounting change (1) 12,010
Change for provision of expected credit losses 620
Balance at end of period $ 4,621,937 $ 13,994

~~(1) Adoption of~~ ~~ASU 2016-13, “Financial Instruments - Credit Losses (Topic 326)”.~~

The following table summarizes the Company’s reinsurance recoverables on paid and unpaid losses (not including ceded unearned premiums):


		September 30,			December 31				September 30,			December 31
		2021			2020				2022			2021
Reinsurance recoverable on unpaid and paid losses and loss adjustment expenses	Reinsurance recoverable on unpaid and paid losses and loss adjustment expenses	$	5,358,852		$	4,500,802		Reinsurance recoverable on unpaid and paid losses and loss adjustment expenses	$	6,356,456		$	5,880,735
% due from carriers with A.M. Best rating of “A-” or better	% due from carriers with A.M. Best rating of “A-” or better	69.1		%	63.9		%	% due from carriers with A.M. Best rating of “A-” or better	69.5		%	69.7		%
% due from all other rated carriers								% due from all other rated carriers	0.1		%	0.1		%
% due from all other carriers with no A.M. Best rating (1)	% due from all other carriers with no A.M. Best rating (1)	30.9		%	36.1		%	% due from all other carriers with no A.M. Best rating (1)	30.4		%	30.2		%
Largest balance due from any one carrier as % of total shareholders’ equity	Largest balance due from any one carrier as % of total shareholders’ equity	6.5		%	1.8		%	Largest balance due from any one carrier as % of total shareholders’ equity	9.1		%	6.7		%

(1) At September 30, ~~2021~~2022 and December 31, ~~2020~~2021 over ~~93%~~95% and ~~94%~~91% of such amount were collateralized through reinsurance trusts, funds withheld arrangements, letters of credit or other, respectively.

Contractholder Receivables

The following table provides a roll forward of the allowance for expected credit losses of the Company’s contractholder receivables:


				Contract-holder Receivables, Net of Allowance			Allowance for Expected Credit Losses
Three Months Ended September 30, 2022								Three Months Ended September 30, 2022
Balance at beginning of period								Balance at beginning of period	$	1,758,018	$	3,005
Change for provision of expected credit losses								Change for provision of expected credit losses			(645)
Balance at end of period								Balance at end of period	$	1,735,730	$	2,360
		Contract-holder Receivables, Net of Allowance			Allowance for Expected Credit Losses
Three Months Ended September 30, 2021	Three Months Ended September 30, 2021							Three Months Ended September 30, 2021
Balance at beginning of period	Balance at beginning of period	$	1,882,948		$	4,471		Balance at beginning of period	$	1,882,948	$	4,471

Change for provision of expected credit losses	Change for provision of expected credit losses				(987)			Change for provision of expected credit losses			(987)

Balance at end of period	Balance at end of period	$	1,824,990		$	3,484		Balance at end of period	1,824,990		$	3,484

Three Months Ended September 30, 2020
Nine Months Ended September 30, 2022								Nine Months Ended September 30, 2022
Balance at beginning of period	Balance at beginning of period	$	2,179,124		$	6,290		Balance at beginning of period	$	1,828,691	$	3,437

Change for provision of expected credit losses	Change for provision of expected credit losses				(389)			Change for provision of expected credit losses			(1,077)

Balance at end of period	Balance at end of period	2,185,614			$	5,901		Balance at end of period	$	1,735,730	$	2,360

Nine Months Ended September 30, 2021	Nine Months Ended September 30, 2021							Nine Months Ended September 30, 2021
Balance at beginning of period	Balance at beginning of period	$	1,986,924		$	8,638		Balance at beginning of period	$	1,986,924	$	8,638

Change for provision of expected credit losses	Change for provision of expected credit losses				(5,154)			Change for provision of expected credit losses			(5,154)

Balance at end of period	Balance at end of period	$	1,824,990		$	3,484		Balance at end of period	1,824,990		$	3,484

Nine Months Ended September 30, 2020
Balance at beginning of period		$	2,119,460		$	—
Cumulative effect of accounting change (1)					6,663
Change for provision of expected credit losses					(762)

Balance at end of period		$	2,185,614		$	5,901

~~(1) Adoption of~~ ~~ASU 2016-13, “Financial Instruments - Credit Losses (Topic 326)”.~~


ARCH CAPITAL			2223			~~2021~~2022 THIRD QUARTER FORM 10-Q

Table of Contents

ARCH CAPITAL GROUP LTD. AND SUBSIDIARIES

NOTES TO CONSOLIDATED FINANCIAL STATEMENTS (UNAUDITED)

8.7. Investment Information

Available For Sale Investments

The following table summarizes the fair value and cost or amortized cost of the Company’s securities classified as available for sale:

Estimated
Fair
Value Gross
Unrealized
Gains Gross
Unrealized
Losses Allowance for Expected Credit Losses (2) Cost or
Amortized
Cost
September 30, 2021
Fixed maturities (1):
Corporate bonds $ 6,403,617 $ 155,246 $ (40,649) $ (1,440) $ 6,290,460
Mortgage backed securities 405,797 3,384 (3,966) (24) 406,403
Municipal bonds 382,722 20,096 (1,206) (2) 363,834
Commercial mortgage backed securities 579,424 3,598 (548) (3) 576,377
U.S. government and government agencies 4,460,515 12,912 (30,320) — 4,477,923
Non-U.S. government securities 1,863,734 46,378 (28,948) (82) 1,846,386
Asset backed securities 2,672,554 12,576 (7,700) (560) 2,668,238
Total 16,768,363 254,190 (113,337) (2,111) 16,629,621
Short-term investments 3,069,965 1,625 (1,780) — 3,070,120
Total $ 19,838,328 $ 255,815 $ (115,117) $ (2,111) $ 19,699,741
December 31, 2020
Fixed maturities (1):
Corporate bonds $ 7,856,571 $ 414,247 $ (34,388) $ (896) $ 7,477,608
Mortgage backed securities 630,001 8,939 (5,028) (278) 626,368
Municipal bonds 494,522 27,291 (3,835) (11) 471,077
Commercial mortgage backed securities 389,900 8,722 (2,954) (122) 384,254
U.S. government and government agencies 5,557,077 22,612 (12,611) — 5,547,076
Non-U.S. government securities 2,433,733 153,891 (8,060) — 2,287,902
Asset backed securities 1,634,804 19,225 (10,715) (1,090) 1,627,384
Total 18,996,608 654,927 (77,591) (2,397) 18,421,669
Short-term investments 1,924,922 2,693 (2,063) — 1,924,292
Total $ 20,921,530 $ 657,620 $ (79,654) $ (2,397) $ 20,345,961

(1) In securities lending transactions, the Company receives collateral in excess of the fair value of the fixed maturities pledged. For purposes of this table, the Company has excluded the collateral received under securities lending, at fair value and included the securities pledged under securities lending, at fair value. See “—Securities Lending Agreements.” In September 2021, the Company terminated its securities lending program and no longer enters into securities lending agreements with financial institutions.

(2) Effective January 1, 2020, the Company adopted ASU 2016-13 and as a result any credit impairment losses on the Company’s available-for-sale investments are recorded as an allowance, subject to reversal.


	Estimated Fair Value		Gross Unrealized Gains		Gross Unrealized Losses		Allowance for Expected Credit Losses		Cost or Amortized Cost
September 30, 2022
Fixed maturities:
Corporate bonds	$	7,096,269	$	51,777	$	(895,365)	$	(35,657)	$	7,975,514
Residential mortgage backed securities	763,371		7,561		(84,183)		2		839,991
Municipal bonds	407,724		5,437		(37,692)		(99)		440,078
Commercial mortgage backed securities	1,064,238		3,079		(50,010)		(1,583)		1,112,752
U.S. government and government agencies	5,126,407		36,074		(400,784)		—		5,491,117
Non-U.S. government securities	2,073,170		9,315		(287,583)		(1,720)		2,353,158
Asset backed securities	1,589,548		1,076		(105,037)		(6,936)		1,700,445
Total	18,120,727		114,319		(1,860,654)		(45,993)		19,913,055

Short-term investments	1,940,857		1,419		(1,633)		—		1,941,071
Total	$	20,061,584	$	115,738	$	(1,862,287)	$	(45,993)	$	21,854,126

December 31, 2021
Fixed maturities:
Corporate bonds	$	6,553,333	$	104,170	$	(69,194)	$	(2,037)	$	6,520,394
Residential mortgage backed securities	408,477		2,825		(5,410)		(48)		411,110
Municipal bonds	404,666		18,724		(1,409)		(2)		387,353
Commercial mortgage backed securities	1,046,484		1,740		(3,117)		(6)		1,047,867
U.S. government and government agencies	4,772,764		10,076		(45,967)		—		4,808,655
Non-U.S. government securities	2,120,294		54,048		(34,749)		(82)		2,101,077
Asset backed securities	2,692,091		6,540		(11,108)		(708)		2,697,367
Total	17,998,109		198,123		(170,954)		(2,883)		17,973,823

Short-term investments	1,734,716		568		(590)		—		1,734,738
Total	$	19,732,825	$	198,691	$	(171,544)	$	(2,883)	$	19,708,561


ARCH CAPITAL			2324			~~2021~~2022 THIRD QUARTER FORM 10-Q

Table of Contents

ARCH CAPITAL GROUP LTD. AND SUBSIDIARIES

NOTES TO CONSOLIDATED FINANCIAL STATEMENTS (UNAUDITED)

The following table summarizes, for all available for sale securities in an unrealized loss position, the fair value and gross unrealized loss by length of time the security has been in a continual unrealized loss position:

Less than 12 Months 12 Months or More Total
Estimated
Fair
Value Gross
Unrealized
Losses Estimated
Fair
Value Gross
Unrealized
Losses Estimated
Fair
Value Gross
Unrealized
Losses
September 30, 2021
Fixed maturities (1):
Corporate bonds $ 2,744,615 $ (36,595) $ 68,450 $ (4,054) $ 2,813,065 $ (40,649)
Mortgage backed securities 257,789 (3,113) 22,769 (853) 280,558 (3,966)
Municipal bonds 46,450 (731) 7,148 (475) 53,598 (1,206)
Commercial mortgage backed securities 76,518 (256) 6,578 (292) 83,096 (548)
U.S. government and government agencies 3,621,719 (29,797) 9,755 (523) 3,631,474 (30,320)
Non-U.S. government securities 1,283,266 (27,523) 22,304 (1,425) 1,305,570 (28,948)
Asset backed securities 1,119,638 (6,524) 37,078 (1,176) 1,156,716 (7,700)
Total 9,149,995 (104,539) 174,082 (8,798) 9,324,077 (113,337)
Short-term investments 265,011 (1,780) — — 265,011 (1,780)
Total $ 9,415,006 $ (106,319) $ 174,082 $ (8,798) $ 9,589,088 $ (115,117)
December 31, 2020
Fixed maturities (1):
Corporate bonds $ 747,442 $ (33,086) $ 3,934 $ (1,302) $ 751,376 $ (34,388)
Mortgage backed securities 284,619 (4,788) 3,637 (240) 288,256 (5,028)
Municipal bonds 67,937 (3,835) — — 67,937 (3,835)
Commercial mortgage backed securities 126,624 (2,916) 2,655 (38) 129,279 (2,954)
U.S. government and government agencies 1,285,907 (12,611) — — 1,285,907 (12,611)
Non-U.S. government securities 543,844 (7,658) 2,441 (402) 546,285 (8,060)
Asset backed securities 634,470 (9,110) 57,737 (1,605) 692,207 (10,715)
Total 3,690,843 (74,004) 70,404 (3,587) 3,761,247 (77,591)
Short-term investments 97,920 (2,063) — — 97,920 (2,063)
Total $ 3,788,763 $ (76,067) $ 70,404 $ (3,587) $ 3,859,167 $ (79,654)


	Less than 12 Months				12 Months or More				Total
	Estimated Fair Value		Gross Unrealized Losses		Estimated Fair Value		Gross Unrealized Losses		Estimated Fair Value		Gross Unrealized Losses
September 30, 2022
Fixed maturities:
Corporate bonds	$	5,596,229	$	(625,774)	$	1,470,800	$	(269,591)	$	7,067,029	$	(895,365)
Residential mortgage backed securities	620,572		(63,732)		93,902		(20,451)		714,474		(84,183)
Municipal bonds	373,219		(36,039)		9,399		(1,653)		382,618		(37,692)
Commercial mortgage backed securities	995,680		(49,215)		34,445		(795)		1,030,125		(50,010)
U.S. government and government agencies	4,205,475		(303,805)		715,347		(96,979)		4,920,822		(400,784)
Non-U.S. government securities	1,728,965		(221,540)		301,298		(66,043)		2,030,263		(287,583)
Asset backed securities	1,193,405		(74,885)		310,838		(30,152)		1,504,243		(105,037)
Total	14,713,545		(1,374,990)		2,936,029		(485,664)		17,649,574		(1,860,654)

Short-term investments	227,201		(1,633)		—		—		227,201		(1,633)
Total	$	14,940,746	$	(1,376,623)	$	2,936,029	$	(485,664)	$	17,876,775	$	(1,862,287)

December 31, 2021
Fixed maturities:
Corporate bonds	$	3,639,582	$	(63,938)	$	98,867	$	(5,256)	$	3,738,449	$	(69,194)
Residential mortgage backed securities	222,176		(3,545)		46,809		(1,865)		268,985		(5,410)
Municipal bonds	26,665		(385)		16,361		(1,024)		43,026		(1,409)
Commercial mortgage backed securities	675,603		(2,805)		5,908		(312)		681,511		(3,117)
U.S. government and government agencies	4,211,621		(44,180)		33,373		(1,787)		4,244,994		(45,967)
Non-U.S. government securities	1,511,301		(31,983)		62,957		(2,766)		1,574,258		(34,749)
Asset backed securities	1,667,002		(9,853)		33,082		(1,255)		1,700,084		(11,108)
Total	11,953,950		(156,689)		297,357		(14,265)		12,251,307		(170,954)

Short-term investments	284,733		(590)		—		—		284,733		(590)
Total	$	12,238,683	$	(157,279)	$	297,357	$	(14,265)	$	12,536,040	$	(171,544)

At September 30, ~~2021,~~2022, on a lot level basis, approximately ~~3,910~~9,590 security lots out of a total of approximately ~~10,020~~11,500 security lots were in an unrealized loss position and the largest single unrealized loss from a single lot in the Company’s fixed maturity portfolio was ~~$2.5~~$7.2 million. At December 31, ~~2020,~~2021, on a lot level basis, approximately ~~2,320~~4,700 security lots out of a total of approximately ~~11,180~~10,240 security lots were in an unrealized loss position and the largest single unrealized loss from a single lot in the Company’s fixed maturity portfolio was ~~$0.9~~$1.1 million.


ARCH CAPITAL			2425			~~2021~~2022 THIRD QUARTER FORM 10-Q

Table of Contents

ARCH CAPITAL GROUP LTD. AND SUBSIDIARIES

NOTES TO CONSOLIDATED FINANCIAL STATEMENTS (UNAUDITED)

The contractual maturities of the Company’s fixed maturities are shown in the following table. Expected maturities, which are management’s best estimates, will differ from contractual maturities because borrowers may have the right to call or prepay obligations with or without call or prepayment penalties.

September 30, 2021 December 31, 2020
Maturity Estimated
Fair
Value Amortized
Cost Estimated
Fair
Value Amortized
Cost
Due in one year or less $ 416,601 $ 410,373 $ 348,200 $ 339,951
Due after one year through five years 7,862,472 7,772,773 10,629,959 10,340,819
Due after five years through 10 years 4,483,025 4,453,526 4,881,564 4,654,754
Due after 10 years 348,490 341,931 482,180 448,139
13,110,588 12,978,603 16,341,903 15,783,663
Mortgage backed securities 405,797 406,403 630,001 626,368
Commercial mortgage backed securities 579,424 576,377 389,900 384,254
Asset backed securities 2,672,554 2,668,238 1,634,804 1,627,384
Total (1) $ 16,768,363 $ 16,629,621 $ 18,996,608 $ 18,421,669

~~Securities Lending Agreements~~

In September 2021, the Company terminated its securities lending program and no longer enters into securities lending agreements with financial institutions to enhance investment income. Prior to the termination of this program, the Company loaned certain of its securities to third parties, primarily major brokerage firms, for short periods of time through a lending agent. The Company maintained legal control over the securities it lent (shown as ‘Securities pledged under securities lending, at fair value’ on the Company’s balance sheet), retained the earnings and cash flows associated with the loaned securities and received a fee from the borrower for the temporary use of the securities. An indemnification agreement with the lending agent protected the Company in the event a borrower became insolvent or failed to return any of the securities on loan from the Company.

The Company received collateral (shown as ‘Collateral received under securities lending, at fair value’ on the Company’s balance sheet) in the form of cash or U.S. government and government agency securities. At September 30, 2021, the Company had no cash collateral or security collateral due to the termination of the program. At December 31, 2020, the fair value of the cash collateral received on securities lending was NaN, and the fair value of security collateral received was $301.1 million.

The carrying value of collateral held under the Company’s securities lending transactions by significant investment category and remaining contractual maturity of the underlying agreements was as follows at December 31, 2020 (no balances at September 30, 2021 due to the termination of the program):

Remaining Contractual Maturity of the Agreements
Overnight and Continuous Less than 30 Days 30-90 Days 90 Days or More Total
December 31, 2020
U.S. government and government agencies $ 142,317 $ — $ 139,290 $ — $ 281,607
Corporate bonds 3,021 — — — 3,021
Equity securities 16,461 — — — 16,461
Total $ 161,799 $ — $ 139,290 $ — $ 301,089
Gross amount of recognized liabilities for securities lending in offsetting disclosure in note 10
$ —
Amounts related to securities lending not included in offsetting disclosure in note 10
$ 301,089


	September 30, 2022				December 31, 2021
Maturity	Estimated Fair Value		Amortized Cost		Estimated Fair Value		Amortized Cost
Due in one year or less	$	579,231	$	599,970	$	300,889	$	299,772
Due after one year through five years	10,029,151		10,808,495		8,355,255		8,339,387
Due after five years through 10 years	3,856,180		4,495,113		4,689,155		4,684,393
Due after 10 years	239,008		356,289		505,758		493,927
	14,703,570		16,259,867		13,851,057		13,817,479
Residential mortgage backed securities	763,371		839,991		408,477		411,110
Commercial mortgage backed securities	1,064,238		1,112,752		1,046,484		1,047,867
Asset backed securities	1,589,548		1,700,445		2,692,091		2,697,367
Total	$	18,120,727	$	19,913,055	$	17,998,109	$	17,973,823

Equity Securities, at Fair Value

At September 30, ~~2021,~~2022, the Company held ~~$1.8~~$0.8 billion of equity securities, at fair value, compared to ~~$1.4~~$1.8 billion at

December 31, ~~2020.~~2021. Such holdings include publicly traded common stocks primarily in the consumer cyclical and non-cyclical, technology, communication and financial sectors


~~ARCH CAPITAL~~			25			~~2021 THIRD QUARTER FORM 10-Q~~

~~Table of Contents~~

~~ARCH CAPITAL GROUP LTD. AND SUBSIDIARIES~~

~~NOTES TO CONSOLIDATED FINANCIAL STATEMENTS (UNAUDITED)~~

and exchange-traded funds in fixed income, equity and other sectors.

Other Investments, at Fair Value

The following table summarizes the Company’s other investments and other investable assets:

September 30,
2021 December 31,
2020
Fixed maturities $ 414,007 $ 843,354
Other investments 1,489,759 2,331,885
Short-term investments 115,681 557,008
Equity securities 24,523 92,549
Investments accounted for using the fair value option $ 2,043,970 $ 3,824,796
Other investable assets (1) — 500,000
Total other investments $ 2,043,970 $ 4,324,796

~~(1) Participation interests in a receivable of a reverse repurchase agreement.~~


	September 30, 2022		December 31, 2021
Fixed maturities	$	530,303	$	416,698
Other investments	1,005,929		1,432,553
Short-term investments	28,614		97,806
Equity securities	13,905		26,493



Total	$	1,578,751	$	1,973,550

The following table summarizes the Company’s other investments, as detailed in the previous table, by strategy:


		September 30, 2021		December 31, 2020			September 30, 2022		December 31, 2021
Lending						Lending	$	398,789	$	536,345
Investment grade fixed income						Investment grade fixed income	229,262		147,810
Term loan investments	Term loan investments	$	528,585	$	1,231,731	Term loan investments	151,649		484,950
Lending		579,563		572,636
Private equity						Private equity	117,856		91,126
Energy						Energy	55,250		81,692
Credit related funds	Credit related funds	56,997		90,780		Credit related funds	53,123		70,278
Energy		84,880		65,813
Investment grade fixed income		131,910		138,646
Infrastructure	Infrastructure	26,359		165,516		Infrastructure	—		20,352
Private equity		81,465		48,750
Real estate		—		18,013

Total	Total	$	1,489,759	$	2,331,885	Total	$	1,005,929	$	1,432,553

Investments Accounted For Using the Equity Method

The following table summarizes the Company’s investments accounted for using the equity method, by strategy:


		September 30, 2021		December 31, 2020			September 30, 2022		December 31, 2021
Credit related funds	Credit related funds	$	952,794	$	740,060	Credit related funds	$	1,135,623	$	1,022,334
Equities		414,322		343,058
Private equity						Private equity	761,997		436,042
Real estate	Real estate	340,510		258,518		Real estate	474,666		396,395
Lending	Lending	330,368		179,629		Lending	454,196		376,649
Private equity		365,840		235,289
Equities						Equities	261,650		395,090
Infrastructure	Infrastructure	222,484		175,882		Infrastructure	236,920		230,070
Energy	Energy	114,975		115,453		Energy	113,778		119,141
Fixed income						Fixed income	127,116		101,890
Total	Total	$	2,741,293	$	2,047,889	Total	$	3,565,946	$	3,077,611

Certain of the Company’s other investments are in investment funds for which the Company has the option to redeem at agreed upon values as described in each investment fund’s subscription agreement. Depending on the terms of the various subscription agreements, investments in investment funds may be redeemed daily, monthly, quarterly or on other terms. Two common redemption restrictions

which may impact the Company’s ability to redeem these investment funds are gates and lockups. A gate is a suspension of redemptions which may be implemented by the general partner or investment manager of the fund in order to defer, in whole or in part, the redemption request in the event the aggregate amount of redemption requests exceeds a predetermined percentage of the investment fund’s net assets which may otherwise hinder the general partner or investment manager’s ability to liquidate holdings in an orderly fashion in order to generate the cash necessary to fund extraordinarily large redemption payouts. A lockup period is the initial amount of time an investor is contractually required to hold the security before having the ability to redeem. If the investment funds are eligible to be


ARCH CAPITAL			26			2022 THIRD QUARTER FORM 10-Q

Table of Contents

ARCH CAPITAL GROUP LTD. AND SUBSIDIARIES

NOTES TO CONSOLIDATED FINANCIAL STATEMENTS (UNAUDITED)

redeemed, the time to redeem such fund can take weeks or months following the notification.

Limited Partnership Interests

In the normal course of its activities, the Company invests in limited partnerships as part of its overall investment strategy. Such amounts are included in ‘investments accounted for using the equity method’ and ‘investments accounted for using the fair value option.’ The Company has determined that it is not required to consolidate these investments because it is not the primary beneficiary of the funds. The Company’s maximum exposure to loss with respect to these investments is limited to the investment carrying amounts reported in the Company’s consolidated balance sheet and any unfunded commitment.

The following table summarizes investments in limited partnership interests where the Company has a variable interest by balance sheet line item:


		September 30, 2021		December 31, 2020			September 30, 2022		December 31, 2021
Investments accounted for using the equity method (1)	Investments accounted for using the equity method (1)	2,741,293		2,047,889		Investments accounted for using the equity method (1)	$	3,565,946	$	3,077,611
Investments accounted for using the fair value option (2)	Investments accounted for using the fair value option (2)	176,884		184,720		Investments accounted for using the fair value option (2)	120,498		170,595
Total	Total	$	2,918,177	$	2,232,609	Total	$	3,686,444	$	3,248,206

(1) Aggregate unfunded commitments were ~~$2.3~~$2.8 billion at September 30, ~~2021,~~2022, compared to ~~$1.8~~$2.6 billion at December 31, ~~2020.~~2021.

(2) Aggregate unfunded commitments were ~~$22.9~~$21.5 million at September 30, ~~2021,~~2022, compared to ~~$35.6~~$18.8 million at December 31, ~~2020.~~2021.


~~ARCH CAPITAL~~			26			~~2021 THIRD QUARTER FORM 10-Q~~

~~Table of Contents~~

~~ARCH CAPITAL GROUP LTD. AND SUBSIDIARIES~~

~~NOTES TO CONSOLIDATED FINANCIAL STATEMENTS (UNAUDITED)~~

Net Investment Income

The components of net investment income were derived from the following sources:


		September 30,					September 30,
		2021		2020			2022		2021
Three Months Ended	Three Months Ended					Three Months Ended
Fixed maturities	Fixed maturities	$	75,964	$	98,344	Fixed maturities	$	123,568	$	75,964
Term loans	Term loans	1,736		22,459		Term loans	88		1,736
Equity securities	Equity securities	9,867		6,659		Equity securities	4,261		9,867
Short-term investments	Short-term investments	1,858		1,332		Short-term investments	9,304		1,858
Other (1)	Other (1)	17,378		22,060		Other (1)	8,556		17,378
Gross investment income	Gross investment income	106,803		150,854		Gross investment income	145,777		106,803
Investment expenses	Investment expenses	(18,608)		(22,342)		Investment expenses	(17,137)		(18,608)
Net investment income	Net investment income	$	88,195	$	128,512	Net investment income	$	128,640	$	88,195

Nine Months Ended	Nine Months Ended					Nine Months Ended
Fixed maturities	Fixed maturities	$	255,215	$	318,582	Fixed maturities	$	310,963	$	255,215
Term loans	Term loans	33,343		66,141		Term loans	2,106		33,343
Equity securities	Equity securities	24,101		18,885		Equity securities	16,620		24,101
Short-term investments	Short-term investments	3,603		9,611		Short-term investments	15,999		3,603
Other (1)	Other (1)	51,683		57,926		Other (1)	26,598		51,683
Gross investment income	Gross investment income	367,945		471,145		Gross investment income	372,286		367,945
Investment expenses	Investment expenses	(69,281)		(65,995)		Investment expenses	(56,818)		(69,281)
Net investment income	Net investment income	$	298,664	$	405,150	Net investment income	$	315,468	$	298,664

(1) Includes income distributions from investment funds and other items.

Net Realized Gains (Losses)

Net realized gains (losses), which include changes in the allowance for credit losses on financial assets and net impairment losses recognized in earnings were as follows:


		September 30,					September 30,
		2021		2020			2022		2021
Three Months Ended	Three Months Ended					Three Months Ended
Available for sale securities:	Available for sale securities:					Available for sale securities:
Gross gains on investment sales	Gross gains on investment sales	$	86,819	$	104,733	Gross gains on investment sales	$	18,030	$	86,819
Gross losses on investment sales	Gross losses on investment sales	(18,446)		(16,862)		Gross losses on investment sales	(73,970)		(18,446)
Change in fair value of assets and liabilities accounted for using the fair value option:	Change in fair value of assets and liabilities accounted for using the fair value option:					Change in fair value of assets and liabilities accounted for using the fair value option:
Fixed maturities	Fixed maturities	(7,492)		34,115		Fixed maturities	(19,304)		(7,492)
Other investments	Other investments	3,811		61,622		Other investments	(17,882)		3,811
Equity securities	Equity securities	3,042		4,048		Equity securities	(584)		3,042
Short-term investments	Short-term investments	16		3,377		Short-term investments	(975)		16
Equity securities, at fair value:	Equity securities, at fair value:					Equity securities, at fair value:
Net realized gains (losses) on sales during the period	Net realized gains (losses) on sales during the period	14,736		26,549		Net realized gains (losses) on sales during the period	(6,401)		14,736
Net unrealized gains (losses) on equity securities still held at reporting date	Net unrealized gains (losses) on equity securities still held at reporting date	(40,155)		33,562		Net unrealized gains (losses) on equity securities still held at reporting date	(36,162)		(40,155)
Allowance for credit losses:	Allowance for credit losses:					Allowance for credit losses:
Investments related	Investments related	(456)		1,332		Investments related	8,652		(456)
Underwriting related	Underwriting related	(3,985)		351		Underwriting related	(4,232)		(3,985)

Derivative instruments (1)	Derivative instruments (1)	(21,435)		20,369		Derivative instruments (1)	(48,196)		(21,435)
Other (2)		(41,495)		7,303
Other						Other	(2,649)		(41,495)
Net realized gains (losses)	Net realized gains (losses)	$	(25,040)	$	280,499	Net realized gains (losses)	$	(183,673)	$	(25,040)

Nine Months Ended	Nine Months Ended					Nine Months Ended
Available for sale securities:	Available for sale securities:					Available for sale securities:
Gross gains on investment sales	Gross gains on investment sales	$	267,362	$	515,086	Gross gains on investment sales	$	52,923	$	267,362
Gross losses on investment sales	Gross losses on investment sales	(132,071)		(98,654)		Gross losses on investment sales	(239,493)		(132,071)
Change in fair value of assets and liabilities accounted for using the fair value option:	Change in fair value of assets and liabilities accounted for using the fair value option:					Change in fair value of assets and liabilities accounted for using the fair value option:
Fixed maturities	Fixed maturities	19,973		(25,370)		Fixed maturities	(89,148)		19,973
Other investments	Other investments	111,550		(67,608)		Other investments	(35,203)		111,550
Equity securities	Equity securities	10,599		5,803		Equity securities	(6,021)		10,599
Short-term investments	Short-term investments	648		(1,936)		Short-term investments	(3,132)		648
Equity securities, at fair value:	Equity securities, at fair value:					Equity securities, at fair value:
Net realized gains (losses) on sales during the period	Net realized gains (losses) on sales during the period	86,155		7,760		Net realized gains (losses) on sales during the period	75,689		86,155
Net unrealized gains (losses) on equity securities still held at reporting date	Net unrealized gains (losses) on equity securities still held at reporting date	45,400		3,682		Net unrealized gains (losses) on equity securities still held at reporting date	(318,732)		45,400
Allowance for credit losses:	Allowance for credit losses:					Allowance for credit losses:
Investments related	Investments related	(1,208)		(4,763)		Investments related	(48,096)		(1,208)
Underwriting related	Underwriting related	2,664		(8,753)		Underwriting related	(7,676)		2,664
Net impairments losses		—		(533)

Derivative instruments (1)	Derivative instruments (1)	(36,428)		146,722		Derivative instruments (1)	(117,591)		(36,428)
Other (2)		(54,316)		(1,309)
Other						Other	(6,186)		(54,316)
Net realized gains (losses)	Net realized gains (losses)	$	320,328	$	470,127	Net realized gains (losses)	$	(742,666)	$	320,328

(1) See note 109 for information on the Company’s derivative instruments.

~~(2) 2021 periods reflected $33.1 million of losses related to the Company’s deconsolidation of Watford.~~


ARCH CAPITAL			27			~~2021~~2022 THIRD QUARTER FORM 10-Q

Table of Contents

ARCH CAPITAL GROUP LTD. AND SUBSIDIARIES

NOTES TO CONSOLIDATED FINANCIAL STATEMENTS (UNAUDITED)

Equity in Net Income (Loss) of Investment Funds Accounted for Using the Equity Method

The Company recorded ~~$105.4~~a loss of $18.9 million ~~of equity in net income~~ related to investment funds accounted for using the equity method in the ~~2021~~2022 third quarter, compared to income of ~~$126.7~~$105.4 million for the ~~2020~~2021 third quarter and an income of ~~$299.3~~$75.5 million for the nine months ended September 30, ~~2021,~~2022, compared to income of ~~$57.4~~$299.3 million for nine months ended September 30, ~~2020.~~2021. In applying the equity method, 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 market value of the underlying securities in the funds). Such investments are generally recorded on a one to three month lag based on the availability of reports from the investment funds.

Investments in Operating Affiliates

Investments in which the Company has significant influence over the operating and financial policies are classified as ‘investments in operating affiliates’ on the Company’s balance sheets and are accounted for under the equity method. Such investments primarily include the Company’s investment in Coface SA (“Coface”), Greysbridge and Premia. Investments in Coface and Premia are generally recorded on a three month lag, while the Company’s investment in Greysbridge is not recorded on a lag.

In 2021, the Company completed the share purchase agreement with Natixis to purchase 29.5% of the common equity of Coface, a France-based leader in the global trade credit insurance market. The consideration paid was €9.95 per share, or an aggregate €453 million (approximately ~~$546~~

$546 million) including related fees. Income (loss) from

operating affiliates reflected a one-time gain of $74.5 million realized from the acquisition. As ~~a result of equity method accounting rules, approximately $36 million of additional gain was deferred and will generally be recognized over the next five years. As~~ of September 30, ~~2021,~~2022, the Company owned approximately 29.86% of the issued shares of Coface, or ~~30.10%~~30.05% excluding treasury shares, with a carrying value of ~~$615.9 million.~~$506.7 million, compared to $630.5 million at December 31, 2021.

In July 2021, the Company announced the completion of the previously disclosed acquisition of ~~Watford~~Somers by Greysbridge for a cash purchase price of $35.00 per common share.

Effective July 1, 2021, ~~Watford~~Somers is wholly owned by Greysbridge, and Greysbridge is owned 40% by the Company, 30% by certain investment funds managed by Kelso and 30% by certain investment funds managed by Warburg. At September 30, ~~2021~~2022 the Company’s carrying value in Greysbridge was ~~$363.3~~$277.6 million, compared to $375.7 million at December 31, 2021, which reflected the Company’s aggregate purchase price of $278.9 million along with income (loss) from operating affiliates, which included a one-time gain of $95.7 million recognized from the acquisition. In addition, the ‘net realized gains (losses)’ line on the Company’s consolidated statements of income included a $33.1 million loss as a result of deconsolidation of Watford in the Company’s financial statements following the close of the transaction. See n ~~ote 12~~.

Income from operating affiliates for the ~~2021~~2022 third quarter was ~~$124.1~~income of $8.5 million, compared to an income of ~~$0.9~~$124.1 million, for the ~~2020~~2021 third quarter and income of ~~$224.1~~$37.7 million for the nine months ended September 30, ~~2021,~~2022, compared to an income of ~~$6.3~~$224.1 million for ~~the~~ nine months ended September 30, ~~2020. The income from operating affiliates for the 2021 period, primarily related to the Company’s recent acquisitions of Coface and Greysbridge.~~2021.


ARCH CAPITAL			28			~~2021~~2022 THIRD QUARTER FORM 10-Q

Table of Contents

ARCH CAPITAL GROUP LTD. AND SUBSIDIARIES

NOTES TO CONSOLIDATED FINANCIAL STATEMENTS (UNAUDITED)

Allowance for Expected Credit Losses

The following table provides a roll forward of the allowance for expected credit losses of the Company’s securities classified as available for sale:


		Structured Securities (1)		Municipal Bonds		Corporate Bonds		Total			Structured Securities (1)		Municipal Bonds		Corporate Bonds		Total
Three Months Ended September 30, 2021
Balance at beginning of period		$	759	$	6	$	1,359	$	2,124

Additions for current-period provision for expected credit losses		48		—		—		48
Additions (reductions) for previously recognized expected credit losses		14		(4)		395		405
Reductions due to disposals (3)		(234)		—		(232)		(466)

Balance at end of period		$	587	$	2	$	1,522	$	2,111

Three Months Ended September 30, 2020
Three Months Ended September 30, 2022										Three Months Ended September 30, 2022
Balance at beginning of period	Balance at beginning of period	$	1,726	$	28	$	4,115	$	5,869	Balance at beginning of period	$	18,283	$	298	$	39,829	$	58,410

Additions for current-period provision for expected credit losses	Additions for current-period provision for expected credit losses	27		—		202		229		Additions for current-period provision for expected credit losses	1,782		12		1,986		3,780
Additions (reductions) for previously recognized expected credit losses	Additions (reductions) for previously recognized expected credit losses	403		33		(1,996)		(1,560)		Additions (reductions) for previously recognized expected credit losses	(9,767)		(211)		(2,552)		(12,530)
Reductions due to disposals	Reductions due to disposals	(28)		—		(577)		(605)		Reductions due to disposals	(1,780)		—		(1,887)		(3,667)

Balance at end of period	Balance at end of period	$	2,128	$	61	$	1,744	$	3,933	Balance at end of period	$	8,518	$	99	$	37,376	$	45,993

Three Months Ended September 30, 2021										Three Months Ended September 30, 2021
Balance at beginning of period										Balance at beginning of period	$	759	$	6	$	1,359	$	2,124

Additions for current-period provision for expected credit losses										Additions for current-period provision for expected credit losses	48		—		—		48
Additions (reductions) for previously recognized expected credit losses										Additions (reductions) for previously recognized expected credit losses	14		(4)		395		405
Reductions due to disposals										Reductions due to disposals	(234)		—		(232)		(466)

Balance at end of period										Balance at end of period	$	587	$	2	$	1,522	$	2,111

Nine Months Ended September 30, 2022										Nine Months Ended September 30, 2022
Balance at beginning of period										Balance at beginning of period	$	802	$	2	$	2,079	$	2,883

Additions for current-period provision for expected credit losses										Additions for current-period provision for expected credit losses	12,560		359		40,602		53,521
Additions (reductions) for previously recognized expected credit losses										Additions (reductions) for previously recognized expected credit losses	(2,575)		(262)		(2,772)		(5,609)
Reductions due to disposals										Reductions due to disposals	(2,269)		—		(2,533)		(4,802)

Balance at end of period										Balance at end of period	$	8,518	$	99	$	37,376	$	45,993

Nine Months Ended September 30, 2021	Nine Months Ended September 30, 2021									Nine Months Ended September 30, 2021
Balance at beginning of period	Balance at beginning of period	$	1,490	$	11	$	896	$	2,397	Balance at beginning of period	$	1,490	$	11	$	896	$	2,397

Additions for current-period provision for expected credit losses	Additions for current-period provision for expected credit losses	282		—		2,428		2,710		Additions for current-period provision for expected credit losses	282		—		2,428		2,710
Additions (reductions) for previously recognized expected credit losses	Additions (reductions) for previously recognized expected credit losses	(751)		(9)		(557)		(1,317)		Additions (reductions) for previously recognized expected credit losses	(751)		(9)		(557)		(1,317)
Reductions due to disposals (3)		(434)		—		(1,245)		(1,679)

Balance at end of period		$	587	$	2	$	1,522	$	2,111

Nine Months Ended September 30, 2020
Balance at beginning of period		$	—	$	—	$	—	$	—
Cumulative effect of accounting change (2)		517		—		117		634
Additions for current-period provision for expected credit losses		2,868		67		7,643		10,578
Additions (reductions) for previously recognized expected credit losses		(903)		8		(4,920)		(5,815)
Reductions due to disposals	Reductions due to disposals	(354)		(14)		(1,096)		(1,464)		Reductions due to disposals	(434)		—		(1,245)		(1,679)

Balance at end of period	Balance at end of period	$	2,128	$	61	$	1,744	$	3,933	Balance at end of period	$	587	$	2	$	1,522	$	2,111

(1) Includes asset backed securities, residential mortgage backed securities and commercial mortgage backed securities.

~~(2) Adoption of~~ ~~ASU 2016-13, “Financial Instruments - Credit Losses (Topic 326)”.~~

~~(3) Reduction for the 2021 periods primarily related to the Company’s deconsolidation of Watford.~~


ARCH CAPITAL			29			~~2021~~2022 THIRD QUARTER FORM 10-Q

Table of Contents

ARCH CAPITAL GROUP LTD. AND SUBSIDIARIES

NOTES TO CONSOLIDATED FINANCIAL STATEMENTS (UNAUDITED)

Restricted Assets

The Company is required to maintain assets on deposit, which primarily consist of fixed maturities, with various regulatory authorities to support its underwriting operations. The Company’s subsidiaries maintain assets in trust accounts as collateral for transactions with affiliated companies and also have investments in segregated portfolios primarily to provide collateral or guarantees for letters of credit to third parties. See note 18, “Commitments and Contingencies,” of the notes to consolidated financial statements in the Company’s ~~2020~~2021 Form 10-K.

The following table details the value of the Company’s restricted assets:


		September 30, 2021		December 31, 2020			September 30, 2022		December 31, 2021
Assets used for collateral or guarantees:	Assets used for collateral or guarantees:					Assets used for collateral or guarantees:
Affiliated transactions	Affiliated transactions	$	4,271,208	$	4,643,334	Affiliated transactions	$	4,212,521	$	4,223,955
Third party agreements	Third party agreements	2,594,053		3,083,324		Third party agreements	2,847,814		2,721,160
Deposits with U.S. regulatory authorities	Deposits with U.S. regulatory authorities	803,878		827,552		Deposits with U.S. regulatory authorities	756,368		798,100
Deposits with non-U.S. regulatory authorities	Deposits with non-U.S. regulatory authorities	469,497		179,099		Deposits with non-U.S. regulatory authorities	519,254		506,517

Total restricted assets	Total restricted assets	$	8,138,636	$	8,733,309	Total restricted assets	$	8,335,957	$	8,249,732

Reconciliation of Cash and Restricted Cash

The following table details reconciliation of cash and restricted cash within the Consolidated Balance Sheets:

September 30,
2021 December 31,
2020
Cash $ 1,137,721 $ 906,448
Restricted cash (included in ‘other assets’) $ 411,188 $ 384,096
Cash and restricted cash $ 1,548,909 $ 1,290,544


	September 30, 2022		December 31, 2021
Cash	$	813,583	$	858,668
Restricted cash (included in ‘other assets’)	444,741		456,103
Cash and restricted cash	$	1,258,324	$	1,314,771

9.8. Fair Value

Accounting guidance regarding fair value measurements addresses how companies should measure fair value when they are required to use a fair value measure for recognition or disclosure purposes under GAAP and provides a common definition of fair value to be used throughout GAAP. It defines fair value as the price that would be received to sell an asset or paid to transfer a liability in an orderly fashion between market participants at the measurement date. In addition, it establishes a three-level valuation hierarchy for the disclosure of fair value measurements. The valuation hierarchy is based upon the transparency of inputs to the valuation of an asset or liability as of the measurement date. The level in the hierarchy within which a given fair value measurement falls is determined based on the lowest level input that is significant to the measurement (Level 1 being the highest priority and Level 3 being the lowest priority).

The levels in the hierarchy are defined as follows:


Level 1:						Inputs to the valuation methodology are observable inputs that reflect quoted prices (unadjusted) for identical assets or liabilities in active markets

Level 2:						Inputs to the valuation methodology include quoted prices for similar assets and liabilities in active markets, and inputs that are observable for the asset or liability, either directly or indirectly, for substantially the full term of the financial instrument

Level 3:						Inputs to the valuation methodology are unobservable and significant to the fair value measurement

Following is a description of the valuation methodologies used for securities measured at fair value, as well as the general classification of such securities pursuant to the valuation hierarchy. The Company reviews its securities measured at fair value and discusses the proper classification of such investments with investment advisers and others.

The Company determines the existence of an active market based on its judgment as to whether transactions for the financial instrument occur in such market with sufficient frequency and volume to provide reliable pricing information. The independent pricing sources obtain market quotations and actual transaction prices for securities that have quoted prices in active markets. The Company uses quoted values and other data provided by nationally recognized independent pricing sources as inputs into its process for determining fair values of its fixed maturity investments. To validate the techniques or models used by pricing sources, the Company's review process includes, but is not limited to: (i) quantitative analysis (e.g., comparing the quarterly return for each managed portfolio to its target benchmark, with significant differences identified and investigated); (ii) a review of the average number of prices obtained in the pricing process and the range of resulting fair values; (iii) initial and ongoing evaluation of methodologies used by outside parties to calculate fair value; (iv) a comparison of the fair value estimates to the Company’s knowledge of the current market; (v) a comparison of the pricing services' fair values to other pricing services' fair values for the same investments; and (vi) periodic back-testing, which includes randomly selecting purchased or sold securities and comparing the executed prices to the fair value estimates from the pricing service. A price source hierarchy was maintained in order to determine which price source would be used (i.e., a price obtained from a pricing service with more seniority in the hierarchy will be used over a less senior one in all cases). The hierarchy prioritizes pricing services based on availability and reliability and assigns the highest priority to index providers. Based on the above


ARCH CAPITAL			30			~~2021~~2022 THIRD QUARTER FORM 10-Q

Table of Contents

ARCH CAPITAL GROUP LTD. AND SUBSIDIARIES

NOTES TO CONSOLIDATED FINANCIAL STATEMENTS (UNAUDITED)

review, the Company will challenge any prices for a security or portfolio which are considered not to be representative of fair value. The Company did not adjust any of the prices obtained from the independent pricing sources at September 30, ~~2021.~~2022.

In certain circumstances, when fair values are unavailable from these independent pricing sources, quotes are obtained directly from broker-dealers who are active in the corresponding markets. Such quotes are subject to the validation procedures noted above. Where quotes are unavailable, fair value is determined by the Investment Manager using quantitative and qualitative assessments such as internally modeled values. Of the ~~$23.8~~$22.8 billion of financial assets and liabilities measured at fair value at September 30, ~~2021,~~2022, approximately ~~$9.0~~$12.6 million, or ~~0.0%~~0.1%, were priced using non-binding broker-dealer quotes or modeled valuations. Of the ~~$26.5~~$23.8 billion of financial assets and liabilities measured at fair value at December 31, ~~2020,~~2021, approximately ~~$150.1~~$7.7 million, or ~~0.6%~~0.0%, were priced using non-binding broker-dealer quotes or modeled valuations.

Fixed maturities

The Company uses the market approach valuation technique to estimate the fair value of its fixed maturity securities, when possible. The market approach includes obtaining prices from independent pricing services, such as index providers and pricing vendors, as well as to a lesser extent quotes from broker-dealers. The independent pricing sources obtain market quotations and actual transaction prices for securities that have quoted prices in active markets. Each source has its own proprietary method for determining the fair value of securities that are not actively traded. In general, these methods involve the use of “matrix pricing” in which the independent pricing source uses observable market inputs including, but not limited to, investment yields, credit risks and spreads, benchmarking of like securities, broker-dealer quotes, reported trades and sector groupings to determine a reasonable fair value.

The following describes the significant inputs generally used to determine the fair value of the Company’s fixed maturity securities by asset class:

•U.S. government and government agencies — – valuations provided by independent pricing services, with all prices provided through index providers and pricing vendors. The Company determined that all U.S. Treasuries would be classified as Level 1 securities due to observed levels of trading activity, the high number of strongly correlated pricing quotes received on U.S. Treasuries and other factors. The fair values of U.S. government agency securities are generally determined using the spread above the risk-free yield curve. As the yields for the risk-free yield curve and the spreads for these securities are observable market inputs, the

fair values of U.S. government agency securities are classified within Level 2.

•Corporate bonds —– valuations provided by independent pricing services, substantially all through index providers and pricing vendors with a small amount through broker-dealers. The fair values of these securities are generally determined using the spread above the risk-free yield curve. These spreads are generally obtained from the new issue market, secondary trading and from broker-dealers who trade in the relevant security market. As the significant inputs used in the pricing process for corporate bonds are observable market inputs, the fair value of these securities are classified within Level 2. A small number of securities are included in Level 3 due to a low level of transparency on the inputs used in the pricing process.

•Municipal bonds~~Mortgage-backed~~– valuations provided by independent pricing services, with all prices provided through index providers and pricing vendors. The fair values of these securities —are generally determined using spreads obtained from broker-dealers who trade in the relevant security market, trade prices and the new issue market. As the significant inputs used in the pricing process for municipal bonds are observable market inputs, the fair value of these securities are classified within Level 2.

Residential mortgage-backed securities– valuations provided by independent pricing services, substantially all through pricing vendors and index providers with a small amount through broker-dealers. The fair values of these securities are generally determined through the use of pricing models (including Option Adjusted Spread) which use spreads to determine the expected average life of the securities. These spreads are generally obtained from the new issue market, secondary trading and from broker-dealers who trade in the relevant security market. The pricing services also review prepayment speeds and other indicators, when applicable. As the significant inputs used in the pricing process for mortgage-backed securities are observable market inputs, the fair value of these securities are classified within Level 2. A small number of securities are included in Level 3 due to a low level of transparency on the inputs used in the pricing process.

•Municipal bonds — valuations provided by independent pricing services, with all prices provided through index providers and pricing vendors. The fair values of these securities are generally determined using spreads obtained from broker-dealers who trade in the relevant security market, trade prices and the new issue market. As the significant inputs used in the pricing process for municipal bonds are observable market inputs, the fair value of these securities are classified within Level 2.

•Commercial mortgage-backed securities —– valuations provided by independent pricing services, substantially all through index providers and pricing vendors with a small amount through broker-dealers. The fair values of these securities are generally determined through the use of pricing models which use spreads to determine the appropriate average life of the securities. These spreads are generally obtained from the new issue market, secondary trading and from broker-dealers who trade in the relevant security market. The pricing services also review prepayment speeds and other indicators, when applicable. As the significant inputs used in the pricing process for commercial mortgage-


ARCH CAPITAL			31			~~2021~~2022 THIRD QUARTER FORM 10-Q

Table of Contents

ARCH CAPITAL GROUP LTD. AND SUBSIDIARIES

NOTES TO CONSOLIDATED FINANCIAL STATEMENTS (UNAUDITED)

~~mortgage-backed~~backed securities are observable market inputs, the fair value of these securities are classified within Level 2.

•Non-U.S. government securities —– valuations provided by independent pricing services, with all prices provided through index providers and pricing vendors. The fair values of these securities are generally based on international indices or valuation models which include daily observed yield curves, cross-currency basis index spreads and country credit spreads. As the significant inputs used in the pricing process for non-U.S. government securities are observable market inputs, the fair value of these securities are classified within Level 2.

•Asset-backed securities —– valuations provided by independent pricing services, substantially all through index providers and pricing vendors with a small amount through broker-dealers. The fair values of these securities are generally determined through the use of pricing models (including Option Adjusted Spread) which use spreads to determine the appropriate average life of the securities. These spreads are generally obtained from the new issue market, secondary trading and from broker-dealers who trade in the relevant security market. The pricing services also review prepayment speeds and other indicators, when applicable. As the significant inputs used in the pricing process for asset-backed securities are observable market inputs, the fair value of these securities are classified within Level 2. A small number of securities are included in Level 3 due to a low level of transparency on the inputs used in the pricing process.

Equity securities

The Company determined that exchange-traded equity securities would be included in Level 1 as their fair values are based on quoted market prices in active markets. Certain equity securities are included in Level 2 of the valuation hierarchy as the significant inputs used in the pricing process for such securities are observable market inputs. Other equity securities are included in Level 3 due to the lack of an available independent price source for such securities. As the significant inputs used to price these securities are unobservable, the fair value of such securities are classified as Level 3.

Other investments

The Company’s other investments include term loan investments for which fair values are estimated by using quoted prices of term loan investments with similar characteristics, pricing models or matrix pricing. Such investments are generally classified within Level 2. The fair values for certain of the Company’s other investments are determined using net asset values as advised by external fund managers. The net asset value is based on the fund manager’s valuation of the underlying holdings in accordance with the fund’s governing documents. In accordance with applicable

accounting guidance, certain investments that are measured at

fair value using the net asset value per share (or its equivalent) practical expedient have not been classified in the fair value hierarchy. A small number of securities are included in Level 3 due to the lack of an available independent price source for such securities.

Derivative instruments

The Company’s futures contracts, foreign currency forward contracts, interest rate swaps and other derivatives trade in the over-the-counter derivative market. The Company uses the market approach valuation technique to estimate the fair value for these derivatives based on significant observable market inputs from third party pricing vendors, non-binding broker-dealer quotes and/or recent trading activity. As the significant inputs used in the pricing process for these derivative instruments are observable market inputs, the fair value of these securities are classified within Level 2.

Short-term investments

The Company determined that certain of its short-term investments held in highly liquid money market-type funds, Treasury bills and commercial paper would be included in Level 1 as their fair values are based on quoted market prices in active markets. The fair values of other short-term investments are generally determined using the spread above the risk-free yield curve and are classified within Level 2.

Residential mortgage loans

The Company’s residential mortgage loans (included in ‘other assets’ in the consolidated balance sheets) include amounts related to the Company’s whole mortgage loan purchase and sell program. Fair values of residential mortgage loans are generally determined based on market prices. As significant inputs used in pricing process for these residential mortgage loans are observable market inputs, the fair value of these securities are classified within Level 2.

Other liabilities

The Company’s other liabilities include contingent and deferred consideration liabilities related to the Company’s acquisitions. Contingent consideration liabilities

~~Contingent consideration liabilities (included in ‘other liabilities’ in the consolidated balance sheets) include amounts related to various Company’s acquisitions. Such amounts~~ are remeasured at fair value at each balance sheet date with changes in fair value recognized in ‘net realized gains (losses).’ To determine the fair value of contingent consideration liabilities, the Company estimates the future payments using an income approach based on modeled inputs which include a weighted average cost of capital. Deferred consideration liabilities are measured at fair value on the transaction date. The Company determined that contingent and deferred consideration liabilities would be included within Level 3.


ARCH CAPITAL			32			~~2021~~2022 THIRD QUARTER FORM 10-Q

Table of Contents

ARCH CAPITAL GROUP LTD. AND SUBSIDIARIES

NOTES TO CONSOLIDATED FINANCIAL STATEMENTS (UNAUDITED)

The following table presents the Company’s financial assets and liabilities measured at fair value by level at September 30, ~~2021:~~2022:


				Estimated Fair Value Measurements Using:									Estimated Fair Value Measurements Using:
		Estimated Fair Value		Quoted Prices in Active Markets for Identical Assets (Level 1)		Significant Other Observable Inputs (Level 2)		Significant Unobservable Inputs (Level 3)			Estimated Fair Value		Quoted Prices in Active Markets for Identical Assets (Level 1)		Significant Other Observable Inputs (Level 2)		Significant Unobservable Inputs (Level 3)
Assets measured at fair value (1):
Assets measured at fair value:										Assets measured at fair value:
Available for sale securities:	Available for sale securities:									Available for sale securities:
Fixed maturities:	Fixed maturities:									Fixed maturities:
Corporate bonds	Corporate bonds	$	6,403,617	$	—	$	6,403,604	$	13	Corporate bonds	$	7,096,269	$	—	$	7,096,256	$	13
Mortgage backed securities		405,797		—		405,797		—
Residential mortgage backed securities										Residential mortgage backed securities	763,371		—		763,371		—
Municipal bonds	Municipal bonds	382,722		—		382,722		—		Municipal bonds	407,724		—		407,724		—
Commercial mortgage backed securities	Commercial mortgage backed securities	579,424		—		579,424		—		Commercial mortgage backed securities	1,064,238		—		1,064,238		—
U.S. government and government agencies	U.S. government and government agencies	4,460,515		4,431,935		28,580		—		U.S. government and government agencies	5,126,407		5,100,908		25,499		—
Non-U.S. government securities	Non-U.S. government securities	1,863,734		—		1,863,734		—		Non-U.S. government securities	2,073,170		—		2,073,170		—
Asset backed securities	Asset backed securities	2,672,554		—		2,669,110		3,444		Asset backed securities	1,589,548		—		1,589,548		—
Total	Total	16,768,363		4,431,935		12,332,971		3,457		Total	18,120,727		5,100,908		13,019,806		13

Short-term investments	Short-term investments	3,069,965		2,046,391		1,023,574		—		Short-term investments	1,940,857		1,873,480		67,377		—

Equity securities, at fair value	Equity securities, at fair value	1,790,640		1,756,462		31,596		2,582		Equity securities, at fair value	809,869		775,264		31,566		3,039

Derivative instruments ~~(4)~~(2)	Derivative instruments ~~(4)~~(2)	89,958		—		89,958		—		Derivative instruments ~~(4)~~(2)	176,160		—		176,160		—

Residential mortgage loans	Residential mortgage loans	7,701		—		7,701		—		Residential mortgage loans	2,255		—		2,255		—

Fair value option:	Fair value option:									Fair value option:
Corporate bonds	Corporate bonds	374,326		—		374,326		—		Corporate bonds	524,177		—		524,177		—
Non-U.S. government bonds	Non-U.S. government bonds	19,829		—		19,829		—		Non-U.S. government bonds	4,032		—		4,032		—
Mortgage backed securities		—		—		—		—

Commercial mortgage backed securities		—		—		—		—

Asset backed securities	Asset backed securities	19,852		—		19,852		—		Asset backed securities	2,094		—		2,094		—
U.S. government and government agencies		—		—		—		—

Short-term investments	Short-term investments	115,681		1,190		114,491		—		Short-term investments	28,614		405		28,209		—
Equity securities	Equity securities	24,522		19,987		—		4,535		Equity securities	13,905		9,312		1		4,592
Other investments	Other investments	359,011		17,861		311,393		29,757		Other investments	175,259		—		141,021		34,238
Other investments measured at net asset value ~~(2)~~(1)	Other investments measured at net asset value ~~(2)~~(1)	1,130,748								Other investments measured at net asset value ~~(2)~~(1)	830,670
Total	Total	2,043,969		39,038		839,891		34,292		Total	1,578,751		9,717		699,534		38,830

Total assets measured at fair value	Total assets measured at fair value	$	23,770,596	$	8,273,826	$	14,325,691	$	40,331	Total assets measured at fair value	$	22,628,619	$	7,759,369	$	13,996,698	$	41,882

Liabilities measured at fair value:	Liabilities measured at fair value:									Liabilities measured at fair value:
Contingent consideration liabilities		$	(17,811)	$	—	$	—	$	(17,811)
Securities sold but not yet purchased (3)		—		—		—		—
Other liabilities										Other liabilities	$	(13,421)	$	—	$	—	$	(13,421)

Derivative instruments ~~(4)~~(2)	Derivative instruments ~~(4)~~(2)	(43,526)		—		(43,526)		—		Derivative instruments ~~(4)~~(2)	(112,577)		—		(112,577)		—
Total liabilities measured at fair value	Total liabilities measured at fair value	$	(61,337)	$	—	$	(43,526)	$	(17,811)	Total liabilities measured at fair value	$	(125,998)	$	—	$	(112,577)	$	(13,421)

(1) In securities lending transactions, the Company receives collateral in excess of the fair value of the securities pledged. For purposes of this table, the Company has excluded the collateral received under securities lending, at fair value and included the securities pledged under securities lending, at fair value. See ~~note 8, “—Securities Lending Agreements.” In September 2021, the Company terminated its securities lending program and no longer enters into securities lending agreements with financial institutions.~~

~~(2)~~ In accordance with applicable accounting guidance, certain investments that are measured at fair value using the net asset value per share (or its equivalent) practical expedient have not been classified in the fair value hierarchy. The fair value amounts presented in this table are intended to permit reconciliation of the fair value hierarchy to the amounts presented in the consolidated balance sheets.

(3) Represents the Company’s obligations to deliver securities that it did not own at the time of sale. Such amounts are included in “other liabilities” on the Company’s consolidated balance sheets.

~~(4)~~(2) See note 109.


ARCH CAPITAL			33			~~2021~~2022 THIRD QUARTER FORM 10-Q

Table of Contents

ARCH CAPITAL GROUP LTD. AND SUBSIDIARIES

NOTES TO CONSOLIDATED FINANCIAL STATEMENTS (UNAUDITED)

The following table presents the Company’s financial assets and liabilities measured at fair value by level at December 31, ~~2020:~~2021:


				Estimated Fair Value Measurements Using:									Estimated Fair Value Measurements Using:
		Estimated Fair Value		Quoted Prices in Active Markets for Identical Assets (Level 1)		Significant Other Observable Inputs (Level 2)		Significant Unobservable Inputs (Level 3)			Estimated Fair Value		Quoted Prices in Active Markets for Identical Assets (Level 1)		Significant Other Observable Inputs (Level 2)		Significant Unobservable Inputs (Level 3)
Assets measured at fair value (1):
Assets measured at fair value:										Assets measured at fair value:
Available for sale securities:	Available for sale securities:									Available for sale securities:
Fixed maturities:	Fixed maturities:									Fixed maturities:
Corporate bonds	Corporate bonds	$	7,856,571	$	—	$	7,856,558	$	13	Corporate bonds	$	6,553,333	$	—	$	6,553,320	$	13
Mortgage backed securities		630,001		—		630,001		—
Residential mortgage backed securities										Residential mortgage backed securities	408,477		—		408,477		—
Municipal bonds	Municipal bonds	494,522		—		494,522		—		Municipal bonds	404,666		—		404,666		—
Commercial mortgage backed securities	Commercial mortgage backed securities	389,900		—		389,900		—		Commercial mortgage backed securities	1,046,484		—		1,046,484		—
U.S. government and government agencies	U.S. government and government agencies	5,557,077		5,463,356		93,721		—		U.S. government and government agencies	4,772,764		4,744,517		28,247		—
Non-U.S. government securities	Non-U.S. government securities	2,433,733		—		2,433,733		—		Non-U.S. government securities	2,120,294		—		2,120,294		—
Asset backed securities	Asset backed securities	1,634,804		—		1,631,378		3,426		Asset backed securities	2,692,091		—		2,688,744		3,347
Total	Total	18,996,608		5,463,356		13,529,813		3,439		Total	17,998,109		4,744,517		13,250,232		3,360

Short-term investments	Short-term investments	1,924,922		1,920,565		4,357		—		Short-term investments	1,734,716		1,052,822		681,894		—

Equity securities, at fair value	Equity securities, at fair value	1,460,959		1,401,653		17,291		42,015		Equity securities, at fair value	1,804,170		1,762,864		38,388		2,918

Derivative instruments ~~(4)~~(2)	Derivative instruments ~~(4)~~(2)	177,383		—		177,383		—		Derivative instruments ~~(4)~~(2)	127,121		—		127,121		—

Residential mortgage loans										Residential mortgage loans	49,847		—		49,847		—

Fair value option:	Fair value option:									Fair value option:
Corporate bonds	Corporate bonds	651,294		—		650,309		985		Corporate bonds	388,546		—		388,546		—
Non-U.S. government bonds	Non-U.S. government bonds	35,263		—		35,263		—		Non-U.S. government bonds	23,785		—		23,785		—
Mortgage backed securities		3,282		—		3,282		—

Commercial mortgage backed securities		1,090		—		1,090		—

Asset backed securities	Asset backed securities	152,151		—		152,151		—		Asset backed securities	4,367		—		4,367		—
U.S. government and government agencies		274		164		110		—

Short-term investments	Short-term investments	557,008		420,131		136,877		—		Short-term investments	97,806		528		97,278		—
Equity securities	Equity securities	92,549		23,373		188		68,988		Equity securities	26,493		21,745		—		4,748
Other investments	Other investments	1,134,229		51,149		1,015,977		67,103		Other investments	310,798		20,352		262,465		27,981
Other investments measured at net asset value (2)		1,197,656
Other investments measured at net asset value (1)										Other investments measured at net asset value (1)	1,121,755
Total	Total	3,824,796		494,817		1,995,247		137,076		Total	1,973,550		42,625		776,441		32,729

Total assets measured at fair value	Total assets measured at fair value	$	26,384,668	$	9,280,391	$	15,724,091	$	182,530	Total assets measured at fair value	$	23,687,513	$	7,602,828	$	14,923,923	$	39,007

Liabilities measured at fair value:	Liabilities measured at fair value:									Liabilities measured at fair value:
Contingent consideration liabilities		$	(461)	$	—	$	—	$	(461)
Securities sold but not yet purchased (3)		(21,679)		—		(21,679)		—
Derivative instruments (4)		(108,705)		—		(108,705)		—
Other liabilities										Other liabilities	$	(16,960)	$	—	$	—	$	(16,960)

Derivative instruments (2)										Derivative instruments (2)	(54,224)		—		(54,224)		—
Total liabilities measured at fair value	Total liabilities measured at fair value	$	(130,845)	$	—	$	(130,384)	$	(461)	Total liabilities measured at fair value	$	(71,184)	$	—	$	(54,224)	$	(16,960)

~~(4)~~(2) See note 109.


ARCH CAPITAL			34			~~2021~~2022 THIRD QUARTER FORM 10-Q

Table of Contents

ARCH CAPITAL GROUP LTD. AND SUBSIDIARIES

NOTES TO CONSOLIDATED FINANCIAL STATEMENTS (UNAUDITED)

The following table presents a reconciliation of the beginning and ending balances for all financial assets and liabilities measured at fair value on a recurring basis using Level 3 inputs:


		Assets												Liabilities			Assets												Liabilities
s	s	Available For Sale				Fair Value Option						Fair Value				s	Available For Sale				Fair Value Option						Fair Value
																	Structured Securities (1)		Corporate Bonds		Corporate Bonds		Other Investments		Equity Securities		Equity Securities		Other Liabilities
Three Months Ended September 30, 2022																Three Months Ended September 30, 2022
Balance at beginning of period																Balance at beginning of period	$	2,867	$	3,570	$	—	$	33,331	$	4,392	$	2,906	$	(16,205)
Total gains or (losses) (realized/unrealized)																Total gains or (losses) (realized/unrealized)
Included in earnings (2)																Included in earnings (2)	(601)		52		—		116		200		133		(89)
Included in other comprehensive income																Included in other comprehensive income	144		(59)		—		—		—		—		965
Purchases, issuances, sales and settlements																Purchases, issuances, sales and settlements
Purchases																Purchases	—		—		—		1,458		—		—		—
Issuances																Issuances	—		—		—		—		—		—		—
Sales ~~(3)~~																Sales ~~(3)~~	(2,051)		(3,550)		—		(667)		—		—		—
Settlements																Settlements	(359)		—		—		—		—		—		1,908
Transfers in and/or out of Level 3																Transfers in and/or out of Level 3	—		—		—		—		—		—		—
Balance at end of period																Balance at end of period	$	—	$	13	$	—	$	34,238	$	4,592	$	3,039	$	(13,421)
		Structured Securities (1)		Corporate Bonds		Corporate Bonds		Other Investments		Equity Securities		Equity Securities		Contingent Consideration Liabilities
Three Months Ended September 30, 2021	Three Months Ended September 30, 2021															Three Months Ended September 30, 2021
Balance at beginning of period	Balance at beginning of period	$	3,424	$	13	$	998	$	73,900	$	73,678	$	49,136	$	(466)	Balance at beginning of period	$	3,424	$	13	$	998	$	73,900	$	73,678	$	49,136	$	(466)
Total gains or (losses) (realized/unrealized)	Total gains or (losses) (realized/unrealized)															Total gains or (losses) (realized/unrealized)
Included in earnings (2)	Included in earnings (2)	10		—		—		—		38		11		—		Included in earnings (2)	10		—		—		—		38		11		—
Included in other comprehensive income	Included in other comprehensive income	10		—		—		—		—		—		—		Included in other comprehensive income	10		—		—		—		—		—		—
Purchases, issuances, sales and settlements	Purchases, issuances, sales and settlements															Purchases, issuances, sales and settlements
Purchases	Purchases	—		—		—		—		—		208		(17,345)		Purchases	—		—		—		—		—		208		(17,345)
Issuances	Issuances	—		—		—		—		—		—		—		Issuances	—		—		—		—		—		—		—
Sales ~~(3)~~	Sales ~~(3)~~	—		—		(998)		(44,143)		(69,181)		(46,773)		—		Sales (3)	—		—		(998)		(44,143)		(69,181)		(46,773)		—
Settlements	Settlements	—		—		—		—		—		—		—		Settlements	—		—		—		—		—		—		—
Transfers in and/or out of Level 3	Transfers in and/or out of Level 3	—		—		—		—		—		—		—		Transfers in and/or out of Level 3	—		—		—		—		—		—		—
Balance at end of period	Balance at end of period	$	3,444	$	13	$	—	$	29,757	$	4,535	$	2,582	$	(17,811)	Balance at end of period	$	3,444	$	13	$	—	$	29,757	$	4,535	$	2,582	$	(17,811)

Three Months Ended September 30, 2020
Balance at beginning of period		$	3,450	$	857	$	998	$	46,453	$	61,447	$	51,981	$	(1,250)
Nine Months Ended September 30, 2022																Nine Months Ended September 30, 2022
Balance at beginning of year																Balance at beginning of year	$	3,347	$	13	$	—	$	27,981	$	4,748	$	2,918	$	(16,960)
Total gains or (losses) (realized/unrealized)	Total gains or (losses) (realized/unrealized)															Total gains or (losses) (realized/unrealized)
Included in earnings (2)	Included in earnings (2)	(75)		(5,872)		(34)		885		2,076		(946)		—		Included in earnings (2)	(592)		52		—		150		(156)		(103)		(284)
Included in other comprehensive income	Included in other comprehensive income	191		6,936		—		—		—		—		—		Included in other comprehensive income	(1)		(59)		—		—		—		—		1,915
Purchases, issuances, sales and settlements	Purchases, issuances, sales and settlements															Purchases, issuances, sales and settlements
Purchases	Purchases	—		—		—		22,436		—		—		—		Purchases	—		—		—		12,228		—		227		—
Issuances	Issuances	—		—		—		—		—		—		—		Issuances	—		—		—		—		—		—		—
Sales		—		—		—		(3,588)		—		(8,349)		—
Sales ~~(3)~~																Sales ~~(3)~~	(2,051)		(3,550)		—		(3,138)		—		(3)		—
Settlements	Settlements	(11)		—		—		—		—		—		620		Settlements	(703)		—		—		(2,983)		—		—		1,908
Transfers in and/or out of Level 3	Transfers in and/or out of Level 3	—		(1,908)		—		—		—		—		—		Transfers in and/or out of Level 3	—		3,557		—		—		—		—		—
Balance at end of period	Balance at end of period	$	3,555	$	13	$	964	$	66,186	$	63,523	$	42,686	$	(630)	Balance at end of period	$	—	$	13	$	—	$	34,238	$	4,592	$	3,039	$	(13,421)

Nine Months Ended September 30, 2021	Nine Months Ended September 30, 2021															Nine Months Ended September 30, 2021
Balance at beginning of year	Balance at beginning of year	$	3,426	$	13	$	985	$	67,103	$	68,988	$	42,015	$	(461)	Balance at beginning of year	$	3,426	$	13	$	985	$	67,103	$	68,988	$	42,015	$	(461)
Total gains or (losses) (realized/unrealized)	Total gains or (losses) (realized/unrealized)															Total gains or (losses) (realized/unrealized)
Included in earnings (2)	Included in earnings (2)	(46)		—		13		881		4,728		1,837		—		Included in earnings (2)	(46)		—		13		881		4,728		1,837		—
Included in other comprehensive income	Included in other comprehensive income	67		—		—		—		—		—		—		Included in other comprehensive income	67		—		—		—		—		—		—
Purchases, issuances, sales and settlements	Purchases, issuances, sales and settlements															Purchases, issuances, sales and settlements
Purchases	Purchases	—		—		—		13,003		—		5,503		(17,345)		Purchases	—		—		—		13,003		—		5,503		(17,345)
Issuances	Issuances	—		—		—		—		—		—		—		Issuances	—		—		—		—		—		—		—
Sales ~~(3)~~	Sales ~~(3)~~	—		—		(998)		(51,230)		(69,181)		(46,773)		—		Sales (3)	—		—		(998)		(51,230)		(69,181)		(46,773)		—
Settlements	Settlements	(3)		—		—		—		—		—		(5)		Settlements	(3)		—		—		—		—		—		(5)
Transfers in and/or out of Level 3	Transfers in and/or out of Level 3	—		—		—		—		—		—		—		Transfers in and/or out of Level 3	—		—		—		—		—		—		—
Balance at end of period	Balance at end of period	$	3,444	$	13	$	—	$	29,757	$	4,535	$	2,582	$	(17,811)	Balance at end of period	$	3,444	$	13	$	—	$	29,757	$	4,535	$	2,582	$	(17,811)

Nine Months Ended September 30, 2020
Balance at beginning of year		$	5,216	$	8,851	$	932	$	68,817	$	58,094	$	55,889	$	(7,998)
Total gains or (losses) (realized/unrealized)
Included in earnings (2)		(130)		(5,865)		(34)		(129)		5,429		7,132		(72)
Included in other comprehensive income		(118)		397		—		—		—		—		—
Purchases, issuances, sales and settlements
Purchases		—		—		66		22,460		—		3,464		—
Issuances		—		—		—		—		—		—		—
Sales		—		—		—		(27,946)		—		(23,799)		—
Settlements		(1,413)		(1,462)		—		—		—		—		7,440
Transfers in and/or out of Level 3		—		(1,908)		—		2,984		—		—		—
Balance at end of period		$	3,555	$	13	$	964	$	66,186	$	63,523	$	42,686	$	(630)

(1) Includes asset backed securities, residential mortgage backed securities and commercial mortgage backed securities.

(2) Gains or losses were included in net realized gains (losses).

(3) Sales for the 2021 periods primarily related to the Company’s deconsolidation of ~~Watford.~~Somers..


ARCH CAPITAL			35			~~2021~~2022 THIRD QUARTER FORM 10-Q

Table of Contents

ARCH CAPITAL GROUP LTD. AND SUBSIDIARIES

NOTES TO CONSOLIDATED FINANCIAL STATEMENTS (UNAUDITED)

Financial Instruments Disclosed, But Not Carried, At Fair Value

The Company uses various financial instruments in the normal course of its business. The carrying values of cash, accrued investment income, receivable for securities sold, certain other assets, payable for securities purchased and certain other liabilities approximated their fair values at September 30, ~~2021,~~2022, due to their respective short maturities. As these financial instruments are not actively traded, their respective fair values are classified within Level 2.

At September 30, 2022, the Company’s senior notes were carried at their cost, net of debt issuance costs, of $2.7 billion and had a fair value of $2.3 billion. At December 31, 2021, the Company’s senior notes were carried at their cost, net of debt issuance costs, of $2.7 billion and had a fair value of $3.3 ~~billion. At December 31, 2020, the Company’s senior notes were carried at their cost, net of debt issuance costs, of $2.9 billion and had a fair value of $3.7~~ billion. The fair values of the senior notes were obtained from a third party pricing service and are based on observable market inputs. As such, the fair values of the senior notes are classified within Level 2.

~~10.~~9. Derivative Instruments

The Company’s investment strategy allows for the use of derivative instruments. The Company’s derivative instruments are recorded on its consolidated balance sheets at fair value. The Company utilizes exchange traded U.S. Treasury note, Eurodollar and other futures contracts and commodity futures to manage portfolio duration or replicate investment positions in its portfolios and the Company routinely utilizes foreign currency forward contracts, currency options, index futures contracts and other derivatives as part of its total return objective. In addition, certain of the Company’s investments are managed in portfolios which incorporate the use of foreign currency forward contracts which are intended to provide an economic hedge against foreign currency movements.

In addition, the Company purchases to-be-announced mortgage backed securities (“TBAs”) as part of its investment strategy. TBAs represent commitments to purchase a future issuance of agency mortgage backed securities. For the period between purchase of a TBA and issuance of the underlying security, the Company’s position is accounted for as a derivative. The Company purchases TBAs in both long and short positions to enhance investment performance and as part of its overall investment strategy.

The following table summarizes information on the fair values and notional values of the Company’s derivative instruments:


		Estimated Fair Value							Estimated Fair Value
		Asset Derivatives		Liability Derivatives		Notional Value (1)			Asset Derivatives (1)		Liability Derivatives (1)		Notional Value (2)
September 30, 2021
September 30, 2022								September 30, 2022
Futures contracts ~~(2)~~	Futures contracts ~~(2)~~	$	36,010	$	(17,562)	$	2,796,442	Futures contracts ~~(2)~~	$	72,730	$	(60,684)	$	2,189,945
Foreign currency forward contracts ~~(2)~~	Foreign currency forward contracts ~~(2)~~	7,380		(13,914)		1,234,665		Foreign currency forward contracts ~~(2)~~	25,281		(26,995)		835,941
TBAs ~~(3)~~	TBAs ~~(3)~~	49,227		—		47,603		TBAs ~~(3)~~	—		—		—
Other ~~(2)~~	Other ~~(2)~~	46,568		(12,050)		4,184,225		Other ~~(2)~~	78,149		(24,898)		3,766,549
Total	Total	$	139,185	$	(43,526)			Total	$	176,160	$	(112,577)

December 31, 2020
December 31, 2021								December 31, 2021
Futures contracts ~~(2)~~	Futures contracts ~~(2)~~	$	11,046	$	(4,496)	$	3,099,796	Futures contracts ~~(2)~~	$	34,999	$	(9,808)	$	2,826,564
Foreign currency forward contracts ~~(2)~~	Foreign currency forward contracts ~~(2)~~	52,716		(6,202)		1,656,729		Foreign currency forward contracts ~~(2)~~	7,734		(11,390)		915,962
TBAs ~~(3)~~	TBAs ~~(3)~~	—		—		—		TBAs ~~(3)~~	11,227		—		11,227
Other ~~(2)~~	Other ~~(2)~~	113,621		(98,007)		5,763,919		Other ~~(2)~~	73,161		(33,026)		3,736,773
Total	Total	$	177,383	$	(108,705)			Total	$	127,121	$	(54,224)

(1) The fair value of asset derivatives are included in ‘other assets’ and the fair value of liability derivatives are included in ‘other liabilities.’

(2) Represents the absolute notional value of all outstanding contracts, consisting of long and short positions.

~~(2) The fair value of asset derivatives are included in ‘other assets’ and the fair value of liability derivatives are included in ‘other liabilities.’~~

~~(3) The fair value of TBAs are included in ‘fixed maturities available for~~

~~sale, at fair value.’~~

The Company did not hold any derivatives which were designated as hedging instruments at September 30, ~~2021~~2022 or December 31, ~~2020.~~2021.

The Company’s derivative instruments can be traded under master netting agreements, which establish terms that apply to all derivative transactions with a counterparty. In the event of a bankruptcy or other stipulated event of default, such agreements provide that the non-defaulting party may elect to terminate all outstanding derivative transactions, in which case all individual derivative positions (loss or gain) with a counterparty are closed out and netted and replaced with a single amount, usually referred to as the termination amount, which is expressed in a single currency. The resulting single net amount, where positive, is payable to the party “in-the-money” regardless of whether or not it is the defaulting party, unless the parties have agreed that only the non-defaulting party is entitled to receive a termination payment where the net amount is positive and is in its favor. Contractual close-out netting reduces derivatives credit exposure from gross to net exposure.

At September 30, ~~2021,~~2022, asset derivatives and liability derivatives of ~~$133.1~~$164.9 million and ~~$42.2~~$112.6 million, respectively, were subject to a master netting agreement, compared to ~~$138.8~~$122.3 million and ~~$93.0~~$53.9 million, respectively, at December 31, ~~2020.~~2021. The remaining derivatives included in the preceding table were not subject to a master netting agreement.


ARCH CAPITAL			36			~~2021~~2022 THIRD QUARTER FORM 10-Q

Table of Contents

ARCH CAPITAL GROUP LTD. AND SUBSIDIARIES

NOTES TO CONSOLIDATED FINANCIAL STATEMENTS (UNAUDITED)

Realized and unrealized contract gains and losses on the Company’s derivative instruments are reflected in ‘net realized gains (losses)’ in the consolidated statements of income, as summarized in the following table:


Derivatives not designated as	Derivatives not designated as	September 30,				Derivatives not designated as	September 30,
hedging instruments:	hedging instruments:	2021		2020		hedging instruments:	2022		2021

Three Months Ended	Three Months Ended					Three Months Ended
Net realized gains (losses):	Net realized gains (losses):					Net realized gains (losses):
Futures contracts	Futures contracts	$	(10,073)	$	10,945	Futures contracts	$	(26,347)	$	(10,073)
Foreign currency forward contracts	Foreign currency forward contracts	(16,146)		10,813		Foreign currency forward contracts	(18,340)		(16,146)
TBAs	TBAs	(46)		120		TBAs	—		(46)
Other (1)	Other (1)	4,830		(1,509)		Other (1)	(3,509)		4,830
Total	Total	$	(21,435)	$	20,369	Total	$	(48,196)	$	(21,435)

Nine Months Ended	Nine Months Ended					Nine Months Ended
Net realized gains (losses):	Net realized gains (losses):					Net realized gains (losses):
Futures contracts	Futures contracts	$	(17,394)	$	105,282	Futures contracts	$	(112,326)	$	(17,394)
Foreign currency forward contracts	Foreign currency forward contracts	(36,922)		3,466		Foreign currency forward contracts	(46,016)		(36,922)
TBAs	TBAs	(46)		1,129		TBAs	(51)		(46)
Other (1)	Other (1)	17,934		36,845		Other (1)	40,802		17,934
Total	Total	$	(36,428)	$	146,722	Total	$	(117,591)	$	(36,428)

(1) Includes realized gains and losses on swaps, options and other derivatives contracts.

~~11.~~10. Commitments and Contingencies

Letter of Credit and Revolving Credit Facilities

In the normal course of its operations, the Company enters into agreements with financial institutions to obtain secured and unsecured credit facilities. On April 7, 2022, Arch Capital and certain of its subsidiaries amended the existing five-year credit agreement into a $925.0 million facility (the “Credit Facility”) with a syndication of lenders. The Credit Facility, as amended, consists of a $425.0 million secured facility for letters of credit (the “Secured Facility”) and a $500.0 million unsecured facility for revolving loans and letters of credit (the “Unsecured Facility”). Obligations of each borrower under the Secured Facility for letters of credit are secured by cash and eligible securities of such borrower held in collateral accounts. Commitments under the Credit Facility may be increased up to, but not exceeding, an aggregate of $1.3 billion. Arch Capital has a one-time option to convert any or all outstanding revolving loans of Arch Capital and/or Arch-U.S. to term loans with the same terms as the revolving loans except that any prepayments may not be re-borrowed. Arch-U.S. guarantees the obligations of Arch Capital, and Arch Capital guarantees the obligations of Arch-U.S. Borrowings of revolving loans may be made at a variable rate based on SOFR. Secured letters of credit are available for issuance on behalf of certain Arch Capital subsidiaries. At September 30, 2022, the $425.0 million secured letter of credit facility, had $311.8 million of letters of credit outstanding and remaining capacity of

$113.2 million. In addition, certain of Arch Capital’s subsidiaries had outstanding secured and unsecured letters of credit through other facilities of $22.7 million and $290.0 million respectively, which were issued in the normal course of business.

Investment Commitments

The Company’s investment commitments, which are primarily related to agreements entered into by the Company to invest in funds and separately managed accounts when called upon, were approximately ~~$2.6~~$3.1 billion at September 30, ~~2021,~~2022, compared to ~~$2.1~~$3.0 billion at December 31, ~~2020.~~2021.

Interest Paid

Interest paid on the Company’s senior notes and other borrowings were ~~$75.8~~$65.0 million for the nine months ended September 30, ~~2021,~~2022, compared to ~~$60.6~~$75.8 million for the ~~2020~~2021 period.

~~12.~~11. Variable Interest Entities and Noncontrolling Interests

~~Watford~~Somers

In March 2014, the Company invested $100.0 million and acquired approximately 11% of ~~Watford’s~~Somers’ outstanding common equity. ~~Watford~~Somers was considered a VIE and the Company concluded that it was the primary beneficiary of ~~Watford,~~Somers, through June 30, 2021. As such, the results of ~~Watford~~Somers were included in the Company’s consolidated

financial statements as of and for the periods ended June 30, 2021.

In the 2020 fourth quarter, Arch Capital, ~~Watford~~Somers and Greysbridge, a wholly-owned subsidiary of Arch Capital, entered into an Agreement and Plan of Merger (as amended, the “Merger Agreement”). The merger contemplated by the Merger Agreement and the related Greysbridge equity financing closed on July 1, 2021. ~~Effective~~In connection therewith and effective July 1, 2021, ~~Watford is~~Somers became wholly owned by Greysbridge, and Greysbridge is now owned 40% by the Company, 30% by certain investment funds managed by Kelso and 30% by certain investment funds managed by Warburg. Based on the governing documents of Greysbridge, the Company concluded that, while it retains significant influence over ~~Watford, Watford~~Somers, Somers no longer constitutes a variable interest entity. Accordingly, effective July 1, 2021, the Company no longer consolidates the results of ~~Watford~~Somers in its consolidated financial statements and footnotes. Beginning in the 2021 third quarter, the Company classifies its investment as ‘investments in operating affiliates’ on the Company’s balance sheets and is accounted for under the equity method.

~~The following table provides the carrying amount and balance sheet caption in which the assets and liabilities of Watford were reported at December 31, 2020:~~


	~~December 31,~~
	~~2020~~
~~Assets~~
~~Investments accounted for using the fair value option (1)~~	$	~~1,790,385~~
~~Fixed maturities available for sale, at fair value~~	~~655,249~~
~~Equity securities, at fair value~~	~~52,410~~
~~Cash~~	~~211,451~~
~~Accrued investment income~~	~~14,679~~
~~Premiums receivable~~	~~224,377~~
~~Reinsurance recoverable on unpaid and paid losses and loss adjustment expenses~~	~~286,590~~
~~Ceded unearned premiums~~	~~122,339~~
~~Deferred acquisition costs~~	~~53,705~~
~~Receivable for securities sold~~	~~37,423~~
~~Goodwill and intangible assets~~	~~7,650~~
~~Other assets~~	~~75,801~~
~~Total assets of consolidated VIE~~	$	~~3,532,059~~

~~Liabilities~~
~~Reserve for losses and loss adjustment expenses~~	$	~~1,519,583~~
~~Unearned premiums~~	~~407,714~~
~~Reinsurance balances payable~~	~~63,269~~
~~Revolving credit agreement borrowings~~	~~155,687~~
~~Senior notes~~	~~172,689~~
~~Payable for securities purchased~~	~~25,881~~
~~Other liabilities~~	~~193,494~~
~~Total liabilities of consolidated VIE~~	$	~~2,538,317~~

~~Redeemable noncontrolling interests~~	$	~~52,398~~

~~(1) Included in “other investments” on the Company’s balance sheet.~~


ARCH CAPITAL			37			~~2021~~2022 THIRD QUARTER FORM 10-Q

Table of Contents

ARCH CAPITAL GROUP LTD. AND SUBSIDIARIES

NOTES TO CONSOLIDATED FINANCIAL STATEMENTS (UNAUDITED)

Through June 30, 2021, ~~Watford~~Somers generated $47.0 million of cash provided by operating activities, $96.3 million of cash provided by investing activities and $2.0 million of cash used for financing activities, compared to $133.6 million of cash provided by operating activities, $242.0 million of cash provided by investing activities and $279.7 million of cash used for financing activities for the nine months ended September 30, 2020.

~~Non-redeemable noncontrolling interests~~

Through June 30, 2021, the Company accounted for the portion of Watford’s common equity attributable to third party investors in the shareholders’ equity section of its consolidated balance sheets. The portion of Watford’s income or loss attributable to third party investors was recorded in the consolidated statements of income in ‘net (income) loss attributable to noncontrolling interests.’

~~The following table sets forth activity in the non-redeemable noncontrolling interests:~~

September 30,
2021 2020
Three Months Ended
Balance, beginning of period $ 918,874 $ 679,089
Impact of deconsolidation of Watford (918,874) —
Additional paid in capital attributable to noncontrolling interests — 243
Amounts attributable to noncontrolling interests — 67,768
Other comprehensive income (loss) attributable to noncontrolling interests — 10,820
Balance, end of period $ — $ 757,920
Nine Months Ended
Balance, beginning of year $ 823,007 $ 762,777
Impact of deconsolidation of Watford (918,874)
Additional paid in capital attributable to noncontrolling interests 22,113 715
Repurchases attributable to non-redeemable noncontrolling interests (1) — (2,867)
Amounts attributable to noncontrolling interests 78,314 (578)
Other comprehensive income (loss) attributable to noncontrolling interests (4,560) (2,127)
Balance, end of period $ — $ 757,920

~~(1) During 2020, Watford’s board of directors authorized the investment in Watford’s common shares through a share repurchase program.~~

activities.

Redeemable noncontrolling interests

Through June 30, 2021, the Company accounted for redeemable noncontrolling interests in the mezzanine section of its consolidated balance sheets in accordance with applicable accounting guidance. Such redeemable noncontrolling interests primarily related to the Watford Preference Shares issued in late March 2014 with a par value of $0.01 per share and a liquidation preference of $25.00 per

share. The Watford Preference Shares were issued at a discounted amount of $24.50 per share. Through June 30, 2021 preferred dividends, including the accretion of the discount and issuance costs, were included in ‘net (income) loss attributable to noncontrolling interests’ in the Company’s consolidated statements of income.

The following table sets forth activity in the redeemable non-controlling interests:


		September 30,					September 30,
		2021		2020			2022		2021
Three Months Ended	Three Months Ended					Three Months Ended
Balance, beginning of period	Balance, beginning of period	$	57,533	$	55,986	Balance, beginning of period	$	8,459	$	57,533

Impact of deconsolidation of Watford		(48,919)		—
Accretion of preference share issuance costs		—		23
Impact of deconsolidation of Somers						Impact of deconsolidation of Somers	—		(48,919)

Other	Other	1,623		1,826		Other	449		1,623
Balance, end of period	Balance, end of period	$	10,237	$	57,835	Balance, end of period	$	8,908	$	10,237

Nine Months Ended	Nine Months Ended					Nine Months Ended
Balance, beginning of year	Balance, beginning of year	$	58,548	$	55,404	Balance, beginning of year	$	9,233	$	58,548

Impact of deconsolidation of Watford		(48,919)		—
Accretion of preference share issuance costs		—		70
Impact of deconsolidation of Somers						Impact of deconsolidation of Somers	—		(48,919)

Other	Other	608		2,361		Other	(325)		608
Balance, end of period	Balance, end of period	$	10,237	$	57,835	Balance, end of period	$	8,908	$	10,237

The portion of income or loss attributable to third party investors, recorded in the Company’s consolidated statements of income in ‘net (income) loss attributable to noncontrolling interests,’ are summarized in the table below:


		September 30,					September 30,
		2021		2020			2022		2021
Three Months Ended	Three Months Ended					Three Months Ended
Amounts attributable to non-redeemable noncontrolling interests	Amounts attributable to non-redeemable noncontrolling interests	$	—	$	(67,768)	Amounts attributable to non-redeemable noncontrolling interests	$	—	$	—
Amounts attributable to redeemable noncontrolling interests	Amounts attributable to redeemable noncontrolling interests	(1,473)		(1,875)		Amounts attributable to redeemable noncontrolling interests	(1,157)		(1,473)
Net (income) loss attributable to noncontrolling interests	Net (income) loss attributable to noncontrolling interests	$	(1,473)	$	(69,643)	Net (income) loss attributable to noncontrolling interests	$	(1,157)	$	(1,473)

Nine Months Ended	Nine Months Ended					Nine Months Ended
Amounts attributable to non-redeemable noncontrolling interests	Amounts attributable to non-redeemable noncontrolling interests	$	(78,314)	$	578	Amounts attributable to non-redeemable noncontrolling interests	$	—	$	(78,314)
Amounts attributable to redeemable noncontrolling interests	Amounts attributable to redeemable noncontrolling interests	(3,889)		(4,998)		Amounts attributable to redeemable noncontrolling interests	(2,390)		(3,889)
Net (income) loss attributable to noncontrolling interests	Net (income) loss attributable to noncontrolling interests	$	(82,203)	$	(4,420)	Net (income) loss attributable to noncontrolling interests	$	(2,390)	$	(82,203)


~~ARCH CAPITAL~~			38			~~2021 THIRD QUARTER FORM 10-Q~~

~~Table of Contents~~

~~ARCH CAPITAL GROUP LTD. AND SUBSIDIARIES~~

~~NOTES TO CONSOLIDATED FINANCIAL STATEMENTS (UNAUDITED)~~

Bellemeade Re

The Company has entered into aggregate excess of loss mortgage reinsurance agreements with various special purpose reinsurance companies domiciled in Bermuda (the “Bellemeade Agreements”). At the time the Bellemeade Agreements were entered into, the applicability of the accounting guidance that addresses VIEs was evaluated. As a result of the evaluation of the Bellemeade Agreements, the Company concluded that these entities are VIEs. However, given that the ceding insurers do not have the unilateral power to direct those activities that are significant to their economic performance, the Company does not consolidate such entities in its consolidated financial statements.

The following table presents the total assets of the Bellemeade entities, as well as the Company’s maximum exposure to loss associated with these VIEs, calculated as the maximum historical observable spread between the benchmark index for each respective transaction and short term invested trust asset yields. The benchmark index for agreements effective prior to 2021 is based on one-month LIBOR, while the 2021 and later agreements benchmark index is based on the Secured Overnight Financing Rate (“SOFR”). SOFR is a measure of the cost of borrowing cash overnight, collateralized by U.S. Treasury securities, and is based on directly observable U.S. Treasury-backed repurchase transactions.

September 30, 2021 December 31, 2020
Maximum Exposure to Loss Maximum Exposure to Loss
Bellemeade Entities (Issue Date) Total VIE Assets On-Balance Sheet (Asset) Liability Off-Balance Sheet Total Total VIE Assets On-Balance Sheet (Asset) Liability Off-Balance Sheet Total
Bellemeade 2017-1 Ltd. (Oct-17) $ 145,573 $ (214) $ 585 $ 371 $ 145,573 $ (245) $ 844 $ 599
Bellemeade 2018-1 Ltd. (Apr-18) 228,938 (764) 1,683 919 250,095 (903) 2,245 1,342
Bellemeade 2018-2 Ltd. (Aug-18) — — — — 108,395 (138) 280 142
Bellemeade 2018-3 Ltd. (Oct-18) 302,563 (1,049) 2,328 1,279 302,563 (1,320) 3,262 1,942
Bellemeade 2019-1 Ltd. (Mar-19) 210,529 (931) 8,142 7,211 219,256 (1,361) 8,461 7,100
Bellemeade 2019-2 Ltd. (Apr-19) 398,316 (787) 5,658 4,871 398,316 (730) 5,201 4,471
Bellemeade 2019-3 Ltd. (Jul-19) 491,634 (826) 3,971 3,145 528,084 (861) 5,079 4,218
Bellemeade 2019-4 Ltd. (Oct-19) 468,737 (682) 4,761 4,079 468,737 (890) 6,676 5,786
Bellemeade 2020-1 Ltd. (Jun-20) (1) — — — — 275,068 (178) 1,012 834
Bellemeade 2020-2 Ltd. (Sep-20) (2) 266,704 (279) 2,629 2,350 423,420 (556) 6,839 6,283
Bellemeade 2020-3 Ltd. (Nov-20) (3) 381,410 (395) 6,646 6,251 418,158 (631) 9,605 8,974
Bellemeade 2020-4 Ltd. (Dec-20) (4) 226,916 (100) 2,190 2,090 321,393 (156) 6,816 6,660
Bellemeade 2021-1 Ltd. (Mar-21) (5) 579,717 229 4,217 4,446 — — — —
Bellemeade 2021-2 Ltd. (Jun-21) (6) 522,807 906 5,090 5,996 — — — —
Bellemeade 2021-3 Ltd. (Sep-21) (7) 507,873 182 4,561 4,743 — — — —
Total $ 4,731,717 $ (4,710) $ 52,461 $ 47,751 $ 3,859,058 $ (7,969) $ 56,320 $ 48,351


			September 30, 2022										December 31, 2021
			Maximum Exposure to Loss										Maximum Exposure to Loss
Bellemeade Entities (Issue Date)	Total VIE Assets		On-Balance Sheet (Asset) Liability		Off-Balance Sheet		Total		Coverage Remaining from Reinsurers (1)		Total VIE Assets		On-Balance Sheet (Asset) Liability		Off-Balance Sheet		Total

2017-1 Ltd. (Oct-17)	$	46,772	$	(23)	$	88	$	65	$	—	$	108,368	$	(159)	$	424	$	265
2018-1 Ltd. (Apr-18)	103,131		(220)		644		424		—		181,136		(528)		1,268		740
2018-3 Ltd. (Oct-18)	217,701		(862)		2,107		1,245		—		302,563		(1,018)		2,496		1,478
2019-1 Ltd. (Mar-19)	119,193		(496)		2,704		2,208		—		181,324		(380)		5,807		5,427
2019-2 Ltd. (Apr-19)	347,050		(656)		4,308		3,652		—		398,316		(515)		3,998		3,483
2019-3 Ltd. (Jul-19)	257,663		(192)		1,492		1,300		—		409,859		(584)		3,190		2,606
2019-4 Ltd. (Oct-19)	283,684		(532)		3,663		3,131		—		411,954		(462)		4,759		4,297
2020-2 Ltd. (Sep-20)	122,897		(20)		595		575		153		217,766		(177)		1,984		1,807
2020-3 Ltd. (Nov-20)	268,385		(204)		2,845		2,641		8,569		348,818		(128)		5,793		5,665
2020-4 Ltd. (Dec-20)	107,396		10		707		717		4,795		176,826		(50)		1,630		1,580
2021-1 Ltd. (Mar-21)	497,069		(2,234)		936		(1,298)		43,198		568,986		(303)		3,283		2,980
2021-2 Ltd. (Jun-21)	471,039		(2,047)		984		(1,063)		80,268		522,807		281		4,124		4,405
2021-3 Ltd. (Sep-21)	498,309		(2,414)		991		(1,423)		129,127		507,873		(411)		3,446		3,035
2022-1 Ltd. (Jan-22)	283,500		(1,326)		627		(699)		33,260
2022-2 Ltd. (Sep-22)	201,005		—		744		744		126,160
Total	$	3,824,794	$	(11,216)	$	23,435	$	12,219	$	425,530	$	4,336,596	$	(4,434)	$	42,202	$	37,768

(1) ~~An additional $79 million capacity was provided directly to Arch MI U.S. by~~Coverage from a separate panel of reinsurers ~~and is not reflected in this table.~~

~~(2) An additional $26 million capacity was provided directly to Arch MI U.S. by a separate panel of reinsurers and is not reflected in this table.~~

~~(3) An additional $34 million capacity was provided directly to Arch MI U.S. by a separate panel of reinsurers and is not reflected in this table.~~

~~(4) An additional $16 million capacity was provided directly to Arch MI U.S. by a separate panel of reinsurers and is not reflected in this table.~~

~~(5) An additional $64 million capacity was provided directly to Arch MI U.S. by a separate panel of reinsurers and is not reflected in this table.~~

~~(6) An additional $93 million capacity was provided directly to Arch MI U.S. by a separate panel of reinsurers and is not reflected in this table.~~

~~(7) An additional $131 million capacity was provided directly to Arch MI U.S. by a separate panel of reinsurers and is not reflected in this table.~~remaining at September 30, 2022.


ARCH CAPITAL			3938			~~2021~~2022 THIRD QUARTER FORM 10-Q

Table of Contents

ARCH CAPITAL GROUP LTD. AND SUBSIDIARIES

NOTES TO CONSOLIDATED FINANCIAL STATEMENTS (UNAUDITED)

~~13.~~12. Other Comprehensive Income (Loss)

The following tables present details about amounts reclassified from accumulated other comprehensive income and the tax effects allocated to each component of other comprehensive income (loss):


			Amounts Reclassified from AOCI										Amounts Reclassified from AOCI
		Consolidated Statement of Income	Three Months Ended				Nine Months Ended					Consolidated Statement of Income	Three Months Ended				Nine Months Ended
Details About	Details About	Line Item That Includes	September 30,				September 30,				Details About	Line Item That Includes	September 30,				September 30,
AOCI Components	AOCI Components	Reclassification	2021		2020		2021		2020		AOCI Components	Reclassification	2022		2021		2022		2021

Unrealized appreciation on available-for-sale investments
Unrealized appreciation (decline) on available-for-sale investments											Unrealized appreciation (decline) on available-for-sale investments
		Net realized gains (losses)	$	68,373	$	87,871	$	135,291	$	416,432		Net realized gains (losses)	$	(55,940)	$	68,373	$	(186,570)	$	135,291
		Provision for credit losses	(457)		1,333		(1,208)		(4,762)			Provision for credit losses	8,652		(457)		(48,096)		(1,208)
		Other-than-temporary impairment losses	—		—		—		(533)
		Total before tax	67,916		89,204		134,083		411,137			Total before tax	(47,288)		67,916		(234,666)		134,083
		Income tax (expense) benefit	(5,262)		(9,401)		(13,579)		(42,714)			Income tax (expense) benefit	703		(5,262)		28,093		(13,579)
		Net of tax	$	62,654	$	79,803	$	120,504	$	368,423		Net of tax	$	(46,585)	$	62,654	$	(206,573)	$	120,504


									Before Tax Amount		Tax Expense (Benefit)		Net of Tax Amount
Three Months Ended September 30, 2022								Three Months Ended September 30, 2022
Unrealized appreciation (decline) in value of investments:								Unrealized appreciation (decline) in value of investments:
Unrealized holding gains (losses) arising during period								Unrealized holding gains (losses) arising during period	$	(671,907)	$	(62,148)	$	(609,759)

Less reclassification of net realized gains (losses) included in net income								Less reclassification of net realized gains (losses) included in net income	(47,288)		(703)		(46,585)
Foreign currency translation adjustments								Foreign currency translation adjustments	(70,388)		—		(70,388)
Other comprehensive income (loss)								Other comprehensive income (loss)	$	(695,007)	$	(61,445)	$	(633,562)
		Before Tax Amount		Tax Expense (Benefit)		Net of Tax Amount
Three Months Ended September 30, 2021	Three Months Ended September 30, 2021							Three Months Ended September 30, 2021
Unrealized appreciation (decline) in value of investments:	Unrealized appreciation (decline) in value of investments:							Unrealized appreciation (decline) in value of investments:
Unrealized holding gains (losses) arising during period	Unrealized holding gains (losses) arising during period	$	(104,607)	$	(8,684)	$	(95,923)	Unrealized holding gains (losses) arising during period	$	(104,607)	$	(8,684)	$	(95,923)

Less reclassification of net realized gains (losses) included in net income	Less reclassification of net realized gains (losses) included in net income	67,916		5,262		62,654		Less reclassification of net realized gains (losses) included in net income	67,916		5,262		62,654
Foreign currency translation adjustments	Foreign currency translation adjustments	(32,060)		(350)		(31,710)		Foreign currency translation adjustments	(32,060)		(350)		(31,710)
Other comprehensive income (loss)	Other comprehensive income (loss)	$	(204,583)	$	(14,296)	$	(190,287)	Other comprehensive income (loss)	$	(204,583)	$	(14,296)	$	(190,287)

Three Months Ended September 30, 2020
Nine Months Ended September 30, 2022								Nine Months Ended September 30, 2022
Unrealized appreciation (decline) in value of investments:	Unrealized appreciation (decline) in value of investments:							Unrealized appreciation (decline) in value of investments:
Unrealized holding gains (losses) arising during period	Unrealized holding gains (losses) arising during period	$	119,265	$	8,483	$	110,782	Unrealized holding gains (losses) arising during period	$	(2,132,845)	$	(240,726)	$	(1,892,119)

Less reclassification of net realized gains (losses) included in net income	Less reclassification of net realized gains (losses) included in net income	89,204		9,401		79,803		Less reclassification of net realized gains (losses) included in net income	(234,666)		(28,093)		(206,573)
Foreign currency translation adjustments	Foreign currency translation adjustments	16,918		209		16,709		Foreign currency translation adjustments	(141,515)		166		(141,681)
Other comprehensive income (loss)	Other comprehensive income (loss)	$	46,979	$	(709)	$	47,688	Other comprehensive income (loss)	$	(2,039,694)	$	(212,467)	$	(1,827,227)

Nine Months Ended September 30, 2021	Nine Months Ended September 30, 2021							Nine Months Ended September 30, 2021
Unrealized appreciation (decline) in value of investments:	Unrealized appreciation (decline) in value of investments:							Unrealized appreciation (decline) in value of investments:
Unrealized holding gains (losses) arising during period	Unrealized holding gains (losses) arising during period	$	(307,910)	$	(28,808)	$	(279,102)	Unrealized holding gains (losses) arising during period	$	(307,910)	$	(28,808)	$	(279,102)

Less reclassification of net realized gains (losses) included in net income	Less reclassification of net realized gains (losses) included in net income	134,083		13,579		120,504		Less reclassification of net realized gains (losses) included in net income	134,083		13,579		120,504
Foreign currency translation adjustments	Foreign currency translation adjustments	(54,083)		6		(54,089)		Foreign currency translation adjustments	(54,083)		6		(54,089)
Other comprehensive income (loss)	Other comprehensive income (loss)	$	(496,076)	$	(42,381)	$	(453,695)	Other comprehensive income (loss)	$	(496,076)	$	(42,381)	$	(453,695)

Nine Months Ended September 30, 2020
Unrealized appreciation (decline) in value of investments:
Unrealized holding gains (losses) arising during period		$	611,390	$	65,099	$	546,291

Less reclassification of net realized gains (losses) included in net income		411,137		42,714		368,423
Foreign currency translation adjustments		(5,911)		(182)		(5,729)
Other comprehensive income (loss)		$	194,342	$	22,203	$	172,139


ARCH CAPITAL			4039			~~2021~~2022 THIRD QUARTER FORM 10-Q

Table of Contents

ARCH CAPITAL GROUP LTD. AND SUBSIDIARIES

NOTES TO CONSOLIDATED FINANCIAL STATEMENTS (UNAUDITED)

~~14.~~13. Income Taxes

The Company’s income tax provision on income before income taxes, including income (loss) from operating affiliates, resulted in an effective tax rate of 3.0% for the nine months ended September 30, 2022, compared to 5.5% for the nine months ended September 30, ~~2021, compared to 8.2%~~2021. The effective tax rate for the nine months ended September 30, ~~2020. The effective tax rate for the~~2022 and 2021 ~~period~~periods included discrete income tax benefits of $36.5 million and $28.7 million, ~~which~~respectively. The discrete income tax benefits had the effect of decreasing the effective tax rate on net income available to Arch common shareholders by 5.7% and 1.7%., respectively. The discrete tax items in ~~the 2021 period~~both periods were primarily related to the ~~partial~~ release of a valuation allowance on certain U.K. deferred tax assets.

The Company’s effective tax rate, which is based upon the expected annual effective tax rate, may fluctuate from period to period based on the relative mix of income or loss reported by jurisdiction and the varying tax rates in each jurisdiction.

The Company had a net deferred tax asset of ~~$162.5~~$572.1 million at September 30, ~~2021,~~2022, compared to a net deferred tax asset of ~~$15.7~~$194.0 million at December 31, ~~2020.~~2021. The change is primarily a result of ~~mortgage contingency reserves activity, fixed asset capitalization and~~ market value fluctuations in the investment portfolio. In addition, the Company paid ~~$202.4~~$201.6 million and ~~$146.8~~$202.4 million of income taxes for the nine months ended September 30, ~~2021~~2022 and ~~2020,~~2021, respectively.

~~15.~~14. Legal Proceedings

The Company, in common with the insurance industry in general, is subject to litigation and arbitration in the normal course of its business. As of September 30, ~~2021,~~2022, the Company was not a party to any litigation or arbitration which is expected by management to have a material adverse effect on the Company’s results of operations and financial condition and liquidity.

~~16.~~

15. Transactions with Related Parties

In the 2021 first quarter, as part of the Company’s acquisition of Barbican, the Company entered into an agreement with Premia Managing Agency Limited for the reinsurance to close of Syndicate 1955’s 2018 underwriting year of account into Premia Syndicate 1884’s 2021 underwriting year of account. The reinsurance to close covers legacy business underwritten by Syndicate 1955 on the underwriting 2018 and prior years of account and under the agreement, approximately $380 million of net liabilities was transferred to Syndicate 1884, with an effective date of January 1, 2021. ~~Barbican recorded~~The Company had no reinsurance recoverable on unpaid and paid losses ~~and~~or funds held liability ~~of nil and $8.8 million, respectively,~~ at September 30, ~~2021, compared to~~

~~$199.8 million~~2022 and ~~$149.6 million, respectively, at~~ December 31, ~~2020.~~2021.

In July 2021, following consummation of the Merger Agreement and the related Greysbridge equity financing, pursuant to which ~~Watford is~~Somers became wholly owned by Greysbridge, and Greysbridge isbecame owned 40% by the Company, 30% by certain funds managed by Kelso and 30% by certain funds managed by Warburg, the Company entered into certain reinsurance transactions with ~~Watford.~~Somers. For the three and nine months ended September 30, ~~2021,~~2022, the Company ceded premiums written related to such transactions of ~~$316.2~~$236.5 million and $661.1 million, respectively (which includes reinsurance transactions in force as well as those entered into in conjunction with the Merger Agreement). For the three and nine months ended September 30, 2021, the Company ceded premiums written related to such transactions of $316.2 million. In addition, ~~Watford~~Somers paid certain acquisition costs and administrative fees to the Company. At September 30, ~~2021, the Company recorded a~~2022, reinsurance recoverable on unpaid and paid losses from ~~Watford of $874.9 million and~~Somers was $1.1 billion, with a reinsurance balance payable to ~~Watford~~Somers of ~~$281.2~~$408.0 million. At December 31, 2021, reinsurance recoverable on unpaid and paid losses from Somers was $902.8 million, with a reinsurance balance payable to Somers of $258.4 million. See note ~~12, “Variable Interest Entities and Noncontrolling Interests~~,”11 for information about ~~Watford.~~Somers.

The Company has a put/call option that was entered into in connection with the Greysbridge equity financing, whereby beginning January 1, 2024 the Company will have a call right (but not the obligation) and Warburg and Kelso will each have a put right (but not the obligation) to buy/sell one third of their initial shares annually at the tangible book value per share of Greysbridge for the most recently ended fiscal quarter.

As of September 30, ~~2021,~~2022, the Company owns $35.0 million in aggregate principal amount of ~~Watford~~Somers Group Holdings Ltd’s 6.5% senior notes, due July 2, ~~2029 and approximately 6.6% of Watford’s preference shares.~~

~~17. Subsequent Event~~

~~Share Repurchases~~

In October 2021, the Company announced that its Board of Directors has increased its share repurchase program to an aggregate of up to $1.5 billion, which may be effected from time to time in open market or privately negotiated transactions through December 31, 2022. The timing and amount of the repurchase transactions under this program will depend on a variety of factors, including market conditions and corporate and regulatory considerations.

From October 1 to October 13, 2021, the Company repurchased approximately 1.2 million common shares for an aggregate purchase price of $45.5 million. At October 27, 2021 approximately $1.5 billion of repurchases were available under the share repurchase program.2029.


ARCH CAPITAL			4140			~~2021~~2022 THIRD QUARTER FORM 10-Q

Table of Contents

ITEM 2. MANAGEMENT’S DISCUSSION AND ANALYSIS OF FINANCIAL CONDITION AND RESULTS OF OPERATIONS

The following is a discussion and analysis of our financial condition and results of operations. This should be read in conjunction with our consolidated financial statements included in Item 1 of this report and also our Management’s Discussion and Analysis of Financial Condition and Results of Operations contained in our Annual Report on Form 10-K for the year ended December 31, ~~2020~~2021 (“~~2020~~2021 Form 10-K”). In addition, readers should review “Risk Factors” set forth in Item 1A of Part I of our ~~2020~~2021 Form 10-K and “ITEM 1A—Risk Factors” of this Form 10-Q. Tabular amounts are in U.S. Dollars in thousands, except share amounts, unless otherwise noted.

Arch Capital Group Ltd. (“Arch Capital” and, together with its subsidiaries, “Arch”, “we”, “our” or “us”) is a publicly listed Bermuda exempted company with approximately ~~$16.1~~$14.5 billion in capital at September 30, ~~2021~~2022 and, through operations in Bermuda, the United States, Europe, Canada, Australia and Hong Kong, writes insurance, reinsurance and mortgage insurance on a worldwide basis.


		Page No.

Current Outlook		42
Financial Measures		42
Comments on Non-GAAP Measures		44
Results of Operations		46
	Insurance Segment	46
	Reinsurance Segment	49
	Mortgage Segment	51
	Corporate Segment	54
Critical Accounting Policies, Estimates and Recent Accounting Pronouncements		55
Financial Condition		55
Liquidity		61
Capital Resources and Other		61


ARCH CAPITAL			41			2022 THIRD QUARTER FORM 10-Q

Table of Contents

CURRENT OUTLOOK

As we approach the end of ~~2021,~~2022, we are cautiously optimistic regarding the opportunities ahead of us in the fourth quarter and into 2023. Our objective remains the same, to deliver long term value for our ~~three areas of~~shareholders. We are committed to agile cycle management predicated by a focus ~~during the year have remained constant. In our property~~on risk-adjusted returns, and ~~casualty segments of insurance and reinsurance, we continue~~this commitment has enabled us to accelerate our growth inthrough the deployment of meaningful capacity to our clients. We continue to execute our cycle management strategy by actively allocating capital to the sectors where rates allow for returns that are ~~substantially~~ higher than our cost of capital. ~~Our mortgage insurance segment has transitioned,~~

Inflation continues to be a focus for ~~the most part, from forbearance to recovery~~our industry. We proactively analyze available data and ~~is producing results~~we incorporate emerging trends into our pricing and reserving. We believe that ~~made~~this discipline, coupled with increases in future investment returns and prudent reserving, helps us somewhat mitigate inflation’s impact.

Hurricane Ian, alongside a ~~significant contribution to our underwriting income~~fair amount of other catastrophic activity in the third ~~quarter. We have also been keenly focused on actively managing our investments and capital to enhance our returns over~~quarter, served as a stark reminder of the ~~long run.~~

importance of insurance capacity. The ~~2021~~catastrophic activity in the third quarter ~~reflected the benefits of attractive pricing in almost~~has significantly increased pressure on property catastrophe markets, which could have a ripple effect across all ~~of our insurance markets.~~property and casualty lines. As a result, we ~~currently expect the next several quarters to~~ continue to show improved underwriting margins, partially due to the compounding of rate-on-rate increases and the rebalancing of our mix of business. We believe that this time-tested strategy of protecting capital through soft markets and increasing our writings in hard markets gives us the best chance to generate superior risk adjusted returns over time. As long as rate increases support returns above our required thresholds, we expect to continue to grow our writings.

The trajectory and market acceptance of rate increases reinforce why we remain optimistic that improved economics in the property casualty market will be sustainable for some time. The property casualty industry is facing many degrees

~~of uncertainty, including heightened catastrophe activity, rising inflation, COVID’s ongoing influence on the global economy and perennially low interest rates.~~

Rate improvements have enabled us to continue to expand writings in our property casualty ~~segments as we have been for two years now.~~segments. Rate increases remain ~~well~~ above the long-term loss cost trends and have spread to more lines than last year. ~~Overall, 2021 rates~~In insurance, underwriting conditions remain opportunistic as pricing discipline, terms and conditions, and limits management are ~~up around 10% compared~~stable across most lines. This stability, combined with the uncertainties in the insurance market, should keep the market disciplined and sustain rate increases. Our U.S. operations benefited from growth in professional liability, including cyber, as well as travel where we believe relative returns are attractive. Cyber insurance has become increasingly important to ~~2020~~our insureds globally, and we ~~currently expect~~have substantially increased our focus because we believe that today’s cyber market has changed for the ~~benefit~~better. Additionally, insurance terms and conditions have sufficiently tightened, retentions have increased and rates have reached a level where we have an opportunity to earn an appropriate return for the assumption of ~~higher premium levels will be reflected well into 2022 and beyond. Positive~~risk.

In reinsurance, the emphasis remains on quota share treaties over excess of loss reinsurance. This strategy allows us to participate in the rate increases ~~have accelerated in lower limit accounts which, until now, had lagged~~on primary insurance while improving the ~~increases in larger accounts. Our early focus on Lloyd’s~~balance between risk and business in the UK has improved our scale and our economics in this market. Some of our business lines that were most impacted by COVID, like travel, are recapturing some of the lost volume as both business and consumer travel increases.

In reinsurance, strong growth was observed across most of our lines of business, but especially in our casualty and other specialty lines where strong rates increases and growth in new accounts helped increase the top line. At less than 6% of our tangible equity, wereturn. We remained ~~underweight~~disciplined in property catastrophe exposure and we will deploy more capital to the line if expected returns improve ~~meaningfully above~~meaningfully. Excellent market conditions and the likelihood of capacity constraints will likely create an eventful January 1 renewal period, and our ~~target. Consistent with~~teams are actively planning to meet the demands of our ~~insurance segment,~~clients.

In mortgage, we ~~expect the ongoing rate improvements to be reflected in our underwriting results over the next several quarters.~~

~~For our U.S. primary mortgage operations, delinquencies~~ continue to be ~~better than~~thoughtful in how we manage our ~~expectations at~~portfolio and, because of our diversified model, we have the ~~beginning~~ability to take a measured view of the ~~COVID-19 pandemic,~~business as ~~notices~~just one component of default have declined to pre-pandemic levels at September 30, 2021, which is another indicator of improved conditions. Additionally, loans in forbearance continue to decline as federal programs conclude and we remain optimistic that most of these loans will ultimately cure.

~~In the 2021 third quarter, insurance in force for~~ our U.S. primary mortgage operations remained steady at $280.4 billion, while insurance in force for the total mortgage segment was $457.7 billion. Overall, the market remains competitive but rational and ourdiversified enterprise. Our mortgage business continues to ~~generate returns on capital in the mid teens. Mortgage originations continue at a pace similar to last year’s record~~deliver consistent underwriting results, once again demonstrating its sustainable earnings model. Although higher interest rates affected new loan origination volume, the persistency rate of our portfolio improved and U.S. primary mortgage insurance in force grew to nearly $295 billion. The credit quality of homebuyers remains ~~excellent. Outside~~excellent and we believe our portfolio is well positioned for a variety of ~~the U.S., we increased our writings in Australia as a result of the housing market remaining strong and due to our acquisition of Westpac’s LMI business.~~economic scenarios.


~~ARCH CAPITAL~~			42			~~2021 THIRD QUARTER FORM 10-Q~~

~~Table of Contents~~

We remain committed to providing solutions across many offerings as the marketplace evolves, including the mortgage credit risk transfer programs initiated by government sponsored enterprises, or ~~“GSEs.”~~(“GSEs”). In addition, we ~~enter~~have entered into aggregate excess of loss mortgage reinsurance agreements with various special purpose reinsurance companies domiciled in Bermuda and ~~issue~~have issued mortgage insurance linked notes, increasing our protection for mortgage tail risk. The Bellemeade structures ~~provide~~provided approximately ~~$5.1~~$4.3 billion of aggregate reinsurance coverage at September 30, ~~2021.~~2022.

FINANCIAL MEASURES

Management uses the following three key financial indicators in evaluating our performance and measuring the overall growth in value generated for Arch Capital’s common shareholders:

Book Value per Share

Book value per share represents total common shareholders’ equity available to Arch divided by the number of common shares outstanding. Management uses growth in book value per share as a key measure of the value generated for our common shareholders each period and believes that book value per share is the key driver of Arch Capital’s share price over time. Book value per share is impacted by, among other factors, our underwriting results, investment returns and share repurchase activity, which has an accretive or dilutive impact on book value per share depending on the purchase price.

Book value per share was ~~$32.43~~$29.69 at September 30, ~~2021,~~2022, compared to ~~$32.02~~$31.37 at June 30, ~~2021~~2022 and ~~$28.75~~$32.43 at


ARCH CAPITAL			42			2022 THIRD QUARTER FORM 10-Q

Table of Contents

September 30, ~~2020.~~2021. The ~~1.3% increase~~5.4% decrease in book value per share for the ~~2021~~2022 third quarter reflected ~~strong underwriting returns, which were impacted by a high level of losses from catastrophic events, along with flat~~negative total return on investments ~~for the period. The 12.8% increase in book value per share over the trailing twelve months~~driven by rising interest rates on fixed maturities, along with higher level of catastrophic loss activity, primarily ~~reflected strong underwriting results.~~related to Hurricane Ian.

Operating Return on Average Common Equity

Operating return on average common equity (“Operating ROAE”) represents annualized after-tax operating income available to Arch common shareholders divided by the average of beginning and ending common shareholders’ equity available to Arch during the period. After-tax operating income available to Arch common shareholders, a non-GAAP financial measure as defined in Regulation G, represents 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, loss on redemption of preferred shares and income taxes. Management uses Operating ROAE as a key measure of the return generated to common shareholders. See “Comment on Non-GAAP Financial Measures.”

Our ~~Operating ROAE~~annualized net income return on average common equity was ~~9.3%~~0.2% for the 2022 third quarter, compared to 12.3% for the 2021 third quarter, ~~compared to 4.2% for the 2020 third quarter,~~ and ~~10.1%~~6.6% for the nine months ended September 30, ~~2021,~~2022, compared to ~~3.9%~~15.9% for the ~~2020~~2021 period. ~~Results~~Our Operating ROAE was 3.8% for the 2022 third quarter, compared to 9.3% for the 2021 third quarter, and 11.6% for the nine months ended September 30, 2022, compared to 10.1% for the 2021 period. The 2022 periods reflected ~~a one-time gain~~increased levels of ~~$95.7 million recognized from the Company’s previously disclosed acquisition of a 40% share of Greysbridge. Returns for~~catastrophic activity, while the 2021 periods reflected ~~strong underwriting returns and~~higher income from operating ~~affiliates, while the 2020 period reflected the impact of COVID-19 on underwriting results.~~affiliates.

Total Return on Investments

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. In addition, total return incorporates the timing of investment returns during the periods. The following table summarizes our total return compared to the benchmark return against which we measured our portfolio during the periods. See “Comment on Non-GAAP Financial Measures.”

Arch
Portfolio Benchmark
Return
Pre-tax total return (before investment expenses):
2021 Third Quarter 0.01 % (0.40) %
2020 Third Quarter 2.30 % 2.41 %
Nine Months Ended September 30, 2021 1.50 % 0.87 %
Nine Months Ended September 30, 2020 5.19 % 3.67 %


	Arch Portfolio		Benchmark Return
Pre-tax total return (before investment expenses):
2022 Third Quarter	(3.01)	%	(4.01)	%
2021 Third Quarter	0.01	%	(0.40)	%

Nine Months Ended September 30, 2022	(8.83)	%	(12.78)	%
Nine Months Ended September 30, 2021	1.50	%	0.87	%

Total return for the ~~2021 third quarter~~2022 periods reflected ~~movements in~~rising interest rates on fixed maturities and ~~credit spreads on our fixed income portfolio.~~weak equity markets. We continue to maintain a relative short duration on our portfolio of ~~2.68~~2.84 years at September 30, ~~2021.~~2022.

The benchmark return index is a customized combination of indices intended to approximate a target portfolio by asset mix and average credit quality while also matching the approximate estimated duration and currency mix of our insurance and reinsurance liabilities. Although the estimated duration and average credit quality of this index will move as the duration and rating of its constituent securities change,


~~ARCH CAPITAL~~			43			~~2021 THIRD QUARTER FORM 10-Q~~

~~Table of Contents~~

generally we do not adjust the composition of the benchmark return index except to incorporate changes to the mix of liability currencies and durations noted above. The benchmark return index should not be interpreted as expressing a preference for or aversion to any particular sector or sector weight. The index is intended solely to provide, unlike many master indices that change based on the size of their constituent indices, a relatively stable basket of investable indices. At September 30, ~~2021,~~2022, the benchmark return index had an average credit quality of ~~“Aa2”~~“Aa3” by Moody’s Investors Service (“Moody’s”), and an estimated duration of ~~3.18~~3.15 years.


ARCH CAPITAL			43			2022 THIRD QUARTER FORM 10-Q

Table of Contents

The benchmark return index included weightings to the following indices:


	%
ICE BoAML 1-5 Year A - AAA U.S. Corporate Index	13.00	%
ICE BoAML 5-10 Year A - AAA U.S. Corporate Index	11.00
ICE BoAML 1-5 Year U.S. Treasury Index	11.00
MSCI ACWI Net Total Return USD Index	9.30
ICE BoAML 1-10 Year BBB U.S. Corporate Index	5.00
JPM CLOIE Investment Grade	5.00
S&P/LSTA Leveraged Loan Total Return Index	4.965
ICE BoAML U.S. Mortgage Backed Securities Index	4.00
ICE BoAML AAA US Fixed Rate CMBS	4.00
ICE BoAML 1-5 Year U.K. Gilt Index	4.00
ICE BoAML German Government 1-10 Year Index	3.50
ICE BoAML 0-3 Year U.S. Treasury Index	3.25
ICE BoAML 5-10 Year U.S. Treasury Index	3.00
ICE BoAML 1-10 Year U.S. Municipal Securities Index	3.00
Bloomberg Barclays ABS Aaa Index	3.00
ICE BoAML 1-5 Year Australia Government Index	2.75
ICE BoAML U.S. High Yield Constrained Index	2.50
ICE BoAML 1-5 Year Canada Government Index	2.00
ICE BofA CCC and Lower US High Yield Constrained Index	1.38
Bloomberg Barclays Global High Yield Index	1.38
S&P DJ Global ex-US Select Real Estate Securities Net Index	0.825
FTSE Nareit All Mortgage Capped Index Total Return USD	0.825
Bloomberg Barclays CMBS: Erisa Eligible Unhedged USD	0.825
ICE BoAML 15+ Year Canada Government Index	0.50
Total	100.00	%

COMMENT ON NON-GAAP FINANCIAL MEASURES

Throughout this filing, we present our operations in the way we believe will be the most meaningful and useful to investors, analysts, rating agencies and others who use our financial information in evaluating the performance of our 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, loss on redemption of preferred shares and 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 under “Results of Operations” below.

We believe 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 our business. 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 our 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 net impairment 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 our 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~~our investments represent other-than-temporary declines in expected recovery values on securities without actual realization. The use of the equity method on certain of our investments ~~in certain funds that invest in fixed maturity securities~~ is driven by the ownership structure of such funds


~~ARCH CAPITAL~~			44			~~2021 THIRD QUARTER FORM 10-Q~~

~~Table of Contents~~

~~(either~~ (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 our proportionate share of the net income or loss of the funds (which include changes in the market value of the underlying securities in the funds). This method of accounting is different from the way we account for our other ~~fixed maturity securities~~investments 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. We believe that transaction costs and other, due to their non-recurring nature, are not indicative of the performance of, or trends in, our business performance. The loss on redemption of preferred shares related to the redemption of ~~the Company's Series E~~some of Arch’s preferred shares ~~in September 2021 and~~ had no impact on shareholders' equity or cash flows. Due to these reasons, we exclude 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 available to Arch common shareholders.


ARCH CAPITAL			44			2022 THIRD QUARTER FORM 10-Q

Table of Contents

We believe that showing net income available to Arch common shareholders exclusive of the items referred to above reflects the underlying fundamentals of our business since we evaluate the performance of and manage our business to produce an underwriting profit. In addition to presenting net income available to Arch common shareholders, we believe that this presentation enables investors and other users of our financial information to analyze our performance in a manner similar to how management analyzes performance. We also believe that this measure follows industry practice and, therefore, allows the users of financial information to compare our performance with our industry peer group. We believe that the equity analysts and certain rating agencies which follow us and the insurance industry as a whole generally exclude these items from their analyses for the same reasons.

Our segment information includes the presentation of consolidated underwriting income or loss and a subtotal of underwriting income or loss before the contribution from the ‘other’ segment. The ‘other’ segment includes the results of Somers through June 30, 2021. Such measures represent the pre-tax profitability of our 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 our individual underwriting operations. Underwriting income or loss does not incorporate items included in our corporate

~~(non-underwriting)~~ segment. While these measures are presented in note 5,4, “Segment Information,” of the notes accompanying our 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 subtotal before the contribution from the ‘other’ segment through June 30, 2021, in accordance with Regulation G, is shown in note 5,4, “Segment Information” to our consolidated financial statements.

We measure segment performance for our three underwriting segments based on underwriting income or loss. We do not manage our assets by underwriting segment, with the exception of goodwill and intangibles and, accordingly, investment income and other non-underwriting related items are not allocated to each underwriting segment. The ‘other’ segment includes the results of ~~Watford~~Somers through June 30, 2021.

Along with consolidated underwriting income, we provide a subtotal of underwriting income or loss before the contribution from the ‘other’ segment. Through June 30, 2021, the ‘other’ segment included the results of ~~Watford~~Somers Group Holdings Ltd. ~~Watford~~Somers Group Holdings Ltd. is the parent of ~~Watford~~Somers Re Ltd., a multi-line Bermuda reinsurance

company (together with ~~Watford~~Somers Group Holdings Ltd., ~~“Watford”~~“Somers”). Pursuant to GAAP, ~~Watford~~Somers was considered a variable interest entity and we concluded that we were the primary beneficiary of ~~Watford.~~Somers. As such, we consolidated the results of ~~Watford~~Somers in our consolidated financial statements through June 30, 2021. In the 2020 fourth quarter, Arch Capital, ~~Watford,~~Somers, and Greysbridge Ltd., a wholly-owned subsidiary of Arch Capital, entered into an Agreement and Plan of Merger (as amended, the “Merger Agreement”). Arch Capital assigned its rights under the Merger Agreement to Greysbridge Holdings Ltd. (“Greysbridge”). The merger contemplated by the Merger Agreement and the related Greysbridge equity financing closed on July 1, 2021. ~~Effective~~In connection therewith and effective July 1, 2021, ~~Watford is~~Somers became wholly owned by Greysbridge, and Greysbridge isbecame owned 40% by Arch and 30% by certain funds managed by Kelso and 30% by certain funds managed by Warburg. 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 ~~Watford~~Somers in our consolidated financial statements and footnotes. See note ~~12,~~11, “Variable Interest Entities and Noncontrolling Interests” and note 5,4, “Segment Information,” to our consolidated financial statements for additional information on ~~Watford.~~

Somers.

Our presentation of segment information includes the use of a current year loss ratio which excludes favorable or adverse


~~ARCH CAPITAL~~			45			~~2021 THIRD QUARTER FORM 10-Q~~

~~Table of Contents~~

development in prior year loss reserves. This ratio is a non-GAAP financial measure as defined in Regulation G. The reconciliation of such measure to the loss ratio (the most directly comparable GAAP financial measure) in accordance with Regulation G is shown on the individual segment pages. Management utilizes the current year loss ratio in its analysis of the underwriting performance of each of our 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. In addition, total return incorporates the timing of investment returns during the periods. There is no directly comparable GAAP financial measure for total return. Management uses total return on investments as a key measure of the return generated to Arch common shareholders, and compares the return generated by our investment portfolio against benchmark returns during the periods.


ARCH CAPITAL			45			2022 THIRD QUARTER FORM 10-Q

Table of Contents

RESULTS OF OPERATIONS

The following table summarizes our 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.


		Three Months Ended				Nine Months Ended					Three Months Ended				Nine Months Ended
		September 30,				September 30,					September 30,				September 30,
		2021		2020		2021		2020			2022		2021		2022		2021
Net income available to Arch common shareholders	Net income available to Arch common shareholders	$	388,751	$	408,636	$	1,480,324	$	830,768	Net income available to Arch common shareholders	$	6,917	$	388,751	$	586,693	$	1,480,324
Net realized (gains) losses	Net realized (gains) losses	25,040		(219,726)		(247,949)		(517,007)		Net realized (gains) losses	183,674		25,040		742,667		(247,949)

Equity in net (income) loss of investment funds accounted for using the equity method	Equity in net (income) loss of investment funds accounted for using the equity method	(105,398)		(126,735)		(299,270)		(57,407)		Equity in net (income) loss of investment funds accounted for using the equity method	18,861		(105,398)		(75,505)		(299,270)
Net foreign exchange (gains) losses	Net foreign exchange (gains) losses	(36,078)		39,462		(39,522)		17,003		Net foreign exchange (gains) losses	(90,537)		(36,078)		(182,189)		(39,522)
Transaction costs and other	Transaction costs and other	1,036		1,674		889		5,246		Transaction costs and other	76		1,036		734		889
Loss on redemption of preferred shares	Loss on redemption of preferred shares	15,101		—		15,101		—		Loss on redemption of preferred shares	—		15,101		—		15,101
Income tax expense (1)		6,236		17,010		32,100		48,088
Income tax expense (benefit) (1)										Income tax expense (benefit) (1)	(13,019)		6,236		(37,933)		32,100
After-tax operating income available to Arch common shareholders	After-tax operating income available to Arch common shareholders	$	294,688	$	120,321	$	941,673	$	326,691	After-tax operating income available to Arch common shareholders	$	105,972	$	294,688	$	1,034,467	$	941,673

Beginning common shareholders’ equity	Beginning common shareholders’ equity	$	12,706,072	$	11,211,825	$	12,325,886	$	10,717,371	Beginning common shareholders’ equity	$	11,587,566	$	12,706,072	$	12,715,896	$	12,325,886
Ending common shareholders’ equity	Ending common shareholders’ equity	$	12,557,526	$	11,671,997	$	12,557,526	$	11,671,997	Ending common shareholders’ equity	$	10,965,110	$	12,557,526	$	10,965,110	$	12,557,526
Average common shareholders’ equity	Average common shareholders’ equity	$	12,631,799	$	11,441,911	$	12,441,706	$	11,194,684	Average common shareholders’ equity	$	11,276,338	$	12,631,799	$	11,840,503	$	12,441,706

Annualized net income return on average common equity %	Annualized net income return on average common equity %	12.3		14.3		15.9		9.9		Annualized net income return on average common equity %	0.2		12.3		6.6		15.9
Annualized operating return on average common equity %	Annualized operating return on average common equity %	9.3		4.2		10.1		3.9		Annualized operating return on average common equity %	3.8		9.3		11.6		10.1

(1) Income tax expense on 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 reflects the relative mix reported by jurisdiction and the varying tax rates in each jurisdiction.


~~ARCH CAPITAL~~			46			~~2021 THIRD QUARTER FORM 10-Q~~

~~Table of Contents~~

Segment Information

We classify our businesses into three underwriting segments — insurance, reinsurance and mortgage — and two other operating segments — corporate ~~(non-underwriting)~~ and ‘other.’ Our 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 our chief operating decision makers, the Chief Executive Officer of Arch Capital, the Chief Financial Officer and Treasurer of Arch Capital and the President and Chief Underwriting Officer of Arch Capital. 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 our three underwriting segments based on underwriting income or loss. We do not manage our assets by underwriting segment, with the exception of goodwill and intangible assets, and, accordingly, investment income is not allocated to each underwriting segment.

We determined our reportable 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 our consolidated financial statements. Intersegment business is allocated to the segment accountable for the underwriting results.

Insurance Segment

The following tables set forth our insurance segment’s underwriting results:


		Three Months Ended September 30,								Three Months Ended September 30,
		2021			2020			% Change		2022			2021			% Change
Gross premiums written	Gross premiums written	$	1,596,619		$	1,206,328		32.4	Gross premiums written	$	1,862,026		$	1,596,619		16.6
Premiums ceded	Premiums ceded	(442,806)			(382,167)				Premiums ceded	(493,267)			(442,806)
Net premiums written	Net premiums written	1,153,813			824,161			40.0	Net premiums written	1,368,759			1,153,813			18.6
Change in unearned premiums	Change in unearned premiums	(215,143)			(105,007)				Change in unearned premiums	(181,851)			(215,143)
Net premiums earned	Net premiums earned	938,670			719,154			30.5	Net premiums earned	1,186,908			938,670			26.4
Other underwriting income (loss)		—			(31)

Losses and loss adjustment expenses	Losses and loss adjustment expenses	(668,630)			(525,321)				Losses and loss adjustment expenses	(822,663)			(668,630)
Acquisition expenses	Acquisition expenses	(152,467)			(102,420)				Acquisition expenses	(232,469)			(152,467)
Other operating expenses	Other operating expenses	(138,931)			(122,541)				Other operating expenses	(165,499)			(138,931)
Underwriting income (loss)	Underwriting income (loss)	$	(21,358)		$	(31,159)		31.5	Underwriting income (loss)	$	(33,723)		$	(21,358)		(57.9)

Underwriting Ratios	Underwriting Ratios							% Point Change	Underwriting Ratios							% Point Change
Loss ratio	Loss ratio	71.2		%	73.0		%	(1.8)	Loss ratio	69.3		%	71.2		%	(1.9)
Acquisition expense ratio	Acquisition expense ratio	16.2		%	14.2		%	2.0	Acquisition expense ratio	19.6		%	16.2		%	3.4
Other operating expense ratio	Other operating expense ratio	14.8		%	17.0		%	(2.2)	Other operating expense ratio	13.9		%	14.8		%	(0.9)
Combined ratio	Combined ratio	102.2		%	104.2		%	(2.0)	Combined ratio	102.8		%	102.2		%	0.6


ARCH CAPITAL			46			2022 THIRD QUARTER FORM 10-Q

Table of Contents


		Nine Months Ended September 30,								Nine Months Ended September 30,
		2021			2020			% Change		2022			2021			% Change
Gross premiums written	Gross premiums written	$	4,381,372		$	3,444,335		27.2	Gross premiums written	$	5,286,798		$	4,381,372		20.7
Premiums ceded	Premiums ceded	(1,269,165)			(1,119,165)				Premiums ceded	(1,482,886)			(1,269,165)
Net premiums written	Net premiums written	3,112,207			2,325,170			33.8	Net premiums written	3,803,912			3,112,207			22.2
Change in unearned premiums	Change in unearned premiums	(488,636)			(202,188)				Change in unearned premiums	(488,164)			(488,636)
Net premiums earned	Net premiums earned	2,623,571			2,122,982			23.6	Net premiums earned	3,315,748			2,623,571			26.4
Other underwriting income		—			(31)

Losses and loss adjustment expenses	Losses and loss adjustment expenses	(1,750,257)			(1,550,632)				Losses and loss adjustment expenses	(2,053,161)			(1,750,257)
Acquisition expenses	Acquisition expenses	(417,541)			(317,428)				Acquisition expenses	(641,807)			(417,541)
Other operating expenses	Other operating expenses	(409,386)			(370,947)				Other operating expenses	(493,412)			(409,386)
Underwriting income (loss)	Underwriting income (loss)	$	46,387		$	(116,056)		140.0	Underwriting income (loss)	$	127,368		$	46,387		174.6

Underwriting Ratios	Underwriting Ratios							% Point Change	Underwriting Ratios							% Point Change
Loss ratio	Loss ratio	66.7		%	73.0		%	(6.3)	Loss ratio	61.9		%	66.7		%	(4.8)
Acquisition expense ratio	Acquisition expense ratio	15.9		%	15.0		%	0.9	Acquisition expense ratio	19.4		%	15.9		%	3.5
Other operating expense ratio	Other operating expense ratio	15.6		%	17.5		%	(1.9)	Other operating expense ratio	14.9		%	15.6		%	(0.7)
Combined ratio	Combined ratio	98.2		%	105.5		%	(7.3)	Combined ratio	96.2		%	98.2		%	(2.0)

The insurance segment consists of our 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


~~ARCH CAPITAL~~			47			~~2021 THIRD QUARTER FORM 10-Q~~

~~Table of Contents~~

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 standalone 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.

Premiums Written.

The following tables set forth our insurance segment’s net premiums written by major line of business:


		Three Months Ended September 30,						Three Months Ended September 30,
		2021			2020				2022		2021
		Amount		%	Amount		%				Amount		%	Amount		%
Professional lines										Professional lines	$	412,173	30.1	$	310,185	26.9
Property, energy, marine and aviation	Property, energy, marine and aviation	$	215,062	18.6	$	152,193	18.5			Property, energy, marine and aviation	241,357		17.6	205,021		17.8
Professional lines		310,185		26.9	199,163		24.2
Programs	Programs	196,048		17.0	123,768		15.0			Programs	189,263		13.8	196,048		17.0
Construction and national accounts		92,253		8.0	88,790		10.8
Excess and surplus casualty	Excess and surplus casualty	98,320		8.5	78,889		9.6			Excess and surplus casualty	110,917		8.1	98,320		8.5
Travel, accident and health	Travel, accident and health	62,837		5.4	28,972		3.5			Travel, accident and health	107,434		7.8	62,837		5.4
Construction and national accounts										Construction and national accounts	98,381		7.2	102,294		8.9
Lenders products	Lenders products	38,905		3.4	60,830		7.4			Lenders products	41,889		3.1	38,905		3.4
Other	Other	140,203		12.2	91,556		11.1			Other	167,345		12.2	140,203		12.2
Total	Total	$	1,153,813	100.0	$	824,161	100.0			Total	$	1,368,759	100.0	$	1,153,813	100.0

~~2021~~2022 Third Quarter versus ~~2020~~2021 Period. Gross premiums written by the insurance segment in the ~~2021~~2022 third quarter were ~~32.4%~~16.6% higher than in the ~~2020~~2021 third quarter, while net premiums written were ~~40.0%~~18.6% higher. 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.

Nine Months Ended September 30,
2021 2020
Amount % Amount %
Property, energy, marine and aviation $ 593,322 19.1 $ 439,579 18.9
Professional Lines 803,392 25.8 526,180 22.6
Programs 503,822 16.2 341,230 14.7
Construction and national accounts 304,624 9.8 261,933 11.3
Excess and surplus casualty 258,259 8.3 209,011 9.0
Travel, accident and health 226,214 7.3 183,015 7.9
Lenders products 114,151 3.7 117,812 5.1
Other 308,423 9.9 246,410 10.6
Total $ 3,112,207 100.0 $ 2,325,170 100.0


ARCH CAPITAL			47			2022 THIRD QUARTER FORM 10-Q

Table of Contents


	Nine Months Ended September 30,
	2022			2021
	Amount		%	Amount		%
Professional lines	$	1,109,416	29.2	$	803,392	25.8
Property, energy, marine and aviation	687,742		18.1	564,462		18.1
Programs	482,003		12.7	503,822		16.2
Excess and surplus casualty	331,715		8.7	258,259		8.3
Travel, accident and health	378,736		10.0	226,214		7.3
Construction and national accounts	334,720		8.8	333,484		10.7
Lenders products	103,163		2.7	114,151		3.7
Other	376,417		9.9	308,423		9.9
Total	$	3,803,912	100.0	$	3,112,207	100.0

Nine Months Ended September 30, 2022 versus 2021 ~~versus 2020 Period~~period. Gross premiums written by the insurance segment for the nine months ended September 30, ~~2021~~2022 were ~~27.2%~~20.7% higher than in the ~~2020~~2021 period, while net premiums written were ~~33.8%~~22.2% higher than in the ~~2020~~2021 period. The increase in net premiums written reflected growth ~~across most~~in professional lines ~~of business,~~and in property, primarily due ~~in part~~ to rate increases, new business opportunities and growth in existing accounts, and in travel, primarily due to new business and growth in existing accounts.

Net Premiums Earned.

The following tables set forth our insurance segment’s net premiums earned by major line of business:


		Three Months Ended September 30,						Three Months Ended September 30,
		2021			2020				2022		2021
		Amount		%	Amount		%				Amount		%	Amount		%
Professional lines										Professional lines	$	341,833	28.8	$	249,007	26.5
Property, energy, marine and aviation	Property, energy, marine and aviation	$	187,905	20.0	$	133,827	18.6			Property, energy, marine and aviation	202,483		17.1	178,167		19.0
Professional lines		249,007		26.5	168,502		23.4
Programs	Programs	137,299		14.6	104,861		14.6			Programs	150,453		12.7	137,299		14.6
Construction and national accounts		94,523		10.1	95,386		13.3
Excess and surplus casualty	Excess and surplus casualty	84,048		9.0	69,978		9.7			Excess and surplus casualty	100,175		8.4	84,048		9.0
Travel, accident and health	Travel, accident and health	56,102		6.0	36,726		5.1			Travel, accident and health	133,445		11.2	56,102		6.0
Construction and national accounts										Construction and national accounts	109,905		9.3	104,261		11.1
Lenders products	Lenders products	33,030		3.5	33,401		4.6			Lenders products	33,253		2.8	33,030		3.5
Other	Other	96,756		10.3	76,473		10.6			Other	115,361		9.7	96,756		10.3
Total	Total	$	938,670	100.0	$	719,154	100.0			Total	$	1,186,908	100.0	$	938,670	100.0


~~ARCH CAPITAL~~			48			~~2021 THIRD QUARTER FORM 10-Q~~

~~Table of Contents~~


		Nine Months Ended September 30,						Nine Months Ended September 30,
		2021			2020				2022		2021
		Amount		%	Amount		%				Amount		%	Amount		%
Professional lines										Professional lines	$	945,761	28.5	$	662,776	25.3
Property, energy, marine and aviation	Property, energy, marine and aviation	$	512,880	19.5	$	365,791	17.2			Property, energy, marine and aviation	557,481		16.8	488,326		18.6
Professional Lines		662,776		25.3	475,014		22.4
Programs	Programs	369,113		14.1	322,203		15.2			Programs	438,943		13.2	369,113		14.1
Construction and national accounts		293,043		11.2	286,691		13.5
Excess and surplus casualty	Excess and surplus casualty	232,314		8.9	196,041		9.2			Excess and surplus casualty	289,305		8.7	232,314		8.9
Travel, accident and health	Travel, accident and health	168,378		6.4	166,218		7.8			Travel, accident and health	368,260		11.1	168,378		6.4
Construction and national accounts										Construction and national accounts	306,204		9.2	317,597		12.1
Lenders products	Lenders products	119,507		4.6	81,855		3.9			Lenders products	91,435		2.8	119,507		4.6
Other	Other	265,560		10.1	229,169		10.8			Other	318,359		9.6	265,560		10.1
Total	Total	$	2,623,571	100.0	$	2,122,982	100.0			Total	$	3,315,748	100.0	$	2,623,571	100.0

Net premiums written are primarily earned on a pro rata basis over the terms of the policies for all products, usually 12 months. Net premiums earned reflect changes in net premiums written over the previous five quarters. Net premiums earned ~~in the 2021 third quarter~~for both 2022 periods were ~~30.5%~~26.4% higher than in the ~~2020 third quarter. Net premiums earned for the nine months ended September 30,~~ 2021 ~~were 23.6% higher than in the 2020 period.~~periods.

Losses and Loss Adjustment Expenses.

The table below shows the components of the insurance segment’s loss ratio:


		Three Months Ended				Nine Months Ended					Three Months Ended				Nine Months Ended
		September 30,				September 30,					September 30,				September 30,
		2021		2020		2021		2020			2022		2021		2022		2021
Current year	Current year	71.7	%	73.3	%	67.2	%	73.3	%	Current year	69.8	%	71.7	%	62.5	%	67.2	%
Prior period reserve development	Prior period reserve development	(0.5)	%	(0.3)	%	(0.5)	%	(0.3)	%	Prior period reserve development	(0.5)	%	(0.5)	%	(0.6)	%	(0.5)	%
Loss ratio	Loss ratio	71.2	%	73.0	%	66.7	%	73.0	%	Loss ratio	69.3	%	71.2	%	61.9	%	66.7	%

Current Year Loss Ratio.

~~2021~~2022 Third Quarter versus ~~2020~~2021 Period. The insurance segment’s current year loss ratio in the ~~2021~~2022 third quarter was ~~1.6~~1.9 points lower than in the ~~2020~~2021 third quarter. The ~~2021~~2022 third quarter loss ratio reflected ~~12.2~~13.4 points of current year catastrophic activity, primarily related to Hurricane ~~Ida and other global events,~~Ian, compared to ~~10.3~~12.2 points of catastrophic activity for the ~~2020~~2021 third quarter, ~~which included exposure~~primarily related to ~~the COVID-19 global pandemic.~~ Hurricane Ida.

Nine Months Ended September 30, 2022 versus 2021 Period. The insurance segment’s current year loss ratio for the nine months ended September 30, ~~2021~~2022 was ~~6.1~~4.7 points lower than in the ~~2020~~2021 period and reflected ~~7.0~~6.1 points of current year catastrophic activity, primarily related to Hurricane Ian, Russia’s invasion of Ukraine and other natural catastrophes, compared to ~~9.9~~7.0 points in the ~~2020~~2021 period. The balance of the change in the ~~2021~~2022 loss ratios resulted, in part, from changes in mix of ~~business and the level~~business.


ARCH CAPITAL			48			2022 THIRD QUARTER FORM 10-Q

Table of ~~large attritional losses.~~Contents

Prior Period Reserve Development.

The insurance segment’s net favorable development was $5.4 million, or 0.5 points, for the 2022 third quarter, compared to $5.1 million, or 0.5 points, for the 2021 third quarter, ~~compared to $2.3~~and $19.4 million, or ~~0.3 points, for the 2020 third quarter, and $13.1 million, or 0.5~~0.6 points, for the nine months ended September 30, ~~2021,~~2022, compared to ~~$5.9~~$13.1 million, or ~~0.3~~0.5 points, for the ~~2020~~2021 period. See note 6,5, “Reserve for Losses and Loss Adjustment Expenses,” to our consolidated financial statements for information about the insurance segment’s prior year reserve development.

Underwriting Expenses.

~~2021~~2022 Third Quarter versus ~~2020~~2021 Period. The insurance segment’s underwriting expense ratio was 33.5% in the 2022 third quarter, compared to 31.0% in the 2021 third ~~quarter, consistent with 31.2%~~quarter. The increase in the ~~2020~~2022 third ~~quarter.~~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.

Nine Months Ended September 30, 2022 versus 2021 ~~versus 2020~~period~~Period.~~. The insurance segment’s underwriting expense ratio was ~~31.5%~~34.3% for the nine months ended September 30, ~~2021,~~2022, compared to ~~32.5%~~31.5% for the ~~2020~~2021 period, with the ~~decrease~~increase primarily due to changing mix of business and growth in ~~net premiums earned.~~lines with higher acquisition costs.

Reinsurance Segment

The following tables set forth our reinsurance segment’s underwriting results:


		Three Months Ended September 30,								Three Months Ended September 30,
		2021			2020			% Change		2022			2021			% Change
Gross premiums written	Gross premiums written	$	1,251,760		$	1,004,590		24.6	Gross premiums written	$	1,639,061		$	1,251,760		30.9
Premiums ceded	Premiums ceded	(630,371)			(400,388)				Premiums ceded	(560,225)			(630,371)
Net premiums written	Net premiums written	621,389			604,202			2.8	Net premiums written	1,078,836			621,389			73.6
Change in unearned premiums	Change in unearned premiums	57,313			(49,704)				Change in unearned premiums	(77,062)			57,313
Net premiums earned	Net premiums earned	678,702			554,498			22.4	Net premiums earned	1,001,774			678,702			47.6
Other underwriting income (loss)	Other underwriting income (loss)	3,293			298				Other underwriting income (loss)	452			3,293
Losses and loss adjustment expenses	Losses and loss adjustment expenses	(545,846)			(422,084)				Losses and loss adjustment expenses	(927,911)			(545,846)
Acquisition expenses	Acquisition expenses	(129,450)			(85,388)				Acquisition expenses	(208,425)			(129,450)
Other operating expenses	Other operating expenses	(45,647)			(41,818)				Other operating expenses	(62,777)			(45,647)
Underwriting income (loss)	Underwriting income (loss)	$	(38,948)		$	5,506		(807.4)	Underwriting income (loss)	$	(196,887)		$	(38,948)		(405.5)

Underwriting Ratios	Underwriting Ratios							% Point Change	Underwriting Ratios							% Point Change
Loss ratio	Loss ratio	80.4		%	76.1		%	4.3	Loss ratio	92.6		%	80.4		%	12.2
Acquisition expense ratio	Acquisition expense ratio	19.1		%	15.4		%	3.7	Acquisition expense ratio	20.8		%	19.1		%	1.7
Other operating expense ratio	Other operating expense ratio	6.7		%	7.5		%	(0.8)	Other operating expense ratio	6.3		%	6.7		%	(0.4)
Combined ratio	Combined ratio	106.2		%	99.0		%	7.2	Combined ratio	119.7		%	106.2		%	13.5


~~ARCH CAPITAL~~			49			~~2021 THIRD QUARTER FORM 10-Q~~

~~Table of Contents~~


		Nine Months Ended September 30,								Nine Months Ended September 30,
		2021			2020			% Change		2022			2021			% Change
Gross premiums written	Gross premiums written	$	4,080,840		$	2,934,174		39.1	Gross premiums written	$	5,151,401		$	4,080,840		26.2
Premiums ceded	Premiums ceded	(1,535,607)			(967,698)				Premiums ceded	(1,770,807)			(1,535,607)
Net premiums written	Net premiums written	2,545,233			1,966,476			29.4	Net premiums written	3,380,594			2,545,233			32.8
Change in unearned premiums	Change in unearned premiums	(484,607)			(388,321)				Change in unearned premiums	(646,421)			(484,607)
Net premiums earned	Net premiums earned	2,060,626			1,578,155			30.6	Net premiums earned	2,734,173			2,060,626			32.7
Other underwriting income	Other underwriting income	3,148			1,767				Other underwriting income	5,814			3,148
Losses and loss adjustment expenses	Losses and loss adjustment expenses	(1,494,539)			(1,235,586)				Losses and loss adjustment expenses	(1,920,189)			(1,494,539)
Acquisition expenses	Acquisition expenses	(381,060)			(255,516)				Acquisition expenses	(569,915)			(381,060)
Other operating expenses	Other operating expenses	(150,856)			(125,831)				Other operating expenses	(198,606)			(150,856)
Underwriting income (loss)	Underwriting income (loss)	$	37,319		$	(37,011)		200.8	Underwriting income (loss)	$	51,277		$	37,319		37.4

Underwriting Ratios	Underwriting Ratios							% Point Change	Underwriting Ratios							% Point Change
Loss ratio	Loss ratio	72.5		%	78.3		%	(5.8)	Loss ratio	70.2		%	72.5		%	(2.3)
Acquisition expense ratio	Acquisition expense ratio	18.5		%	16.2		%	2.3	Acquisition expense ratio	20.8		%	18.5		%	2.3
Other operating expense ratio	Other operating expense ratio	7.3		%	8.0		%	(0.7)	Other operating expense ratio	7.3		%	7.3		%	—
Combined ratio	Combined ratio	98.3		%	102.5		%	(4.2)	Combined ratio	98.3		%	98.3		%	—

The reinsurance segment consists of our reinsurance underwriting units which offer specialty product lines on a worldwide basis. ~~Product lines include:~~

•~~Casualty:~~ ~~provides~~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 ~~and workers’ compensation~~ exposures ~~from ceding company clients, primarily on a treaty basis. Exposures include,~~including, among others, executive assurance, professional liability, ~~workers’ compensation,~~ excess and umbrella liability, excess motor and healthcare ~~business.~~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 ~~to ceding company clients~~ for proportional motor reinsurance, whole account multi-line treaties, cyber, trade credit and ~~other lines, including~~ surety, accident and health, workers’ compensation catastrophe, agriculture ~~trade credit~~ and political ~~risk.~~risk, among others.

•Property catastrophe: provides protection for most types of catastrophic losses, ~~that are covered in the underlying policies written by reinsureds,~~ including hurricane, earthquake, flood, tornado, hail and fire, and ~~coverage~~ for other perils on a case-by-case basis. ~~Property catastrophe reinsurance provides coverage on an excess~~Excess of loss ~~basis~~coverages are triggered when aggregate losses and loss adjustment expense from a single occurrence or aggregation of losses from a covered peril exceed the retention specified in the contract.

•Property excluding property catastrophe: provides coverage for ~~both~~ personal lines ~~and~~and/or commercial property exposures and principally covers buildings, structures, equipment and contents. The primary perils in this business include fire,


ARCH CAPITAL			49			2022 THIRD QUARTER FORM 10-Q

Table of Contents

~~include fire,~~ explosion, collapse, riot, vandalism, wind, tornado, flood and earthquake. Business is assumed on ~~both~~either a ~~proportional and excess of loss~~ treaty basis ~~and on a~~or facultative basis. ~~In addition, facultative business is written which focuses on commercial property risks on an excess of loss basis.~~

•Other: includes life reinsurance business, ~~on both a proportional and non-proportional basis,~~ casualty clash business and, in limited instances, non-traditional business which is intended to provide insurers with risk management solutions that complement traditional reinsurance.

Premiums Written.

The following tables set forth our reinsurance segment’s net premiums written by major line of business:


		Three Months Ended September 30,						Three Months Ended September 30,
		2021			2020				2022		2021
		Amount		%	Amount		%				Amount		%	Amount		%
Other specialty										Other specialty	$	381,004	35.3	$	167,006	26.9
Property excluding property catastrophe	Property excluding property catastrophe	$	237,025	38.1	$	223,880	37.1			Property excluding property catastrophe	341,809		31.7	237,025		38.1
Casualty										Casualty	230,308		21.3	187,066		30.1
Property catastrophe	Property catastrophe	(7,125)		(1.1)	42,125		7.0			Property catastrophe	77,606		7.2	(7,125)		(1.1)
Other specialty		167,006		26.9	159,969		26.5
Casualty		187,066		30.1	142,401		23.6
Marine and aviation	Marine and aviation	19,159		3.1	27,839		4.6			Marine and aviation	28,633		2.7	19,159		3.1
Other	Other	18,258		2.9	7,988		1.3			Other	19,476		1.8	18,258		2.9
Total	Total	$	621,389	100.0	$	604,202	100.0			Total	$	1,078,836	100.0	$	621,389	100.0

~~2021~~2022 Third Quarter versus ~~2020~~2021 Period. Gross premiums written by the reinsurance segment in the ~~2021~~2022 third quarter were ~~24.6%~~30.9% higher than in the ~~2020~~2021 third quarter, while net premiums written were ~~2.8%~~73.6% higher. ~~The lower level of growth in net~~Net premiums written ~~compared to gross premiums written primarily reflected~~for the reinsurance segment in the 2021 third quarter were affected by a ~~higher level of premiums ceded due to a one-time~~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 ~~would have been 29.5%, consistent with the level of growth in gross premiums written, reflecting~~reflected increases in ~~most~~all lines of business, ~~due in part~~primarily related to rate increases, new business opportunities and ~~rate increases.~~growth in existing accounts.


~~ARCH CAPITAL~~			50			~~2021 THIRD QUARTER FORM 10-Q~~

~~Table of Contents~~


		Nine Months Ended September 30,						Nine Months Ended September 30,
		2021			2020				2022		2021
		Amount		%	Amount		%				Amount		%	Amount		%
Other specialty										Other specialty	$	1,179,548	34.9	$	747,662	29.4
Property excluding property catastrophe	Property excluding property catastrophe	$	778,959	30.6	$	546,443	27.8			Property excluding property catastrophe	936,270		27.7	778,959		30.6
Casualty										Casualty	709,487		21.0	631,212		24.8
Property catastrophe	Property catastrophe	197,724		7.8	248,893		12.7			Property catastrophe	361,028		10.7	197,724		7.8
Other Specialty		747,662		29.4	562,296		28.6
Casualty		631,212		24.8	438,330		22.3
Marine and aviation	Marine and aviation	131,045		5.1	109,996		5.6			Marine and aviation	115,579		3.4	131,045		5.1
Other	Other	58,631		2.3	60,518		3.1			Other	78,682		2.3	58,631		2.3
Total	Total	$	2,545,233	100.0	$	1,966,476	100.0			Total	$	3,380,594	100.0	$	2,545,233	100.0

Nine Months Ended September 30, 2022 versus 2021 ~~versus 2020 Period~~period. Gross premiums written by the reinsurance segment for the nine months ended September 30, ~~2021~~2022 were ~~39.1%~~26.2% higher than in the ~~2020~~2021 period, while net premiums written were ~~29.4%~~32.8% higher than in the ~~2020~~2021 period. The increase in net premiums written reflected growth in ~~property excluding property catastrophe, other specialty and casualty~~ most lines of business,

primarily due to new business, rate increases and ~~rate increases.~~growth in existing accounts.

Net Premiums Earned.

The following tables set forth our reinsurance segment’s net premiums earned by major line of business:


		Three Months Ended September 30,						Three Months Ended September 30,
		2021			2020				2022		2021
		Amount		%	Amount		%				Amount		%	Amount		%
Other specialty										Other specialty	$	330,142	33.0	$	195,649	28.8
Property excluding property catastrophe	Property excluding property catastrophe	$	210,280	31.0	$	163,081	29.4			Property excluding property catastrophe	282,488		28.2	210,280		31.0
Casualty										Casualty	221,636		22.1	159,697		23.5
Property catastrophe	Property catastrophe	61,107		9.0	69,524		12.5			Property catastrophe	117,820		11.8	61,107		9.0
Other specialty		195,649		28.8	141,201		25.5
Casualty		159,697		23.5	136,421		24.6
Marine and aviation	Marine and aviation	29,818		4.4	26,744		4.8			Marine and aviation	25,182		2.5	29,818		4.4
Other	Other	22,151		3.3	17,527		3.2			Other	24,506		2.4	22,151		3.3
Total	Total	$	678,702	100.0	$	554,498	100.0			Total	$	1,001,774	100.0	$	678,702	100.0


		Nine Months Ended September 30,						Nine Months Ended September 30,
		2021			2020				2022		2021
		Amount		%	Amount		%				Amount		%	Amount		%
Other specialty										Other specialty	$	846,081	30.9	$	571,364	27.7
Property excluding property catastrophe	Property excluding property catastrophe	$	600,842	29.2	$	399,752	25.3			Property excluding property catastrophe	781,562		28.6	600,842		29.2
Casualty										Casualty	634,208		23.2	492,574		23.9
Property catastrophe	Property catastrophe	225,285		10.9	177,750		11.3			Property catastrophe	289,575		10.6	225,285		10.9
Other Specialty		571,364		27.7	467,592		29.6
Casualty		492,574		23.9	404,248		25.6
Marine and aviation	Marine and aviation	112,699		5.5	76,562		4.9			Marine and aviation	109,142		4.0	112,699		5.5
Other	Other	57,862		2.8	52,251		3.3			Other	73,605		2.7	57,862		2.8
Total	Total	$	2,060,626	100.0	$	1,578,155	100.0			Total	$	2,734,173	100.0	$	2,060,626	100.0

Net premiums written, irrespective of the class of business, are generally earned on a pro rata basis over the terms of the underlying policies or reinsurance contracts. Net premiums earned by the reinsurance segment in the ~~2021~~2022 third quarter were ~~22.4%~~47.6% higher than in the ~~2020~~2021 third quarter, and reflect changes in net premiums written over the previous five quarters. ~~For the nine months ended September 30, 2021, net premiums earned were 30.6% higher than in the 2020 period.~~

Other Underwriting Income (Loss).

Other underwriting income for the 2022 third quarter was $0.5 million, compared to $3.3 million for the 2021 third quarter, ~~was $3.3 million, compared to an income of $0.3 million for the 2020 third quarter,~~ and ~~an income of $3.1~~$5.8 million for the nine months ended September 30, ~~2021,~~2022, compared to ~~an income of $1.8~~$3.1 million for the ~~2020~~2021 period.

Losses and Loss Adjustment Expenses.

The table below shows the components of the reinsurance segment’s loss ratio:


		Three Months Ended				Nine Months Ended					Three Months Ended				Nine Months Ended
		September 30,				September 30,					September 30,				September 30,
		2021		2020		2021		2020			2022		2021		2022		2021
Current year	Current year	91.1	%	83.7	%	78.3	%	84.2	%	Current year	97.5	%	91.1	%	74.9	%	78.3	%
Prior period reserve development	Prior period reserve development	(10.7)	%	(7.6)	%	(5.8)	%	(5.9)	%	Prior period reserve development	(4.9)	%	(10.7)	%	(4.7)	%	(5.8)	%
Loss ratio	Loss ratio	80.4	%	76.1	%	72.5	%	78.3	%	Loss ratio	92.6	%	80.4	%	70.2	%	72.5	%


ARCH CAPITAL			50			2022 THIRD QUARTER FORM 10-Q

Table of Contents

Current Year Loss Ratio.

~~2021~~2022 Third Quarter versus ~~2020~~2021 Period. The reinsurance segment’s current year loss ratio in the ~~2021~~2022 third quarter was ~~7.4~~6.4 points higher than in the ~~2020~~2021 third quarter. The ~~2021~~2022 third quarter loss ratio reflected ~~34.6~~42.8 points of current year catastrophic activity, primarily ~~related~~due to Hurricane ~~Ida, European floods~~Ian and other global events. The ~~2020~~2021 third quarter included ~~26.1~~34.6 points of catastrophic activity, ~~which included exposure~~primarily related to ~~the COVID-19 pandemic.~~Hurricane Ida and European floods.

Nine Months Ended September 30, 2022 versus 2021 ~~versus 2020 Period~~Period. . The reinsurance segment’s current year loss ratio for the nine months ended September 30, ~~2021~~2022 was ~~5.9~~3.4 points lower than in the ~~2020~~2021 period and reflected 20.1 points of current year catastrophic activity, primarily related to Hurricane Ian, Russia’s invasion of Ukraine and other global events, compared to ~~21.6~~20.1 points in the ~~2020~~2021 period. ~~The 2020 period loss ratio included exposure to the COVID-19 pandemic.~~

Prior Period Reserve Development.

The reinsurance segment’s net favorable development was $49.2 million, or 4.9 points, for the 2022 third quarter, compared to $72.3 million, or 10.7 points, for the 2021 third quarter, ~~compared to $42.0~~and $128.1 million, or ~~7.6 points, for the 2020 third quarter, and $119.6 million, or 5.8~~4.7 points, for the nine months ended September 30, ~~2021,~~2022, compared to ~~$93.8~~$119.6 million, or ~~5.9~~5.8 points, for the ~~2020~~2021 period. See note 6,5, “Reserve for Losses and Loss Adjustment Expenses,” to our consolidated financial statements for information about the reinsurance segment’s prior year reserve development.

Underwriting Expenses.

~~2021~~2022 Third Quarter versus ~~2020~~2021 Period. The underwriting expense ratio for the reinsurance segment was ~~25.8%~~27.1% in the


~~ARCH CAPITAL~~			51			~~2021 THIRD QUARTER FORM 10-Q~~

~~Table of Contents~~

~~2021~~ 2022 third quarter, compared to ~~22.9%~~25.8% in the ~~2020~~2021 third quarter, with the increase primarily resulting from ~~changes~~higher level of pro rata business, which generally has higher ceding commissions than excess of loss business. Such increase in ~~mix of business~~the acquisition expense ratio was partially offset by a lower operating expense ratio due to ~~lines with higher acquisition costs and~~ a higher level of ~~expenses related to favorable development of prior year loss reserves.~~earned premium.

Nine Months Ended September 30, 2022 versus 2021 ~~versus 2020 Period~~period. The underwriting expense ratio for the reinsurance segment was ~~25.8%~~28.1% for the nine months ended September 30, ~~2021,~~2022, compared to ~~24.2%~~25.8% for the ~~2020~~2021 period. The comparison of the underwriting expense ratios also reflected changes in the mix and type of business and a higher level of net premiums earned for the ~~2021~~2022 period.

Mortgage Segment

Our mortgage operations include U.S. and international mortgage insurance and reinsurance operations as well as participation in GSE credit risk-sharing transactions. Our mortgage group includes direct mortgage insurance in the U.S. primarily through Arch Mortgage Insurance Company, United Guaranty Residential Insurance Company and Arch Mortgage Guaranty Company (together, “Arch MI U.S.”); mortgage reinsurance by Arch Reinsurance Ltd. (“Arch Re Bermuda”) to mortgage insurers on both a proportional and non-proportional basis globally; direct mortgage insurance in Europe through Arch Insurance (EU) Designated Activity Company (“Arch Insurance EU”); in Hong Kong through Arch MI Asia Limited (“Arch MI Asia”); in Australia through Arch Lenders Mortgage Indemnity Limited (“ALMI”) ~~and participation in various GSE credit risk-sharing products primarily through Arch Re Bermuda.~~

The following tables set forth our mortgage segment’s underwriting results.

Three Months Ended September 30,
2021 2020 % Change
Gross premiums written $ 360,934 $ 346,248 4.2
Premiums ceded (60,207) (47,783)
Net premiums written 300,727 298,465 0.8
Change in unearned premiums 11,238 52,944
Net premiums earned 311,965 351,409 (11.2)
Other underwriting income 3,981 4,600
Losses and loss adjustment expenses (11,543) (153,055)
Acquisition expenses (24,098) (35,716)
Other operating expenses (46,254) (36,708)
Underwriting income $ 234,051 $ 130,530 79.3
Underwriting Ratios % Point
Change
Loss ratio 3.7 % 43.6 % (39.9)
Acquisition expense ratio 7.7 % 10.2 % (2.5)
Other operating expense ratio 14.8 % 10.4 % 4.4
Combined ratio 26.2 % 64.2 % (38.0)


		Nine Months Ended September 30,								Three Months Ended September 30,
		2021			2020			% Change		2022			2021			% Change
Gross premiums written	Gross premiums written	$	1,143,691		$	1,084,337		5.5	Gross premiums written	$	362,409		$	360,934		0.4
Premiums ceded	Premiums ceded	(171,923)			(136,154)				Premiums ceded	(86,230)			(60,207)
Net premiums written	Net premiums written	971,768			948,183			2.5	Net premiums written	276,179			300,727			(8.2)
Change in unearned premiums	Change in unearned premiums	10,735			113,965				Change in unearned premiums	5,889			11,238
Net premiums earned	Net premiums earned	982,503			1,062,148			(7.5)	Net premiums earned	282,068			311,965			(9.6)
Other underwriting income	Other underwriting income	15,026			15,649				Other underwriting income	2,625			3,981
Losses and loss adjustment expenses	Losses and loss adjustment expenses	(85,112)			(444,721)				Losses and loss adjustment expenses	67,878			(11,543)
Acquisition expenses	Acquisition expenses	(84,297)			(108,304)				Acquisition expenses	(6,693)			(24,098)
Other operating expenses	Other operating expenses	(143,697)			(120,178)				Other operating expenses	(46,471)			(46,254)
Underwriting income	Underwriting income	$	684,423		$	404,594		69.2	Underwriting income	$	299,407		$	234,051		27.9

Underwriting Ratios	Underwriting Ratios							% Point Change	Underwriting Ratios							% Point Change
Loss ratio	Loss ratio	8.7		%	41.9		%	(33.2)	Loss ratio	(24.1)		%	3.7		%	(27.8)
Acquisition expense ratio	Acquisition expense ratio	8.6		%	10.2		%	(1.6)	Acquisition expense ratio	2.4		%	7.7		%	(5.3)
Other operating expense ratio	Other operating expense ratio	14.6		%	11.3		%	3.3	Other operating expense ratio	16.5		%	14.8		%	1.7
Combined ratio	Combined ratio	31.9		%	63.4		%	(31.5)	Combined ratio	(5.2)		%	26.2		%	(31.4)

~~Premiums Written~~.

~~The following tables set forth our mortgage segment’s net premiums written by underwriting location (i.e., where the business is underwritten):~~

Three Months Ended September 30,
2021 2020
Amount % Amount %
Underwriting location:
United States $ 221,315 73.6 $ 245,971 82.4
Other 79,412 26.4 52,494 17.6
Total $ 300,727 100.0 $ 298,465 100.0

~~2021 Third Quarter versus 2020 Period.~~ Gross premiums written by the mortgage segment in the 2021 third quarter were 4.2% higher than in the 2020 third quarter, while net premiums written were 0.8% higher. The increase in gross premiums written reflected growth in Australian single premium mortgage insurance partially as a result of the previously disclosed acquisition of Westpac Lenders Mortgage Insurance Limited. The lower increase in net premiums written reflected a higher level of premiums ceded on U.S. primary mortgage insurance.

Nine Months Ended September 30,
2021 2020
Amount % Amount %
Underwriting location:
United States $ 703,489 72.4 $ 771,203 81.3
Other 268,279 27.6 176,980 18.7
Total $ 971,768 100.0 $ 948,183 100.0

~~Nine Months Ended September 30, 2021 versus 2020 Period~~. Gross premiums written by the mortgage segment for the nine months ended September 30, 2021 were 5.5% higher than in the 2020 period, while net premiums written for the nine months ended September 30, 2021 were 2.5% higher


	Nine Months Ended September 30,
	2022			2021			% Change
Gross premiums written	$	1,099,144		$	1,143,691		(3.9)
Premiums ceded	(241,097)			(171,923)
Net premiums written	858,047			971,768			(11.7)
Change in unearned premiums	9,190			10,735
Net premiums earned	867,237			982,503			(11.7)
Other underwriting income	6,130			15,026
Losses and loss adjustment expenses	187,163			(85,112)
Acquisition expenses	(27,343)			(84,297)
Other operating expenses	(150,064)			(143,697)
Underwriting income	$	883,123		$	684,423		29.0

Underwriting Ratios							% Point Change
Loss ratio	(21.6)		%	8.7		%	(30.3)
Acquisition expense ratio	3.2		%	8.6		%	(5.4)
Other operating expense ratio	17.3		%	14.6		%	2.7
Combined ratio	(1.1)		%	31.9		%	(33.0)


ARCH CAPITAL			5251			~~2021~~2022 THIRD QUARTER FORM 10-Q

Table of Contents

Premiums Written.

The following tables set forth our mortgage segment’s net premiums written by underwriting location:


	Three Months Ended September 30,
	2022			2021
	Amount		%	Amount		%
Underwriting location:
United States	$	188,290	68.2	$	221,315	73.6
Other	87,889		31.8	79,412		26.4
Total	$	276,179	100.0	$	300,727	100.0

2022 Third Quarter versus 2021 Period. Gross premiums written by the mortgage segment in the 2022 third quarter were 0.4% higher than in the ~~2020 period, primarily reflecting growth in Australian single premium mortgage insurance and~~2021 third quarter, while net premiums written were 8.2% lower. Net premiums written for the ~~benefit~~2022 third quarter reflected a higher level of premiums ~~received related to~~ceded than in the ~~exercise of early redemption options~~2021 third quarter.


	Nine Months Ended September 30,
	2022			2021
	Amount		%	Amount		%





Underwriting location:
United States	$	590,606	68.8	$	703,489	72.4
Other	267,441		31.2	268,279		27.6
Total	$	858,047	100.0	$	971,768	100.0

Nine Months Ended September 30, 2022 versus 2021 Period. Gross premiums written by ~~GSEs~~the mortgage segment for ~~certain seasoned callable credit risk transfer contracts. This growth was partially offset by~~the nine months ended September 30, 2022 were 3.9% lower than in the 2021 period. The reduction in gross premiums written primarily reflected a lower ~~level of~~ U.S. primary mortgage insurance single premium volume and a decrease in ~~force on~~ monthly ~~premium policies, which resulted from~~premiums. Net premiums written for the ~~continued high~~nine months ended September 30, 2022 were 11.7% lower than in the 2021 period and reflected a higher level of ~~refinancing activity.~~premiums ceded than in the 2021 period.

The persistency rate, which represents the percentage of mortgage insurance in force at the beginning of a 12-month period that remains in force at the end of such period, was ~~57.7%~~75.4% for the Arch MI U.S. portfolio of mortgage insurance policies at September 30, ~~2021,~~2022, reflecting ~~the higher~~a lower level of mortgage refinancing activity, compared to ~~58.7%~~57.7% at ~~December 31, 2020.~~September 30, 2021.

The following tables provide details on the new insurance written (“NIW”) generated by Arch MI U.S. NIW represents the original principal balance of all loans that received coverage during the period.


(U.S. Dollars in millions)	(U.S. Dollars in millions)	Three Months Ended September 30,						(U.S. Dollars in millions)	Three Months Ended September 30,
		2021			2020				2022				2021
		Amount		%	Amount		%				Amount		%	Amount		%
Total new insurance written (NIW) (1)	Total new insurance written (NIW) (1)	$	27,841		$	32,787				Total new insurance written (NIW) (1)	$	17,425		$	27,841

Credit quality (FICO):	Credit quality (FICO):									Credit quality (FICO):
>=740	>=740	$	17,514	62.9	$	21,160	64.5			>=740	$	11,615	66.7	$	17,514	62.9
680-739	680-739	9,012		32.4	10,562		32.2			680-739	5,322		30.5	9,012		32.4
620-679	620-679	1,315		4.7	1,065		3.2			620-679	485		2.8	1,315		4.7

<620										<620	3		—	—		—
Total	Total	$	27,841	100.0	$	32,787	100.0			Total	$	17,425	100.0	$	27,841	100.0

Loan-to-value (LTV):	Loan-to-value (LTV):									Loan-to-value (LTV):
95.01% and above	95.01% and above	$	1,554	5.6	$	2,561	7.8			95.01% and above	$	973	5.6	$	1,554	5.6
90.01% to 95.00%	90.01% to 95.00%	14,240		51.1	13,967		42.6			90.01% to 95.00%	9,916		56.9	14,240		51.1
85.01% to 90.00%	85.01% to 90.00%	8,394		30.1	10,052		30.7			85.01% to 90.00%	4,839		27.8	8,394		30.1
85.00% and below	85.00% and below	3,653		13.1	6,207		18.9			85.00% and below	1,697		9.7	3,653		13.1
Total	Total	$	27,841	100.0	$	32,787	100.0			Total	$	17,425	100.0	$	27,841	100.0

Monthly vs. single:	Monthly vs. single:									Monthly vs. single:
Monthly	Monthly	$	26,515	95.2	$	31,928	97.4			Monthly	$	16,911	97.1	$	26,515	95.2
Single	Single	1,326		4.8	859		2.6			Single	514		2.9	1,326		4.8
Total	Total	$	27,841	100.0	$	32,787	100.0			Total	$	17,425	100.0	$	27,841	100.0

Purchase vs. refinance:	Purchase vs. refinance:									Purchase vs. refinance:
Purchase	Purchase	$	25,711	92.3	$	24,256	74.0			Purchase	$	17,159	98.5	$	25,711	92.3
Refinance	Refinance	2,130		7.7	8,531		26.0			Refinance	266		1.5	2,130		7.7
Total	Total	$	27,841	100.0	$	32,787	100.0			Total	$	17,425	100.0	$	27,841	100.0

(1)Represents the original principal balance of all loans that received coverage during the period.

(U.S. Dollars in millions) Nine Months Ended September 30,
2021 2020
Amount % Amount %
Total new insurance written (NIW) (1) $ 83,232 $ 74,116
Credit quality (FICO):
>=740 $ 54,572 65.6 $ 47,080 63.5
680-739 25,543 30.7 24,130 32.6
620-679 3,117 3.7 2,906 3.9
Total $ 83,232 100.0 $ 74,116 100.0
Loan-to-value (LTV):
95.01% and above $ 4,646 5.6 $ 6,177 8.3
90.01% to 95.00% 40,464 48.6 30,569 41.2
85.01% to 90.00% 25,381 30.5 23,521 31.7
85.01% and below 12,741 15.3 13,849 18.7
Total $ 83,232 100.0 $ 74,116 100.0
Monthly vs. single:
Monthly $ 78,229 94.0 $ 71,011 95.8
Single 5,003 6.0 3,105 4.2
Total $ 83,232 100.0 $ 74,116 100.0
Purchase vs. refinance:
Purchase $ 71,226 85.6 $ 51,511 69.5
Refinance 12,006 14.4 22,605 30.5
Total $ 83,232 100.0 $ 74,116 100.0

~~(1)Represents the original principal balance of all loans that received coverage during the period.~~

~~Net Premiums Earned~~.

~~The following tables set forth our mortgage segment’s net premiums earned by underwriting location:~~

Three Months Ended September 30,
2021 2020
Amount % Amount %
Underwriting location:
United States $ 236,892 75.9 $ 290,451 82.7
Other 75,073 24.1 60,958 17.3
Total $ 311,965 100.0 $ 351,409 100.0

~~2021 Third Quarter versus 2020 Period.~~ ~~Net premiums earned for the 2021 third quarter were 11.2% lower than in the 2020 third quarter, and reflected a lower level of single premium policy terminations.~~


ARCH CAPITAL			5352			~~2021~~2022 THIRD QUARTER FORM 10-Q

Table of Contents

Nine Months Ended September 30,
2021 2020
Amount % Amount %
Underwriting location:
United States $ 747,830 76.1 $ 884,265 83.3
Other 234,673 23.9 177,883 16.7
Total $ 982,503 100.0 $ 1,062,148 100.0


(U.S. Dollars in millions)	Nine Months Ended September 30,
	2022			2021
	Amount		%	Amount		%
Total new insurance written (NIW) (1)	$	60,939		$	83,232

Credit quality (FICO):
>=740	$	40,888	67.1	$	54,572	65.6
680-739	18,376		30.2	25,543		30.7
620-679	1,667		2.7	3,117		3.7
<620	8		—	—		—
Total	$	60,939	100.0	$	83,232	100.0

Loan-to-value (LTV):
95.01% and above	$	3,264	5.4	$	4,646	5.6
90.01% to 95.00%	33,984		55.8	40,464		48.6
85.01% to 90.00%	17,163		28.2	25,381		30.5
85.01% and below	6,528		10.7	12,741		15.3
Total	$	60,939	100.0	$	83,232	100.0

Monthly vs. single:
Monthly	$	58,984	96.8	$	78,229	94.0
Single	1,955		3.2	5,003		6.0
Total	$	60,939	100.0	$	83,232	100.0

Purchase vs. refinance:
Purchase	$	59,375	97.4	$	71,226	85.6
Refinance	1,564		2.6	12,006		14.4
Total	$	60,939	100.0	$	83,232	100.0

~~Nine Months Ended September 30,~~Net Premiums Earned.

The following tables set forth our mortgage segment’s net premiums earned by underwriting location:


	Three Months Ended September 30,
	2022			2021
	Amount		%	Amount		%
Underwriting location:
United States	$	196,874	69.8	$	236,892	75.9
Other	85,194		30.2	75,073		24.1
Total	$	282,068	100.0	$	311,965	100.0

2022 Third Quarter versus 2021 ~~versus 2020~~ Period. Net premiums earned for the 2022 third quarter were 9.6% lower than in the 2021 third quarter, and reflected a reduction in earnings from single premium policy terminations and a lower level of monthly premiums.


	Nine Months Ended September 30,
	2022			2021
	Amount		%	Amount		%





Underwriting location:
United States	$	615,599	71.0	$	747,830	76.1
Other	251,638		29.0	234,673		23.9
Total	$	867,237	100.0	$	982,503	100.0

Nine Months Ended September 30, 2022 versus 2021 Period. For the nine months ended September 30, ~~2021~~2022, net premiums earned were ~~7.5%~~11.7% lower than in the ~~2020~~2021 period, ~~primarily reflecting~~and reflected a lower level of ~~single premiums earned, partially offset by an increase in~~ earnings from ~~Australian~~ single premium policy ~~terminations.~~terminations and a decline in monthly premiums.

Other Underwriting Income (Loss).

Other underwriting income, which is primarily related to GSE credit risk-sharing transactions and our whole mortgage loan purchase and sell program was $2.6 million for the 2022 third quarter, compared to $4.0 million for the 2021 ~~third quarter, compared to $4.6 million for the 2020~~ third quarter.

Losses and Loss Adjustment Expenses.

The table below shows the components of the mortgage segment’s loss ratio:


		Three Months Ended				Nine Months Ended					Three Months Ended				Nine Months Ended
		September 30,				September 30,					September 30,				September 30,
		2021		2020		2021		2020			2022		2021		2022		2021
Current year	Current year	18.2	%	44.9	%	18.8	%	42.9	%	Current year	20.6	%	18.2	%	18.3	%	18.8	%
Prior period reserve development	Prior period reserve development	(14.5)	%	(1.3)	%	(10.1)	%	(1.0)	%	Prior period reserve development	(44.7)	%	(14.5)	%	(39.9)	%	(10.1)	%
Loss ratio	Loss ratio	3.7	%	43.6	%	8.7	%	41.9	%	Loss ratio	(24.1)	%	3.7	%	(21.6)	%	8.7	%

Current Year Loss Ratio.

~~2021~~2022 Third Quarter versus ~~2020~~2021 Period. The mortgage segment’s current year loss ratio was ~~26.7~~2.4 points ~~lower~~higher in the ~~2021~~2022 third quarter than in the ~~2020~~2021 third quarter. The higher current year loss ratio for the 2022 period reflected a lower level of net premiums earned in the U.S. primary mortgage insurance business.

Nine Months Ended September 30, 2022 versus 2021 Period. The mortgage segment’s current year loss ratio was ~~24.1~~0.5 points lower for the nine months ended September 30, ~~2021~~2022 than for the ~~2020~~2021 period. The lower current year loss ~~ratios~~ratio for the ~~2021~~2022 period ~~reflect decrease in loss assumptions related to COVID-19 pandemic, primarily driven by~~reflected lower delinquencies.

For the 2020 periods, the increase in incurred losses was primarily due to, the financial stress related to the COVID-19 pandemic. Segregating estimated losses due to COVID-19 from the overall mortgage segment estimated losses would require the number of delinquencies specifically attributable to COVID-19. As this analysis cannot be performed accurately, the Company is not reporting COVID-19 provisions separately from its overall loss provisions.

Prior Period Reserve Development.

The mortgage segment’s net favorable development was $126.2 million, or 44.7 points, for the 2022 third quarter, compared to $45.1 million, or 14.5 points, for the 2021 third quarter, ~~compared to $4.5~~and $346.4 million, or ~~1.3 points, for the 2020 third quarter, and $99.1 million, or 10.1~~39.9 points, for the nine months ended September 30, ~~2021,~~2022, compared to ~~$10.8~~$99.1 million, or ~~1.0~~10.1 points, for the ~~2020~~2021 period. See note 6,5, “Reserve for Losses and Loss Adjustment Expenses,” to our consolidated financial statements for information about the mortgage segment’s prior year reserve development.

Underwriting Expenses.

~~2021~~2022 Third Quarter versus ~~2020~~2021 Period. The underwriting expense ratio for the mortgage segment was 18.9% in the 2022 third quarter, compared to 22.5% in the 2021 third quarter, ~~compared to 20.6% in the 2020 third quarter,~~ with the ~~increase~~decrease primarily due to lower acquisition expenses on Australian mortgage insurance following the acquisition of Westpac LMI in the 2021 third quarter and profit commissions adjustments related to favorable development of prior year loss reserves. Such amounts were partially offset by a lower level inof net premiums earned onin the U.S. primary mortgage insurance business.


ARCH CAPITAL			53			2022 THIRD QUARTER FORM 10-Q

Table of Contents

Nine Months Ended September 30, 2022 versus 2021 ~~versus 2020 Period~~period. The underwriting expense ratio for the mortgage segment was ~~23.2%~~20.5% for the nine months ended September 30, ~~2021,~~2022, compared to ~~21.5%~~23.2% for the ~~2020~~2021 period, with the ~~increase~~decrease primarily due to lower acquisition expenses on Australian mortgage insurance following the acquisition of Westpac LMI in the 2021 third quarter and profit commissions adjustments related to favorable development of prior year loss reserves. Such amounts were partially offset by a lower level inof net premiums earned onin the U.S. primary mortgage insurance business.

Corporate ~~(Non-Underwriting)~~ Segment

The corporate ~~(non-underwriting)~~ segment results include net investment income, ~~other income (loss), corporate expenses, transaction costs and other, amortization of intangible assets, interest expense, items related to our non-cumulative preferred shares,~~ 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~~investments 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 ~~or loss~~taxes, income from operating affiliates and ~~income taxes.~~items related to our non-cumulative preferred shares. Such amounts exclude the results of the ‘other’ segment. ~~See~~ ~~note 1, “Basis of Presentation and Recent Accounting Pronouncements,”~~ ~~to our consolidated financial statements for information about the change in presentation of income or loss from operating affiliates.~~


~~ARCH CAPITAL~~			54			~~2021 THIRD QUARTER FORM 10-Q~~

~~Table of Contents~~

Net Investment Income.

The components of net investment income were derived from the following sources:


		Three Months Ended				Nine Months Ended					Three Months Ended				Nine Months Ended
		September 30,				September 30,					September 30,				September 30,
		2021		2020		2021		2020			2022		2021		2022		2021
Fixed maturities	Fixed maturities	$	75,964	$	84,608	$	232,690	$	277,862	Fixed maturities	$	123,568	$	75,964	$	310,963	$	232,690

Equity securities	Equity securities	9,867		6,659		23,799		18,312		Equity securities	4,261		9,867		16,620		23,799
Short-term investments	Short-term investments	1,858		1,162		3,474		5,444		Short-term investments	9,304		1,858		15,999		3,474

Other (1)	Other (1)	19,114		24,594		55,699		62,898		Other (1)	8,644		19,114		28,704		55,699
Gross investment income	Gross investment income	106,803		117,023		315,662		364,516		Gross investment income	145,777		106,803		372,286		315,662
Investment expenses (2)	Investment expenses (2)	(18,608)		(17,166)		(59,308)		(50,600)		Investment expenses (2)	(17,137)		(18,608)		(56,818)		(59,308)
Net investment income	Net investment income	$	88,195	$	99,857	$	256,354	313,916		Net investment income	$	128,640	$	88,195	$	315,468	256,354

(1) Amounts include dividends and other distributions on investment funds, term loan investments, funds held balances, cash balances and other items.

(2) Investment expenses were approximately ~~0.32%~~0.29% of average invested assets for the ~~2021~~2022 third quarter, compared to 0.32% for the ~~2020~~2021 third quarter, and ~~0.32%~~0.30% for the nine months ended September 30, ~~2021,~~2022, compared to ~~0.31%~~0.32% for the ~~2020~~2021 period.

The ~~lower~~higher level of net investment income for the ~~2021 third quarter~~2022 period, primarily related to ~~lower~~higher yields available in the financial market. The pre-tax investment income yield, calculated based on amortized cost and on an annualized basis, was 2.06% for the 2022 third quarter, compared to 1.41% for the 2021 third quarter, ~~compared to 1.76%~~and 1.72% for the ~~2020 third quarter, and 1.40% for the~~ nine

months ended September 30, ~~2021,~~2022, compared to ~~1.94%~~1.40% for the ~~2020~~2021 period.

Corporate Expenses.

Corporate expenses were $17.6 million for the 2022 third quarter, compared to $18.6 million for the 2021 third quarter, ~~compared to $16.3 million for the 2020 third quarter,~~ and ~~$59.3~~$76.9 million for the nine months ended September 30, ~~2021,~~2022, compared to ~~$51.4~~$59.3 million for the ~~2020~~2021 period. The increase in corporate expenses was primarily due to higher incentive compensation costs.

Other Income (Losses)

Other loss for the 2022 third quarter was $13.7 million, compared to a loss of $4.0 million for the 2021 third quarter, and a loss of $34.5 million for the nine months ended September 30, 2022, compared to an income of $1.2 million for the 2021 period. Amounts in both periods primarily reflect changes in the cash surrender value of our investment in corporate-owned life insurance.

Transaction Costs and Other.

Transaction costs and other were $0.1 million for the 2022 third quarter, compared to $1.0 million for the 2021 third quarter, ~~compared to $1.7 million for the 2020 third quarter,~~ and ~~$0.8~~an expense of $0.7 million for the nine months ended September 30, ~~2021,~~2022, compared to ~~$5.2~~$0.8 million for the ~~2020~~2021 period. Amounts in the 2022 and 2021 ~~and 2020~~ periods ~~are primarily related to~~reflect acquisitions activity for the respective ~~period.~~periods.

Amortization of Intangible Assets.

Amortization of intangible assets for the 2022 third quarter was $26.1 million, compared to $20.1 million for the 2021 third quarter, ~~was $20.1 million, compared to $16.7 million for the 2020 third quarter,~~ and ~~$48.9~~$80.5 million for the nine months ended

September 30, ~~2021,~~2022, compared to ~~$49.8~~$48.9 million for the ~~2020~~2021 period. Amounts in 2022 and 2021 ~~and 2020~~period primarily ~~related~~attributed to amortization of finite-lived intangible assets. The increase in amortization of intangible assets expense was a result of acquisitions closed during the 2021 ~~third quarter.~~period.

Interest Expense.

Interest expense was $33.1 million for the 2022 third quarter, compared to the $33.2 million for the 2021 third quarter, ~~compared to the $36.2 million for the 2020 third quarter,~~ and ~~$98.8~~$98.6 million for the nine months ended September 30, ~~2021, compared to $86.6~~2022, consistent with $98.8 million for the ~~2020 period.The higher level of interest~~2021 period. Interest expense ~~in 2021 period mainly resulted from the issuance of $1.0 billion of 3.635% senior notes on June 30, 2020.~~

~~Loss on Redemption of Preferred Shares.~~

~~In September 2021, we redeemed all 5.25% Series E preferred shares and, in accordance with GAAP, we recorded a loss of $15.1 million to remove original issuance costs~~primarily reflects amounts related to ~~the redeemed shares from additional paid-in capital. Such adjustment had no impact on total shareholders’ equity or cash flows.~~

our outstanding senior notes.

Net Realized Gains or Losses.

We recorded net realized losses of $183.7 million for the 2022 third quarter, of which approximately 40% represented unrealized changes in the fair value of equity securities and assets accounted for using the fair value option, compared to net realized losses of $25.0 million for the 2021 third quarter, ~~compared to~~and net realized ~~gains~~losses of ~~$211.0~~$742.7 million for the ~~2020 third quarter, and~~nine months ended September 30, 2022, compared to net realized gains of $239.7 million for the ~~nine months ended September 30,~~ 2021 ~~compared to net realized gains of $524.0 million for the 2020~~ period. ~~In addition, 2021 third quarter included $33.1 million loss as a result of deconsolidation of Watford in our financial statements following the close of the transaction.~~ Currently, our portfolio is


ARCH CAPITAL			54			2022 THIRD QUARTER FORM 10-Q

Table of Contents

actively managed to maximize total return within certain guidelines. The effect of financial market movements on the investment portfolio will directly impact net realized gains and losses as the portfolio is adjusted and rebalanced. Net realized gains or losses from the sale of fixed maturities primarily results from our decisions to reduce credit exposure, to change duration targets, to rebalance our portfolios or due to relative value determinations.

Net realized gains or losses also include realized and unrealized contract gains and losses on our derivative instruments, changes in the fair value of assets accounted for using the fair value option and in the fair value of equities, along with changes in the allowance for credit losses on financial assets and net impairment losses recognized in earnings. See note 8,7, “Investment Information—Net Realized Gains (Losses),” ~~to our consolidated financial statements for additional information. See~~and note 8,7, “Investment Information—Allowance for Expected Credit Losses,” to our consolidated financial statements for additional information.


~~ARCH CAPITAL~~			55			~~2021 THIRD QUARTER FORM 10-Q~~

~~Table of Contents~~

Equity in Net Income ~~(Loss)~~or Losses of Investment Funds Accounted for Using the Equity Method.

We recorded ~~$105.4~~a loss of $18.9 million ~~of equity in net income~~ related to investment funds accounted for using the equity method in the ~~2021~~2022 third quarter, compared to an income of ~~$126.7~~$105.4 million for the ~~2020~~2021 third quarter, and ~~$299.3~~$75.5 million ~~of income~~ for the nine months ended September 30, ~~2021,~~2022, compared to ~~income of $57.4~~$299.3 million for the ~~2020~~2021 period. Such investments are generally recorded on a one to three month lag based on the availability of reports from the investment funds. Investment funds accounted for using the equity method totaled ~~$2.7~~$3.6 billion at September 30, ~~2021,~~2022, compared to ~~$2.0~~$3.1 billion at December 31, ~~2020.~~2021. See note 8,7, “Investment Information—Investments Accounted For Using the Equity Method,” to our consolidated financial statements for additional information.

Net Foreign Exchange Gains or Losses.

Net foreign exchange gains for the ~~2021~~2022 third quarter were ~~$36.1~~$90.5 million, compared to net foreign exchange ~~losses~~gains for the ~~2020~~2021 third quarter of ~~$38.7~~$36.1 million. Net foreign exchange gains for the nine months ended September 30, ~~2021~~2022 were ~~$39.7~~$182.1 million, compared to net foreign exchange ~~losses~~gains for the ~~2020~~2021 period of ~~$17.8~~$39.7 million. Amounts in both periods were primarily unrealized and resulted from the effects of revaluing our net insurance liabilities required to be settled in foreign currencies at each balance sheet date.

Income Tax Expense.

Our income tax provision on income (loss) before income taxes, including income (loss) from operating affiliates, resulted in an expense of ~~1.0% for the 2021 third quarter, compared to 5.4% for the 2020 third quarter, and 5.8%~~3.0% for the nine months ended September 30, ~~2021,~~2022, compared to ~~8.3%~~5.8% for the ~~2020~~2021 period. The effective tax ~~rates~~rate for the ~~2021 third quarter and~~ nine months ended September 30, 2022 and 2021 periods included discrete income tax

benefits of ~~$25.3~~$36.5 million and $28.7 million, respectively. The discrete income tax benefits had the effect of decreasing the effective tax rate on net income available to Arch common shareholders by 5.7% and 1.7%, respectively. The discrete tax items in the 2022 and 2021 periods primarily related to the ~~partial release~~releases of a valuation allowance on ~~certain~~ U.K. deferred tax ~~assets in the third quarter.~~assets. Our effective tax rate, which is based upon the expected annual effective tax rate, may fluctuate from period to period based on the relative mix of income or loss reported by jurisdiction and the varying tax rates in each jurisdiction.

Income ~~(loss)~~or Losses from Operating Affiliates.

Income from operating ~~affiliates.~~

~~We recorded~~affiliates for 2022 third quarter was $8.5 million, compared to $124.1 million ~~of net income from our operating affiliates in~~for the 2021 third quarter, ~~compared to income of $0.9~~and $37.7 million ~~for the 2020 third quarter, and $224.1 million of income~~ for the nine months ended September 30, ~~2021,~~2022, compared to ~~$6.3~~$224.1 million for the ~~2020~~2021 period. Results for the 2021 ~~third quarter~~period reflected a one-time gain of $95.7 million ~~recognized from the Company’s previously disclosed~~

~~acquisition of a 40% share of Greysbridge. Results for 2021 period, primarily include income~~and $74.5 million realized from our ~~investment~~investments in Somers and Coface ~~Greysbridge and Premia.~~

~~Other Segment~~

Through June 30, 2021, the ‘other’ segment included the results of Watford. Pursuant to GAAP, Watford was considered a variable interest entity and we concluded that we were the primary beneficiary of Watford. As such, we consolidated the results of Watford in our consolidated financial statements through June 30, 2021. In July 2021, we announced the completion of the previously disclosed acquisition of Watford by Greysbridge. Based on the governing documents of Greysbridge, the Company has concluded that, while it retains significant influence over Watford, Watford no longer constitutes a variable interest entity. Accordingly, effective July 1, 2021, Arch no longer consolidates the results of Watford in its consolidated financial statements.SA, respectively. See note ~~12, “Variable Interest Entities and Noncontrolling Interests”~~ ~~and~~ ~~note 5, “Segment Information”~~7, “Investment Information—Investments in Operating Affiliates,” to our consolidated financial statements for additional ~~information on Watford.~~information.

CRITICAL ACCOUNTING POLICIES,

ESTIMATES AND RECENT ACCOUNTING PRONOUNCEMENTS

Critical accounting policies, estimates and recent accounting pronouncements are discussed in Management’s Discussion and Analysis of Financial Condition and Results of Operations contained in our ~~2020~~2021 Form 10-K, updated where applicable in the notes accompanying our consolidated financial statements, including note 1, “Basis of Presentation and Recent Accounting Pronouncements.”

FINANCIAL CONDITION

Investable Assets Held by Arch

At September 30, 2022, approximately $18.3 billion, or 68.4%, of total investable assets held by Arch were internally managed, compared to $18.5 billion, or 67.3%, at December 31, 2021. See note 7, “Investment Information” to our consolidated financial statements for additional information.

September 30, 2022,

December 31, 2021

Average effective duration (in years)

2.84

2.70

Average S&P/Moody’s credit ratings (1)

AA/Aa2

AA-/Aa3

(1)Average credit ratings on our investment portfolio on securities with ratings assigned by Standard & Poor’s Rating Services (“S&P”) and Moody’s Investors Service (“Moody’s”).


ARCH CAPITAL			5655			~~2021~~2022 THIRD QUARTER FORM 10-Q

Table of Contents

~~FINANCIAL CONDITION~~

~~Investable Assets Held by Arch~~

~~The following table summarizes the fair value of the investable assets held by Arch:~~

Investable assets (1): Estimated
Fair Value % of
Total
September 30, 2021
Fixed maturities (2) $ 17,182,370 63.0
Short-term investments (2) 3,185,646 11.7
Cash 1,137,721 4.2
Equity securities (2) 1,815,163 6.7
Other investments (2) 1,489,759 5.5
Other investable assets (3) — —
Investments accounted for using the equity method 2,741,293 10.0
Securities transactions entered into but not settled at the balance sheet date (273,512) (1.0)
Total investable assets held by Arch $ 27,278,440 100.0
Average effective duration (in years) 2.68
Average S&P/Moody’s credit ratings (4) AA-/Aa3
Embedded book yield (5) 1.54 %
December 31, 2020
Fixed maturities (2) $ 18,771,296 69.9
Short-term investments (2) 2,063,240 7.7
Cash 694,997 2.6
Equity securities (2) 1,436,104 5.3
Other investments (2) 1,480,347 5.5
Other investable assets (3) 500,000 1.9
Investments accounted for using the equity method 2,047,889 7.6
Securities transactions entered into but not settled at the balance sheet date (137,578) (0.5)
Total investable assets held by Arch $ 26,856,295 100.0
Average effective duration (in years) 3.01
Average S&P/Moody’s credit ratings (4) AA/Aa2
Embedded book yield (5) 1.56 %

~~(1)~~In securities lending transactions, we receive collateral in excess of the fair value of the securities pledged. For purposes of this table, we have excluded the collateral received under securities lending, at fair value and included the securities pledged under securities lending, at fair value. In September 2021, the Company terminated its securities lending program.

~~(2)Includes investments carried as available for sale, at fair value and at fair value under the fair value option.~~

~~(3)Represents participation interests in a receivable of a reverse repurchase agreement.~~

~~(4)Average credit ratings on our investment portfolio on securities with ratings by Standard & Poor’s Rating Services (“S&P”) and Moody’s Investors Service (“Moody’s”).~~

~~(5)Before investment expenses.~~

~~At September 30, 2021, approximately $18.4 billion, or 67.3%, of total investable assets held by Arch were internally managed, compared to $19.2 billion, or 71.4%, at December 31, 2020.~~

~~The following table summarizes our fixed maturities and fixed maturities pledged under securities lending agreements (“Fixed Maturities”) by type:~~

Estimated
Fair Value % of
Total
September 30, 2021
Corporate bonds $ 6,777,943 39.4
Residential mortgage backed securities 405,797 2.4
Municipal bonds 382,722 2.2
Commercial mortgage backed securities 579,424 3.4
U.S. government and government agencies 4,460,515 26.0
Non-U.S. government securities 1,883,563 11.0
Asset backed securities 2,692,406 15.7
Total $ 17,182,370 100.0
December 31, 2020
Corporate bonds $ 8,039,745 42.8
Residential mortgage backed securities 616,619 3.3
Municipal bonds 492,734 2.6
Commercial mortgage backed securities 390,990 2.1
U.S. government and government agencies 5,354,863 28.5
Non-U.S. government securities 2,310,157 12.3
Asset backed securities 1,566,188 8.3
Total $ 18,771,296 100.0

The following table provides the credit quality distribution of our ~~Fixed Maturities.~~fixed maturities. 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.


		Estimated Fair Value		% of Total		Estimated Fair Value		% of Total
September 30, 2021
September 30, 2022					September 30, 2022
U.S. government and gov’t agencies (1)	U.S. government and gov’t agencies (1)	$	4,830,467	28.1	U.S. government and gov’t agencies (1)	$	5,746,853	30.8
AAA	AAA	3,257,679		19.0	AAA	3,344,746		17.9
AA	AA	2,217,452		12.9	AA	2,030,730		10.9
A	A	2,773,104		16.1	A	3,382,545		18.1
BBB	BBB	2,807,788		16.3	BBB	3,001,304		16.1
BB	BB	522,357		3.0	BB	532,162		2.9
B	B	348,036		2.0	B	357,543		1.9
Lower than B	Lower than B	43,751		0.3	Lower than B	12,417		0.1
Not rated	Not rated	381,736		2.2	Not rated	242,730		1.3
Total	Total	$	17,182,370	100.0	Total	$	18,651,030	100.0

December 31, 2020
December 31, 2021					December 31, 2021
U.S. government and gov’t agencies (1)	U.S. government and gov’t agencies (1)	$	5,963,758	31.8	U.S. government and gov’t agencies (1)	$	5,063,191	27.5
AAA	AAA	3,117,046		16.6	AAA	3,783,386		20.5
AA	AA	2,063,738		11.0	AA	2,459,413		13.4
A	A	3,760,280		20.0	A	2,943,594		16.0
BBB	BBB	2,699,201		14.4	BBB	2,936,398		15.9
BB	BB	574,189		3.1	BB	501,588		2.7
B	B	268,095		1.4	B	371,747		2.0
Lower than B	Lower than B	54,795		0.3	Lower than B	43,756		0.2
Not rated	Not rated	270,194		1.4	Not rated	311,734		1.7
Total	Total	$	18,771,296	100.0	Total	$	18,414,807	100.0

(1)Includes U.S. government-sponsored agency residential mortgage-backed securities and agency commercial mortgage-backed securities.


~~ARCH CAPITAL~~			57			~~2021 THIRD QUARTER FORM 10-Q~~

~~Table of Contents~~

The following table provides information on the severity of the unrealized loss position as a percentage of amortized cost for all ~~Fixed Maturities~~fixed maturities which were in an unrealized loss position:


Severity of gross unrealized losses:	Severity of gross unrealized losses:	Estimated Fair Value		Gross Unrealized Losses		% of Total Gross Unrealized Losses	Severity of gross unrealized losses:	Estimated Fair Value		Gross Unrealized Losses		% of Total Gross Unrealized Losses
September 30, 2021
September 30, 2022							September 30, 2022
0-10%	0-10%	$	9,287,536	$	(106,042)	93.6	0-10%	$	10,662,904	$	(551,217)	29.6
10-20%	10-20%	27,315		(4,173)		3.7	10-20%	5,851,810		(952,285)		51.2
20-30%	20-30%	8,233		(2,034)		1.8	20-30%	1,070,957		(326,093)		17.5
Greater than 30%	Greater than 30%	993		(1,088)		1.0	Greater than 30%	63,903		(31,059)		1.7
Total	Total	$	9,324,077	$	(113,337)	100.0	Total	$	17,649,574	$	(1,860,654)	100.0

December 31, 2020
December 31, 2021							December 31, 2021
0-10%	0-10%	$	3,583,981	$	(55,542)	79.4	0-10%	$	12,231,146	$	(166,867)	97.6
10-20%	10-20%	95,495		(12,183)		17.4	10-20%	16,884		(2,412)		1.4
20-30%	20-30%	1,061		(406)		0.6	20-30%	2,593		(759)		0.4
Greater than 30%	Greater than 30%	1,249		(1,785)		2.6	Greater than 30%	684		(916)		0.5
Total	Total	$	3,681,786	$	(69,916)	100.0	Total	$	12,251,307	$	(170,954)	100.0

The following table summarizes our top ten exposures to fixed income corporate issuers by fair value at September 30, ~~2021,~~2022, excluding guaranteed amounts and covered bonds:


	Estimated Fair Value		Credit Rating (1)
Bank of America Corporation	$	~~359,893~~430,809	A-/A2
JPMorgan Chase & Co.	~~294,411~~297,868		A-~~/A2~~
~~Citigroup Inc.~~	~~247,892~~		~~BBB+/A3~~
~~Wells Fargo & Company~~	~~231,542~~		~~BBB+~~/A1
Morgan Stanley	~~215,424~~268,742		A-/A1
Citigroup Inc.	260,312		BBB+/A1A3
The Goldman Sachs Group, Inc.	~~180,324~~243,516		BBB+/A2
Wells Fargo & Company	237,947		BBB+/A1
Blackstone Inc.	165,585		BBB/Baa3
Blue Owl Capital Inc.	157,904		BBB-/Baa3
UBS Group AG	125,810		A/Aa3
Dai-ichi Life Holdings, Inc.	~~111,418~~106,357		AA-/A1
~~Apple Inc.~~	~~111,280~~		~~AA+/Aa1~~
~~Westpac Banking Corporation~~	~~107,389~~		~~AA-/Aa3~~
~~Nestlé S.A.~~	~~83,838~~		~~AA-/Aa3~~
Total	$	~~1,943,411~~2,294,850

(1)Average credit ratings as assigned by S&P and Moody’s, respectively.

The following table provides information on our structured securities, which includes residential mortgage-backed securities (“RMBS”), commercial mortgage-backed securities (“CMBS”) and asset-backed securities (“ABS”):


		Agencies		Investment Grade		Below Investment Grade		Total			Agencies		Investment Grade		Below Investment Grade		Total
Sep 30, 2021
September 30, 2022										September 30, 2022
RMBS	RMBS	$	345,175	$	48,301	$	12,321	$	405,797	RMBS	$	602,423	$	143,188	$	17,760	$	763,371
CMBS	CMBS	24,779		502,218		52,427		579,424		CMBS	18,022		957,327		88,889		1,064,238
ABS	ABS	—		2,374,981		317,425		2,692,406		ABS	—		1,410,672		180,970		1,591,642
Total	Total	$	369,954	$	2,925,500	$	382,173	$	3,677,627	Total	$	620,445	$	2,511,187	$	287,619	$	3,419,251

Dec 31, 2020
December 31, 2021										December 31, 2021
RMBS	RMBS	$	584,499	$	4,102	$	28,018	$	616,619	RMBS	$	268,229	$	129,296	$	10,952	$	408,477
CMBS	CMBS	24,396		342,491		24,103		390,990		CMBS	22,198		926,302		97,984		1,046,484
ABS	ABS	—		1,403,137		163,051		1,566,188		ABS	—		2,543,907		152,551		2,696,458
Total	Total	$	608,895	$	1,749,730	$	215,172	$	2,573,797	Total	$	290,427	$	3,599,505	$	261,487	$	4,151,419

The following table summarizes our equity securities, which include investments in exchange traded funds:


		September 30, 2021		December 31, 2020			September 30, 2022		December 31, 2021
Equities (1)	Equities (1)	$	856,837	$	676,437	Equities (1)	$	527,658	$	883,722
Exchange traded funds	Exchange traded funds					Exchange traded funds
Fixed income (2)	Fixed income (2)	348,613		341,139		Fixed income (2)	269,276		455,467
Equity and other (3)	Equity and other (3)	609,713		418,528		Equity and other (3)	26,840		491,474
Total	Total	$	1,815,163	$	1,436,104	Total	$	823,774	$	1,830,663

(1)Primarily in consumer non-cyclical, technology, communications, ~~financial~~consumer cyclical and ~~consumer cyclical~~financial at September 30, ~~2021.~~2022.

(2)Primarily in corporate at September 30, ~~2021.~~2022.

(3)Primarily in large cap stocks, foreign equities, technology, ~~financial~~healthcare and ~~utilities~~consumer discretionary at September 30, ~~2021.~~2022.

~~The following table summarizes~~For details on our other investments and other investable ~~assets:~~

September 30,
2021 December 31,
2020
Lending $ 579,563 $ 572,636
Term loan investments 528,585 380,193
Energy 84,880 65,813
Credit related funds 56,997 90,780
Investment grade fixed income 131,910 138,646
Infrastructure 26,359 165,516
Private equity 81,465 48,750
Real estate — 18,013
Total fair value option $ 1,489,759 $ 1,480,347
Other investable assets — 500,000
Total other investments $ 1,489,759 $ 1,980,347

~~For details on our investments accounted for using the equity method,~~assets, see note 8,7, “Investment Information—~~Investments Accounted For Using the Equity Method,”~~Other Investments” to our consolidated financial statements.


ARCH CAPITAL			5856			~~2021~~2022 THIRD QUARTER FORM 10-Q

Table of Contents

For details on our investments accounted for using the equity method, see note 7, “Investment Information—Investments Accounted For Using the Equity Method,” to our consolidated financial statements.

Our investment strategy allows for the use of derivative instruments. We utilize various derivative instruments such as futures contracts to enhance investment performance, replicate investment positions or manage market exposures and duration risk that would be allowed under our investment guidelines if implemented in other ways. See note ~~10,~~9, “Derivative Instruments,” to our consolidated financial statements for additional disclosures related to derivatives.

Reinsurance

The effects of reinsurance on written and earned premiums and losses and loss adjustment expenses (“LAE”) with unaffiliated reinsurers were as follows:


		Three Months Ended				Nine Months Ended					Three Months Ended				Nine Months Ended
		September 30,				September 30,					September 30,				September 30,
		2021		2020		2021		2020			2022		2021		2022		2021
Premiums written:	Premiums written:									Premiums written:
Direct	Direct	$	1,993,098	$	1,667,449	$	5,795,236	$	4,841,874	Direct	$	2,247,480	$	1,993,098	$	6,503,383	$	5,795,236
Assumed	Assumed	1,214,317		1,013,583		4,095,676		2,989,680		Assumed	1,613,203		1,214,317		5,027,802		4,095,676
Ceded	Ceded	(1,131,486)		(806,888)		(2,907,002)		(2,151,853)		Ceded	(1,136,909)		(1,131,486)		(3,488,632)		(2,907,002)
Net	Net	$	2,075,929	$	1,874,144	$	6,983,910	$	5,679,701	Net	$	2,723,774	$	2,075,929	$	8,042,553	$	6,983,910

Premiums earned:	Premiums earned:									Premiums earned:
Direct	Direct	$	1,754,462	$	1,618,583	$	5,263,286	$	4,723,630	Direct	$	2,067,084	$	1,754,462	$	5,925,934	$	5,263,286
Assumed	Assumed	1,129,434		880,024		3,169,016		2,387,286		Assumed	1,525,027		1,129,434		4,037,580		3,169,016
Ceded	Ceded	(954,559)		(727,515)		(2,433,634)		(1,930,026)		Ceded	(1,121,361)		(954,559)		(3,046,356)		(2,433,634)
Net	Net	$	1,929,337	$	1,771,092	$	5,998,668	$	5,180,890	Net	$	2,470,750	$	1,929,337	$	6,917,158	$	5,998,668

Losses and LAE:	Losses and LAE:									Losses and LAE:
Direct	Direct	$	1,101,793	$	1,131,696	$	3,134,305	$	3,279,737	Direct	$	1,228,281	$	1,101,793	$	3,016,634	$	3,134,305
Assumed	Assumed	961,285		635,199		2,182,852		1,689,176		Assumed	1,370,308		961,285		2,661,854		2,182,852
Ceded	Ceded	(837,059)		(550,622)		(1,728,207)		(1,406,699)		Ceded	(915,893)		(837,059)		(1,892,301)		(1,728,207)
Net	Net	$	1,226,019	$	1,216,273	$	3,588,950	$	3,562,214	Net	$	1,682,696	$	1,226,019	$	3,786,187	$	3,588,950

See note 7,6, “Allowance for Expected Credit Losses,” to our consolidated financial statements for information about our reinsurance recoverables and related allowance for credit losses.

Bellemeade Re

We have entered into aggregate excess of loss mortgage reinsurance agreements with various special purpose reinsurance companies domiciled in Bermuda (the “Bellemeade Agreements”). For the respective coverage periods, we will retain the first layer of the respective aggregate losses and the special purpose reinsurance companies will provide second layer coverage up to the outstanding coverage amount. We will then retain losses in excess of the outstanding coverage limit. The aggregate excess of loss reinsurance coverage generally decreases over a ten-year period as the underlying covered mortgages amortize, unless provisional call options embedded within certain of the Bellemeade Agreements are executed or if pre-defined delinquency triggering events occur.

The following table summarizes the respective coverages and retentions at September 30, ~~2021:~~2022:

September 30, 2021
Initial Coverage at Issuance Current Coverage Remaining Retention, Net
Bellemeade 2017-1 Ltd. (1) $ 368,114 $ 145,573 $ 124,777
Bellemeade 2018-1 Ltd. (2) 374,460 228,938 121,411
Bellemeade 2018-3 Ltd. (3) 506,110 302,563 126,578
Bellemeade 2019-1 Ltd. (4) 341,790 210,529 98,340
Bellemeade 2019-2 Ltd. (5) 621,022 398,316 156,085
Bellemeade 2019-3 Ltd. (6) 700,920 491,634 178,759
Bellemeade 2019-4 Ltd. (7) 577,267 468,737 113,674
Bellemeade 2020-2 Ltd. (8) 449,167 268,468 227,140
Bellemeade 2020-3 Ltd. (9) 451,816 405,881 159,615
Bellemeade 2020-4 Ltd. (10) 337,013 238,480 133,872
Bellemeade 2021-1 Ltd. (11) 643,577 643,577 157,685
Bellemeade 2021-2 Ltd. (12) 616,017 616,017 146,956
Bellemeade 2021-3 Ltd. (13) 639,391 639,391 145,790
Total $ 6,626,664 $ 5,058,104 $ 1,890,682


Bellemeade Entities (Issue Date)	Initial Coverage at Issuance		Current Coverage		Remaining Retention, Net
2017-1 Ltd. (1)	$	368,114	$	46,772	$	137,613
2018-1 Ltd. (2)	374,460		103,131		136,200
2018-3 Ltd. (3)	506,110		217,701		143,738
2019-1 Ltd. (4)	341,790		119,193		109,450
2019-2 Ltd. (5)	621,022		347,050		182,251
2019-3 Ltd. (6)	700,920		257,663		203,047
2019-4 Ltd. (7)	577,267		283,684		136,334
2020-2 Ltd. (8)	449,167		123,049		233,262
2020-3 Ltd. (9)	451,816		276,954		159,632
2020-4 Ltd. (10)	337,013		112,191		137,694
2021-1 Ltd. (11)	643,577		540,267		152,499
2021-2 Ltd. (12)	616,017		551,307		140,012
2021-3 Ltd. (13)	639,391		627,436		136,033
2022-1 Ltd. (14)	316,760		316,760		150,269
2022-2 Ltd. (15)	327,165		327,165		222,386
Total	$	7,270,589	$	4,250,323	$	2,380,420

(1) Issued in October 2017, covering in-force policies issued between January 1, 2017 and June 30, 2017.

(2) Issued in April 2018, covering in-force policies issued between July 1, 2017 and December 31, 2017.

(3) Issued in October 2018, covering in-force policies issued between January 1, 2018 and June 30, 2018.

(4) Issued in March 2019, covering in-force policies primarily issued between 2005-2008 under United Guaranty Residential Insurance Company (“UGRIC”); as well as policies issued through 2015 under both UGRIC and Arch Mortgage Insurance Company.

(5) Issued in April 2019, covering in-force policies issued between July 1, 2018 and December 31, 2018.

(6) Issued in July 2019, covering in-force policies issued in 2016.

(7) Issued in October 2019, covering in-force policies issued between January 1, 2019 and June 30, 2019.

(8) Issued in September 2020, covering in-force policies issued between January 1, 2020 and May 31, 2020. $423 million was directly funded by Bellemeade 2020-2 Ltd. with an additional $26 million of capacity provided directly to Arch MI U.S. by a separate panel of reinsurers.


ARCH CAPITAL			5957			~~2021~~2022 THIRD QUARTER FORM 10-Q

Table of Contents

(9) Issued in November 2020, covering in-force policies issued between June 1, 2020 and August 31, 2020. $418 million was directly funded by Bellemeade 2020-3 Ltd. with an additional $34 million of capacity provided directly to Arch MI U.S. by a separate panel of reinsurers.

(10) Issued in December 2020, covering in-force policies issued between July 1, 2019 and December 31, 2019. $321 million was directly funded by Bellemeade 2020-4 Ltd. with an additional $16 million of capacity provided directly to Arch MI U.S. by a separate panel of reinsurers.

(11) Issued in March 2021, covering in-force policies issued between September 1, 2020 and November 30, 2020. $580 million was directly funded by Bellemeade Re 2021-1 Ltd. with an additional $64 million capacity provided directly to Arch MI U.S. by a separate panel of reinsurers.

(12) Issued in June 2021, covering in-force policies issued between December 1, 2020 and March 31, 2021. $523 million was directly funded by Bellemeade Re 2021-2 Ltd. via insurance-linked notes, with an additional $93 million capacity provided directly to Arch MI U.S. by a separate panel of reinsurers.

(13) Issued in September 2021, covering in-force policies issued between April 1, 2021 and June 30, 2021. $508 million was directly funded by Bellemeade Re 2021-3 Ltd. via insurance-linked notes, with an additional $131 million capacity provided directly to Arch MI U.S. by a separate panel of reinsurers.

(14) Issued in January 2022, covering in-force policies issued between July 1, 2021 and November 30, 2021. $284 million was directly funded by Bellemeade Re 2022-1 Ltd. via insurance-linked notes, with an additional $33 million capacity provided directly to Arch MI U.S. by a separate panel of reinsurers.

(15) Issued in September 2022, covering in-force policies issued between November 1, 2021 and June 30, 2022. $201 million was directly funded by Bellemeade Re 2022-2 Ltd. via insurance-linked notes, with an additional $126 million capacity provided directly to Arch MI U.S. by a separate panel of reinsurers.

Reserve for Losses and Loss Adjustment Expenses

We establish reserve for losses and loss adjustment expenses (“Loss Reserves”) which represent estimates involving actuarial and statistical projections, at a given point in time, of our expectations of the ultimate settlement and administration costs of losses incurred. Estimating Loss Reserves is inherently difficult. We utilize actuarial models as well as available historical insurance industry loss ratio experience and loss development patterns to assist in the establishment of Loss Reserves. Actual losses and loss adjustment expenses paid will deviate, perhaps substantially, from the reserve estimates reflected in our financial statements.

At September 30, ~~2021~~2022 and December 31, ~~2020,~~2021, our Loss Reserves, net of unpaid losses and loss adjustment expenses recoverable, by type and by operating segment were as follows:


		September 30, 2021		December 31, 2020			September 30, 2022		December 31, 2021
Insurance segment:	Insurance segment:					Insurance segment:
Case reserves	Case reserves	$	2,147,930	$	2,051,640	Case reserves	$	2,214,924	$	2,102,891
IBNR reserves	IBNR reserves	4,341,016		3,889,823		IBNR reserves	4,797,323		4,269,904
Total net reserves	Total net reserves	6,488,946		5,941,463		Total net reserves	7,012,247		6,372,795
Reinsurance segment:	Reinsurance segment:					Reinsurance segment:
Case reserves	Case reserves	1,562,072		1,560,523		Case reserves	1,720,426		1,733,571
Additional case reserves	Additional case reserves	549,476		280,472		Additional case reserves	583,197		426,531
IBNR reserves	IBNR reserves	2,617,728		2,253,953		IBNR reserves	3,100,704		2,656,527
Total net reserves	Total net reserves	4,729,276		4,094,948		Total net reserves	5,404,327		4,816,629
Mortgage segment:	Mortgage segment:					Mortgage segment:
Case reserves	Case reserves	731,671		631,921		Case reserves	542,975		741,897
IBNR reserves	IBNR reserves	266,007		271,702		IBNR reserves	222,194		226,604
Total net reserves	Total net reserves	997,678		903,623		Total net reserves	765,169		968,501
Other segment:
Case reserves		—		566,587
Additional case reserves		—		32,321
IBNR reserves		—		660,132
Total net reserves		—		1,259,040

Total:	Total:					Total:
Case reserves	Case reserves	4,441,673		4,810,671		Case reserves	4,478,325		4,578,359
Additional case reserves	Additional case reserves	549,476		312,793		Additional case reserves	583,197		426,531
IBNR reserves	IBNR reserves	7,224,751		7,075,610		IBNR reserves	8,120,221		7,153,035
Total net reserves	Total net reserves	$	12,215,900	$	12,199,074	Total net reserves	$	13,181,743	$	12,157,925

At September 30, ~~2021~~2022 and December 31, ~~2020,~~2021, the insurance segment’s Loss Reserves by major line of business, net of unpaid losses and loss adjustment expenses recoverable, were as follows:


		September 30, 2021		December 31, 2020			September 30, 2022		December 31, 2021
Insurance segment:	Insurance segment:					Insurance segment:
Professional lines ~~(1)~~	Professional lines ~~(1)~~	$	1,587,042	$	1,482,820	Professional lines ~~(1)~~	$	1,888,083	$	1,673,615
Construction and national accounts	Construction and national accounts	1,468,668		1,395,067		Construction and national accounts	1,559,888		1,490,206
Excess and surplus casualty (2)		903,966		816,495
Programs	Programs	760,273		699,354		Programs	846,580		793,187
Excess and surplus casualty						Excess and surplus casualty	739,676		657,307
Property, energy, marine and aviation	Property, energy, marine and aviation	599,431		517,692		Property, energy, marine and aviation	713,021		599,093
Travel, accident and health	Travel, accident and health	93,632		98,910		Travel, accident and health	132,337		96,051
Lenders products	Lenders products	70,520		48,946		Lenders products	40,960		58,351
Other ~~(3)~~	Other ~~(3)~~	1,005,414		882,179		Other ~~(3)~~	1,091,702		1,004,985
Total net reserves	Total net reserves	$	6,488,946	$	5,941,463	Total net reserves	$	7,012,247	$	6,372,795

~~(1)Includes professional liability, executive assurance and healthcare business.~~

~~(2)Includes casualty and contract binding business.~~

~~(3)Includes alternative markets, excess workers’ compensation and surety business.~~


~~ARCH CAPITAL~~			60			~~2021 THIRD QUARTER FORM 10-Q~~

~~Table of Contents~~

At September 30, ~~2021~~2022 and December 31, ~~2020,~~2021, the reinsurance segment’s Loss Reserves by major line of business, net of unpaid losses and loss adjustment expenses recoverable, were as follows:


		September 30, 2021		December 31, 2020			September 30, 2022		December 31, 2021
Reinsurance segment:	Reinsurance segment:					Reinsurance segment:
Casualty ~~(1)~~	Casualty ~~(1)~~	$	2,079,990	$	1,995,849	Casualty ~~(1)~~	$	2,223,204	$	2,123,360
Other specialty ~~(2)~~	Other specialty ~~(2)~~	1,093,611		917,178		Other specialty ~~(2)~~	1,215,362		1,113,766
Property excluding property catastrophe	Property excluding property catastrophe	669,922		594,033		Property excluding property catastrophe	971,430		711,859
Property catastrophe						Property catastrophe	586,249		486,911
Marine and aviation	Marine and aviation	231,203		204,205		Marine and aviation	270,574		246,861
Property catastrophe		526,356		268,858
Other ~~(3)~~	Other ~~(3)~~	128,194		114,825		Other ~~(3)~~	137,508		133,872
Total net reserves	Total net reserves	$	4,729,276	$	4,094,948	Total net reserves	$	5,404,327	$	4,816,629


ARCH CAPITAL			58			2022 THIRD QUARTER FORM 10-Q

~~(1)Includes executive assurance, professional liability, workers’ compensation, excess motor, healthcare and other.~~Table of Contents

~~(2)Includes non-excess motor, surety, accident and health, workers’ compensation catastrophe, agriculture, trade credit and other.~~

~~(3)Includes life, casualty clash and other.~~

At September 30, ~~2021~~2022 and December 31, ~~2020,~~2021, the mortgage segment’s Loss Reserves by major line of business, net of unpaid losses and loss adjustment expenses recoverable, were as follows:


		September 30, 2021		December 31, 2020			September 30, 2022		December 31, 2021
U.S. primary mortgage insurance (1)	U.S. primary mortgage insurance (1)	$	726,636	$	649,748	U.S. primary mortgage insurance (1)	$	545,577	$	710,708
Other		271,042		253,875
U.S. credit risk transfer (CRT) and other						U.S. credit risk transfer (CRT) and other	108,667		112,549
International mortgage insurance/ reinsurance						International mortgage insurance/ reinsurance	110,925		145,244
Total net reserves	Total net reserves	$	997,678	$	903,623	Total net reserves	$	765,169	$	968,501

(1) At September 30, ~~2021, 27.9%~~2022, 34.9% of total net reserves represents policy years ~~2011~~2012 and prior and the remainder from later policy years. At December 31, ~~2020, 28.3%~~2021, 27.9% of total net reserves represent policy years ~~2011~~2012 and prior and the remainder from later policy years.

Mortgage Operations Supplemental Information

The mortgage segment’s insurance in force (“IIF”) and risk in force (“RIF”) were as follows at September 30, ~~2021~~2022 and December 31, ~~2020:~~2021:


(U.S. Dollars in millions)	(U.S. Dollars in millions)	September 30, 2021			December 31, 2020			(U.S. Dollars in millions)	September 30, 2022			December 31, 2021
		Amount		%	Amount		%		Amount		%	Amount		%
Insurance In Force (IIF) (1):	Insurance In Force (IIF) (1):							Insurance In Force (IIF) (1):
U.S. primary mortgage insurance	U.S. primary mortgage insurance	$	280,379	61.3	$	280,579	66.2	U.S. primary mortgage insurance	$	294,857	58.8	$	280,945	61.0
U.S. credit risk transfer (CRT) and other (2)	U.S. credit risk transfer (CRT) and other (2)	108,203		23.6	103,535		24.4	U.S. credit risk transfer (CRT) and other (2)	143,897		28.7	110,018		23.9
International mortgage insurance/reinsurance (3)	International mortgage insurance/reinsurance (3)	69,127		15.1	39,425		9.3	International mortgage insurance/reinsurance (3)	63,068		12.6	69,655		15.1
Total	Total	$	457,709	100.0	$	423,539	100.0	Total	$	501,822	100.0	$	460,618	100.0

Risk In Force (RIF) (4):	Risk In Force (RIF) (4):							Risk In Force (RIF) (4):
U.S. primary mortgage insurance	U.S. primary mortgage insurance	$	70,320	84.8	$	70,522	90.5	U.S. primary mortgage insurance	$	75,343	85.1	$	70,619	84.3
U.S. credit risk transfer (CRT) and other (2)	U.S. credit risk transfer (CRT) and other (2)	4,817		5.8	4,699		6.0	U.S. credit risk transfer (CRT) and other (2)	6,473		7.3	5,120		6.1
International mortgage insurance/reinsurance (3)	International mortgage insurance/reinsurance (3)	7,803		9.4	2,673		3.4	International mortgage insurance/reinsurance (3)	6,727		7.6	7,983		9.5
Total	Total	$	82,940	100.0	$	77,894	100.0	Total	$	88,543	100.0	$	83,722	100.0

(1)Represents the aggregate dollar amount of each insured mortgage loan’s current principal balance.

(2)Includes all CRT transactions, which are predominantly with GSEs, and other U.S. reinsurance transactions.

(3)International mortgage insurance and reinsurance with risk primarily located in Australia ~~which reflects WLMI acquisition in the 2021 third quarter~~ and to lesser extent Europe and Asia.

(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.

The IIF and RIF for our U.S. primary mortgage insurance business by policy year were as follows at September 30, 2022:


(U.S. Dollars in millions)	IIF			RIF			Delinquency
	Amount		%	Amount		%	Rate (1)
Policy year:
2012 and prior	$	10,362	3.5	$	2,509	3.3	8.22	%
2013	3,196		1.1	855		1.1	2.12	%
2014	3,903		1.3	1,071		1.4	2.61	%
2015	6,607		2.2	1,780		2.4	2.11	%
2016	11,021		3.7	2,953		3.9	2.47	%
2017	10,017		3.4	2,654		3.5	3.27	%
2018	10,744		3.6	2,742		3.6	3.95	%
2019	19,961		6.8	5,038		6.7	2.24	%
2020	68,974		23.4	17,294		23.0	0.87	%
2021	91,486		31.0	23,152		30.7	0.66	%
2022	58,586		19.9	15,295		20.3	0.17	%
Total	$	294,857	100.0	$	75,343	100.0	1.73	%

(1)Represents the ending percentage of loans in default.

The IIF and RIF for our U.S. primary mortgage insurance business by policy year were as follows at December 31, 2021:


(U.S. Dollars in millions)	(U.S. Dollars in millions)	IIF			RIF			Delinquency		(U.S. Dollars in millions)	IIF			RIF			Delinquency
		Amount		%	Amount		%	Rate (1)			Amount		%	Amount		%	Rate (1)
Policy year:	Policy year:									Policy year:
2011 and prior		$	11,888	4.2	$	2,672	3.8	9.51	%
2012		1,974		0.7	505		0.7	2.76	%
2012 and prior										2012 and prior	$	13,030	4.6	$	2,960	4.2	8.48	%
2013	2013	4,876		1.7	1,342		1.9	2.72	%	2013	4,206		1.5	1,148		1.6	2.63	%
2014	2014	5,454		1.9	1,501		2.1	3.37	%	2014	4,822		1.7	1,328		1.9	3.14	%
2015	2015	9,810		3.5	2,637		3.8	2.92	%	2015	8,703		3.1	2,340		3.3	2.67	%
2016	2016	16,150		5.8	4,324		6.1	3.64	%	2016	14,344		5.1	3,841		5.4	3.29	%
2017	2017	15,001		5.4	3,910		5.6	4.50	%	2017	13,128		4.7	3,436		4.9	4.09	%
2018	2018	16,193		5.8	4,105		5.8	5.75	%	2018	14,046		5.0	3,562		5.0	5.28	%
2019	2019	29,860		10.6	7,463		10.6	3.58	%	2019	25,841		9.2	6,467		9.2	3.13	%
2020	2020	88,737		31.6	21,777		31.0	0.91	%	2020	82,502		29.4	20,341		28.8	0.97	%
2021	2021	80,436		28.7	20,084		28.6	0.19	%	2021	100,323		35.7	25,196		35.7	0.29	%

Total	Total	$	280,379	100.0	$	70,320	100.0	2.67	%	Total	$	280,945	100.0	$	70,619	100.0	2.36	%

(1)Represents the ending percentage of loans in default.


ARCH CAPITAL			6159			~~2021~~2022 THIRD QUARTER FORM 10-Q

Table of Contents

~~The IIF and RIF for our U.S. primary mortgage insurance business by policy year were as follows at December 31, 2020:~~

(U.S. Dollars in millions) IIF RIF Delinquency
Amount % Amount % Rate (1)
Policy year:
2011 and prior $ 14,588 5.2 $ 3,327 4.7 11.36 %
2012 3,651 1.3 992 1.4 2.98 %
2013 7,546 2.7 2,107 3.0 3.30 %
2014 8,261 2.9 2,273 3.2 4.06 %
2015 15,032 5.4 4,048 5.7 3.72 %
2016 24,958 8.9 6,648 9.4 4.77 %
2017 24,748 8.8 6,413 9.1 5.52 %
2018 27,304 9.7 6,918 9.8 6.76 %
2019 48,304 17.2 12,001 17.0 4.61 %
2020 106,187 37.8 25,795 36.6 0.76 %
Total $ 280,579 100.0 $ 70,522 100.0 4.19 %

~~(1)Represents the ending percentage of loans in default.~~

The following tables provide supplemental disclosures on risk in force for our U.S. primary mortgage insurance business at September 30, ~~2021~~2022 and December 31, ~~2020:~~2021:


(U.S. Dollars in millions)	(U.S. Dollars in millions)	September 30, 2021				December 31, 2020				(U.S. Dollars in millions)	September 30, 2022				December 31, 2021
		Amount			%	Amount			%		Amount			%	Amount			%
Credit quality (FICO):	Credit quality (FICO):									Credit quality (FICO):
>=740	>=740	$	41,927		59.6	$	40,774		57.8	>=740	$	46,538		61.8	$	42,451		60.1
680-739	680-739	23,732			33.7	24,498			34.7	680-739	24,671			32.7	23,646			33.5
620-679	620-679	4,323			6.1	4,837			6.9	620-679	3,850			5.1	4,196			5.9
<620	<620	338			0.5	413			0.6	<620	284			0.4	326			0.5
Total	Total	$	70,320		100.0	$	70,522		100.0	Total	$	75,343		100.0	$	70,619		100.0
Weighted average FICO score	Weighted average FICO score	745				743				Weighted average FICO score	748				746

Loan-to-value (LTV):	Loan-to-value (LTV):									Loan-to-value (LTV):
95.01% and above	95.01% and above	$	7,708		11.0	$	8,643		12.3	95.01% and above	$	7,334		9.7	$	7,538		10.7
90.01% to 95.00%	90.01% to 95.00%	38,378			54.6	37,877			53.7	90.01% to 95.00%	43,049			57.1	38,829			55.0
85.01% to 90.00%	85.01% to 90.00%	19,980			28.4	20,013			28.4	85.01% to 90.00%	20,876			27.7	20,006			28.3
85.00% and below	85.00% and below	4,254			6.0	3,989			5.7	85.00% and below	4,084			5.4	4,246			6.0
Total	Total	$	70,320		100.0	$	70,522		100.0	Total	$	75,343		100.0	$	70,619		100.0
Weighted average LTV	Weighted average LTV	92.8		%		92.8		%		Weighted average LTV	92.9		%		92.8		%

Total RIF, net of external reinsurance	Total RIF, net of external reinsurance	$	54,847			$	56,658			Total RIF, net of external reinsurance	$	56,890			$	54,574


(U.S. Dollars in millions)	September 30, 2022			December 31, 2021
	Amount		%	Amount		%
Total RIF by State:
California	$	6,219	8.3	$	5,559	7.9
Texas	6,080		8.1	5,594		7.9
Florida	3,275		4.3	3,303		4.7
Georgia	3,150		4.2	2,902		4.1
North Carolina	3,139		4.2	2,921		4.1
Illinois	3,087		4.1	2,933		4.2
Minnesota	2,996		4.0	2,916		4.1
Massachusetts	2,771		3.7	2,537		3.6
Virginia	2,647		3.5	2,446		3.5
Michigan	2,587		3.4	2,492		3.5
Other	39,392		52.3	37,016		52.4
Total	$	75,343	100.0	$	70,619	100.0

(U.S. Dollars in millions) September 30, 2021 December 31, 2020
Amount % Amount %
Total RIF by State:
Texas $ 5,590 7.9 $ 5,636 8.0
California 5,451 7.8 5,261 7.5
Florida 3,344 4.8 3,632 5.2
Minnesota 2,936 4.2 2,520 3.6
North Carolina 2,921 4.2 2,622 3.7
Illinois 2,920 4.2 2,762 3.9
Georgia 2,908 4.1 2,959 4.2
Massachusetts 2,519 3.6 2,464 3.5
Virginia 2,412 3.4 2,526 3.6
Ohio 2,263 3.2 2,264 3.2
Other 37,056 52.7 37,876 53.7
Total $ 70,320 100.0 $ 70,522 100.0

The following table provides supplemental disclosures for our U.S. primary mortgage insurance business related to insured loans and loss metrics:


(U.S. Dollars in thousands, except policy, loan and claim count)	(U.S. Dollars in thousands, except policy, loan and claim count)	Nine Months Ended						(U.S. Dollars in thousands, except policy, loan and claim count)	Nine Months Ended
		September 30,							September 30,
		2021			2020				2022			2021
Roll-forward of insured loans in default:	Roll-forward of insured loans in default:							Roll-forward of insured loans in default:
Beginning delinquent number of loans	Beginning delinquent number of loans	52,234			20,163			Beginning delinquent number of loans	27,645			52,234
New notices	New notices	26,483			87,760			New notices	26,328			26,483
Cures	Cures	(46,334)			(48,234)			Cures	(33,225)			(46,334)
Paid claims	Paid claims	(613)			(1,327)			Paid claims	(534)			(613)

Ending delinquent number of loans (1)	Ending delinquent number of loans (1)	31,770			58,362			Ending delinquent number of loans (1)	20,214			31,770

Ending number of policies in force (1)	Ending number of policies in force (1)	1,188,768			1,245,408			Ending number of policies in force (1)	1,168,735			1,188,768

Delinquency rate (1)	Delinquency rate (1)	2.67		%	4.69		%	Delinquency rate (1)	1.73		%	2.67		%

Losses:	Losses:							Losses:
Number of claims paid	Number of claims paid	613			1,327			Number of claims paid	534			613
Total paid claims	Total paid claims	$	22,848		$	55,559		Total paid claims	$	16,865		$	22,848
Average per claim	Average per claim	$	37.3		$	41.9		Average per claim	$	31.6		$	37.3
Severity (2)	Severity (2)	80.2		%	93.3		%	Severity (2)	74.3		%	80.2		%
Average case reserve per default (in thousands)(1)	Average case reserve per default (in thousands)(1)	$	23.5		$	10.1		Average case reserve per default (in thousands)(1)	$	27.7		$	23.5

(1)Includes first lien primary and pool policies.

(2)Represents total paid claims divided by RIF of loans for which claims were paid.

The risk to capital ratio, which represents total current (non-delinquent) risk in force, net of reinsurance, divided by total statutory capital, for Arch MI U.S. was approximately ~~8.6~~7.6 to 1 at September 30, ~~2021,~~2022, compared to ~~9.3~~8 to 1 at December 31, ~~2020.~~2021.

Shareholders’ Equity and Book Value per Share

The following table presents the calculation of book value per share:


(U.S. dollars in thousands, except share data)	September 30, 2022		December 31, 2021
Total shareholders’ equity available to Arch	$	11,795,110	$	13,545,896
Less preferred shareholders’ equity	830,000		830,000
Common shareholders’ equity available to Arch	$	10,965,110	$	12,715,896
Common shares and common share equivalents outstanding, net of treasury shares (1)	369,321,990		378,923,894
Book value per share	$	29.69	$	33.56

(1)Excludes the effects of 15,628,546 and 17,083,160 stock options and 560,945 and 729,636 restricted stock units outstanding at September 30, 2022 and December 31, 2021, respectively.


ARCH CAPITAL			6260			~~2021~~2022 THIRD QUARTER FORM 10-Q

Table of Contents

~~Shareholders’ Equity and Book Value per Share~~

~~The following table presents the calculation of book value per share:~~

(U.S. dollars in thousands, except
share data) September 30,
2021 December 31,
2020
Total shareholders’ equity available to Arch $ 13,387,526 $ 13,105,886
Less preferred shareholders’ equity 830,000 780,000
Common shareholders’ equity available to Arch $ 12,557,526 $ 12,325,886
Common shares and common share equivalents outstanding, net of treasury shares (1) 387,257,752 406,720,642
Book value per share $ 32.43 $ 30.31

~~(1)Excludes the effects of 17,419,530 and 17,839,333 stock options and 739,407 and 1,153,784 restricted stock units outstanding at September 30, 2021 and December 31, 2020, respectively.~~

LIQUIDITY

Liquidity is a measure of our ability to access sufficient cash flows to meet the short-term and long-term cash requirements of our business operations.

Arch Capital is a holding company whose assets primarily consist of the shares in its subsidiaries. Generally, Arch Capital depends on its available cash resources, liquid investments and dividends or other distributions from its subsidiaries to make payments, including the payment of debt service obligations and operating expenses it may incur and any dividends or liquidation amounts with respect to our preferred and common shares.

For the nine months ended September 30, ~~2021,~~2022, Arch Capital received dividends of ~~$1.4 billion~~$735.3 million from Arch Reinsurance Ltd. (“Arch Re Bermuda”), our Bermuda ~~our Bermuda-based~~based reinsurer and insurer which can pay approximately ~~$2.3~~$3.1 billion to Arch Capital during the remainder of ~~2021~~2022 without providing an affidavit to the Bermuda Monetary ~~Authority (“BMA”).~~Authority.

For the nine months ended September 30, 2021, Arch-U.S. received $200.0 million of dividends from Arch U.S. MI Holdings Inc., a subsidiary of Arch-U.S., which received a total of $300.0 million of ordinary and extraordinary dividends, $140 million from United Guaranty Residential Insurance Company (“UGRIC”) and $160 million from Arch Mortgage Insurance Company (“AMIC”). UGRIC and AMIC have minimal ordinary dividend capacity remaining for the remainder of 2021.

~~In June 2021, Arch Capital completed a $500.0 million underwritten public offering of 20.0 million depositary shares, each of which represents a 1/1,000th interest in a~~

~~share of its 4.550% Non-Cumulative Preferred Shares.~~ ~~See note 3, “Share Transactions.”~~

We expect that our liquidity needs, including our anticipated (re)insurance obligations and operating and capital expenditure needs, for at least the next twelve months and thereafter for the forseable future, will be met by funds generated from underwriting activities and investment income, as well as by our balance of cash, short-term investments, proceeds on the sale or maturity of our investments, and our credit facilities. On April 7, 2022 Arch Capital and certain of its subsidiaries amended the existing credit agreement. For details on our credit agreement, see note 10, “Commitments and Contingencies” to our consolidated financial statements.

Cash Flows

The following table summarizes our cash flows from operating, investing and financing activities.

Nine Months Ended
September 30,
2021 2020
Total cash provided by (used for):
Operating activities $ 2,580,697 $ 2,198,037
Investing activities (1,184,436) (2,850,392)
Financing activities (895,943) 845,612
Effects of exchange rate changes on foreign currency cash (30,501) (2,878)
Increase (decrease) in cash and restricted cash $ 469,817 $ 190,379


	Nine Months Ended
	September 30,
	2022		2021
Total cash provided by (used for):
Operating activities	$	2,833,717	$	2,580,697
Investing activities	(2,106,721)		(1,184,436)
Financing activities	(703,877)		(895,943)
Effects of exchange rate changes on foreign currency cash	(79,566)		(30,501)
Increase (decrease) in cash and restricted cash	$	(56,447)	$	469,817

•Cash provided by operating activities for the nine months ended September 30, ~~2021~~2022 primarily reflected a higher level ~~of premiums collected~~premium volume than in the ~~2020~~2021 period.

•Cash used for investing activities for the nine months ended September 30, ~~2021~~2022 was ~~lower~~higher than in the ~~2020~~2021 period. Activity for the ~~nine months ended September 30,~~2022 period reflected a lower level of proceeds from sales and redemptions of fixed

income securities. Activity for the 2021 period reflected cash used to ~~purchase our non-controlling interest~~invest in Coface and ~~Watford, while the 2020 period reflected a higher level of securities purchased, and the investing of proceeds from our issuance of the senior notes.~~Somers.

•Cash used for financing activities for the nine months ended September 30, ~~2021~~2022 reflected ~~$485.8 million inflow from issuance of preferred shares, $450.0 million related to redemption of our Series E preferred shares and $872.2~~$585.8 million of repurchases under our share repurchase program. Activity for the ~~2020~~2021 period, ~~primarily~~ reflected ~~the issuance of $1.0 billion of our senior notes and $75.5~~$872.2 million of repurchases under our share repurchase program.


~~ARCH CAPITAL~~			63			~~2021 THIRD QUARTER FORM 10-Q~~

~~Table of Contents~~

CAPITAL RESOURCES

The following table provides an analysis of our capital structure:


(U.S. dollars in thousands, except share data)	(U.S. dollars in thousands, except share data)	Sep 30, 2021		Dec 31, 2020		(U.S. dollars in thousands, except share data)	September 30, 2022		December 31, 2021

Senior notes	Senior notes	$	2,724,149	$	2,723,423	Senior notes	$	2,725,153	$	2,724,394

Shareholders’ equity available to Arch:	Shareholders’ equity available to Arch:					Shareholders’ equity available to Arch:
Series E non-cumulative preferred shares		$	—	$	450,000

Series F non-cumulative preferred shares	Series F non-cumulative preferred shares	330,000		330,000		Series F non-cumulative preferred shares	330,000		330,000
Series G non-cumulative preferred shares	Series G non-cumulative preferred shares	500,000		—		Series G non-cumulative preferred shares	500,000		500,000
Common shareholders’ equity	Common shareholders’ equity	12,557,526		12,325,886		Common shareholders’ equity	10,965,110		12,715,896
Total	Total	$	13,387,526	$	13,105,886	Total	$	11,795,110	$	13,545,896

Total capital available to Arch	Total capital available to Arch	$	16,111,675	$	15,829,309	Total capital available to Arch	$	14,520,263	$	16,270,290

Debt to total capital (%)	Debt to total capital (%)	16.9		17.2		Debt to total capital (%)	18.8		16.7
Preferred to total capital (%)	Preferred to total capital (%)	5.2		4.9		Preferred to total capital (%)	5.7		5.1
Debt and preferred to total capital (%)	Debt and preferred to total capital (%)	22.1		22.1		Debt and preferred to total capital (%)	24.5		21.8

Arch MI U.S. is required to maintain compliance with the GSEs requirements, known as the Private Mortgage Insurer Eligibility Requirements or “PMIERs.” The financial requirements require an eligible mortgage insurer’s available assets, which generally include only the most liquid assets of an insurer, to meet or exceed “minimum required assets” as of each quarter end. Minimum required assets are calculated from PMIERs tables with several risk dimensions (including origination year, original loan-to-value and original credit score of performing loans, and the delinquency status of non-performing loans) and are subject to a minimum amount. Arch MI U.S. satisfied the PMIERs’ financial requirements as of September 30, ~~2021~~2022 with an estimated PMIER sufficiency ratio of ~~195%~~237%, compared to ~~173%~~197% at December 31, ~~2020.~~2021.

Arch Capital, through its subsidiaries, provides financial support to certain of its insurance subsidiaries and affiliates, through certain reinsurance arrangements beneficial to the ratings of such subsidiaries. Historically, our insurance, reinsurance and mortgage insurance subsidiaries have entered into separate reinsurance arrangements with Arch Re Bermuda covering individual lines of business. ~~The reinsurance agreements between our U.S.-based property casualty insurance and reinsurance subsidiaries and Arch Re~~


ARCH CAPITAL			61			2022 THIRD QUARTER FORM 10-Q

Table of Contents

~~Bermuda were canceled on a cutoff basis as of January 1, 2018. In 2019, certain reinsurance agreements between our insurance subsidiaries and Arch Re Bermuda were reinstated.~~

GUARANTOR INFORMATION

The below table provides a description of our senior notes payable at September 30, ~~2021:~~2022:


		Interest		Principal		Carrying			Interest		Principal		Carrying
Issuer/Due	Issuer/Due	(Fixed)		Amount		Amount		Issuer/Due	(Fixed)		Amount		Amount
Arch Capital:	Arch Capital:							Arch Capital:
May 1, 2034	May 1, 2034	7.350	%	$	300,000	$	297,457	May 1, 2034	7.350	%	$	300,000	$	297,585
June 30, 2050	June 30, 2050	3.635	%	1,000,000		988,665		June 30, 2050	3.635	%	1,000,000		988,891
Arch-U.S.:	Arch-U.S.:							Arch-U.S.:
Nov. 1, 2043 (1)	Nov. 1, 2043 (1)	5.144	%	500,000		495,033		Nov. 1, 2043 (1)	5.144	%	500,000		495,156
Arch Finance:	Arch Finance:							Arch Finance:
Dec. 15, 2026 (1)	Dec. 15, 2026 (1)	4.011	%	500,000		497,527		Dec. 15, 2026 (1)	4.011	%	500,000		497,962
Dec. 15, 2046 (1)	Dec. 15, 2046 (1)	5.031	%	450,000		445,467		Dec. 15, 2046 (1)	5.031	%	450,000		445,559
Total	Total			$	2,750,000	$	2,724,149	Total			$	2,750,000	$	2,725,153

(1)Fully and unconditionally guaranteed by Arch Capital.

Our senior notes were issued by Arch Capital, Arch Capital Group (U.S.) Inc. (“Arch-U.S.”) and Arch Capital Finance LLC (“Arch Finance”). Arch-U.S. is a wholly-owned subsidiary of Arch Capital and Arch Finance is a wholly-owned finance subsidiary of Arch-U.S. Our 2034 senior notes and 2050 senior notes issued by Arch Capital are unsecured and unsubordinated obligations of Arch Capital and ranked equally with all of its existing and future unsecured and unsubordinated indebtedness. The 2043 senior notes issued by Arch-U.S. are unsecured and unsubordinated obligations of Arch-U.S. and Arch Capital and rank equally and ratably with the other unsecured and unsubordinated indebtedness of Arch-U.S. and Arch Capital. The 2026 senior notes and 2046 senior notes issued by Arch Finance are unsecured and unsubordinated obligations of Arch Finance and Arch Capital and rank equally and ratably with the other unsecured and unsubordinated indebtedness of Arch Finance and Arch Capital.

Arch-U.S. and Arch Finance depend on their available cash resources, liquid investments and dividends or other distributions from their subsidiaries or affiliates to make payments, including the payment of debt service obligations and operating expenses they may incur.

The following tables present condensed financial information for Arch Capital (parent guarantor) and Arch-U.S. (subsidiary issuer):


	September 30, 2022
	Arch Capital		Arch-U.S.
Assets
Total investments	$	47,722	$	169,143
Cash	12,798		7,463

Investment in operating affiliates	5,448		—
Due from subsidiaries and affiliates	1,485		15






Other assets	7,437		29,346
Total assets	$	74,890	$	205,967

Liabilities






Senior notes	1,286,476		495,156

Due to subsidiaries and affiliates	1,838		507,103
Other liabilities	36,038		41,580
Total liabilities	$	1,324,352	$	1,043,839

Non-cumulative preferred shares	$	830,000	—


	December 31, 2021
		Arch Capital		Arch-U.S.
Assets
Total investments		$	2,038	$	137,124
Cash		16,317		18,392

Investment in operating affiliates		6,877		—
Due from subsidiaries and affiliates		—		26,000






Other assets		9,615		37,040
Total assets		$	34,847	$	218,556

Liabilities






Senior notes		1,286,208		495,063

Due to subsidiaries and affiliates		—		521,839
Other liabilities		24,767		47,410
Total liabilities		$	1,310,975	$	1,064,312

Non-cumulative preferred shares		$	830,000	—



	September 30, 2022
Nine Months Ended	Arch Capital	Arch-U.S.

Revenues

Net investment income		$	1,349	$	600
Net realized gains (losses)		23		(338)


Equity in net income (loss) of investments accounted for using the equity method		—		6,913

Total revenues		1,372		7,175

Expenses



Corporate expenses		70,048		10,882

Interest expense		44,068		35,328

Total expenses		114,116		46,210

Income (loss) before income taxes and income (loss) from operating affiliates		(112,744)		(39,035)
Income tax (expense) benefit		—		7,918

Income (loss) from operating affiliates		(758)		—


Net income available to Arch		(113,502)		(31,117)
Preferred dividends		(30,552)		—

Net income (loss) available to Arch common shareholders		$	(144,054)	$	(31,117)


ARCH CAPITAL			6462			~~2021 THIRD QUARTER FORM 10-Q~~

~~Table of Contents~~

~~The following tables present condensed financial information for Arch Capital (parent guarantor) and Arch-U.S. (subsidiary issuer):~~

September 30, 2021 December 31, 2020
Arch Capital Arch-U.S. Arch Capital Arch-U.S.
Assets
Total investments $ 135 $ 565,314 $ 172 $ 396,547
Cash 10,796 10,386 18,932 11,368
Investment in operating affiliates 7,099 — 7,731 —
Due from subsidiaries and affiliates — 200,786 — 201,515
Other assets 10,281 36,601 10,659 34,405
Total assets $ 28,311 $ 813,087 $ 37,494 $ 643,835
Liabilities
Senior notes 1,286,122 495,033 1,285,867 494,944
Due to subsidiaries and affiliates 4 507,103 — 586,805
Other liabilities 37,226 55,132 23,270 41,876
Total liabilities $ 1,323,352 $ 1,057,268 $ 1,309,137 $ 1,123,625
Non-cumulative preferred shares $ 830,000 — $ 780,000 —

Nine Months Ended Year Ended
September 30, 2021 December 31, 2020
Arch Capital Arch-U.S. Arch Capital Arch-U.S.
Revenues
Net investment income $ 1,160 $ 9,392 $ 53 $ 18,084
Net realized gains (losses) — 66,147 (2,110) 26,096
Equity in net income (loss) of investments accounted for using the equity method — 13,726 — 2,507
Total revenues 1,160 89,265 (2,057) 46,687
Expenses
Corporate expenses 54,726 4,438 65,566 7,227
Interest expense 44,055 35,455 40,445 47,566
Net foreign exchange (gains) losses 7 — 3 —
Total expenses 98,788 39,893 106,014 54,793
Income (loss) before income taxes and income (loss) from operating affiliates (97,628) 49,372 (108,071) (8,106)
Income tax (expense) benefit — (12,843) — 2,689
Income (loss) from operating affiliates (443) — (437) —
Net income available to Arch (98,071) 36,529 (108,508) (5,417)
Preferred dividends (38,159) — (41,612) —
Loss on redemption of preferred shares (15,101) — — —
Net income (loss) available to Arch common shareholders $ (151,331) $ 36,529 $ (150,120) $ (5,417)


~~ARCH CAPITAL~~			65			~~2021~~2022 THIRD QUARTER FORM 10-Q

Table of Contents



	December 31, 2021
Year Ended		Arch Capital	Arch-U.S.

Revenues

Net investment income			1,524		11,596
Net realized gains (losses)			—		72,437


Equity in net income (loss) of investments accounted for using the equity method			—		18,149

Total revenues			1,524		102,182

Expenses



Corporate expenses			71,818		5,875

Interest expense			58,741		47,292
Net foreign exchange (gains) losses			7		—
Total expenses			130,566		53,167

Income (loss) before income taxes and income (loss) from operating affiliates			(129,042)		49,015
Income tax (expense) benefit			—		(12,513)

Income (loss) from operating affiliates			(590)		—


Net income available to Arch			(129,632)		36,502
Preferred dividends			(48,343)		—
Loss on redemption of preferred shares			(15,101)		—
Net income (loss) available to Arch common shareholders			$	(193,076)	$	36,502

SHARE REPURCHASE PROGRAM

The board of directors of Arch Capital has authorized the investment in Arch Capital’s common shares through a share repurchase program. For the nine months ended September 30, ~~2021,~~2022, Arch Capital repurchased ~~22.8~~12.9 million shares under the share repurchase program with an aggregate purchase price of ~~$872.2~~$585.8 million. Since the inception of the share repurchase program through September 30, ~~2021,~~2022, Arch Capital has repurchased ~~412.0~~433.6 million common shares for an aggregate purchase price of ~~$4.92~~$5.9 billion. At September 30, ~~2021,~~2022, approximately ~~$44.3~~$596.4 million of share repurchases were available under the program. On October 8, 2021, the board of directors of ACGL increased the aggregate purchase amount authorized under the share repurchase program to $1.5 billion, which may be effected from time to time in open market or privately negotiated transactions through December 31, 2022. The timing and amount of the repurchase transactions under this program will depend on a variety of factors, including market conditions and corporate and regulatory considerations. We will continue to monitor our share price and, depending upon results of operations, market conditions and the development of the economy, as well as other factors, we will consider share repurchases on an opportunistic basis.~~See note 17, “Subsequent Event.”~~

CATASTROPHIC EVENTS AND SEVERE ECONOMIC EVENTS

We have large aggregate exposures to natural and man-made catastrophic events, pandemic events like COVID-19 and severe economic events. Natural catastrophes can be caused by various events, including hurricanes, floods, windstorms, earthquakes, hailstorms, tornadoes, explosions, severe winter weather, fires, droughts and other natural disasters. Man-made catastrophic events may include acts of war, acts of terrorism and political instability. Catastrophes can also cause

losses in non-property business such as mortgage insurance, workers’ compensation or general liability. In addition to the nature of property business, we believe that economic and geographic trends affecting insured property, including inflation, property value appreciation and geographic concentration, tend to generally increase the size of losses from catastrophic events over time.

Our models employ both proprietary and vendor-based systems and include cross-line correlations for property, marine, offshore energy, aviation, workers compensation and personal accident. We seek to limit the probable maximum pre-tax loss to a specific level for severe catastrophic events. Currently, we seek to limit our 1-in-250 year return period net probable maximum loss from a severe catastrophic event in any geographic zone to approximately 25% of tangible shareholders’ equity available to Arch (total shareholders’

equity available to Arch less goodwill and intangible assets). We reserve the right to change this threshold at any time.

Based on in-force exposure estimated as of October 1, ~~2021,~~2022, our modeled peak zone catastrophe exposure was a windstorm affecting the Florida Tri-County, with a net probable maximum pre-tax loss of ~~$671~~$851 million, followed by windstorms affecting the ~~Northeastern U.S.~~Gulf of Mexico and the ~~Gulf of Mexico~~Northeastern U.S. regions with net probable maximum pre-tax losses of ~~$650~~$748 and ~~$661~~$747 million, respectively. Our exposures to other perils, such as U.S. earthquake and international events, were less than the exposures arising from U.S. windstorms and hurricanes. As of October 1, ~~2021,~~2022, our modeled peak zone earthquake exposure (San Francisco earthquake) represented approximately ~~75%~~69% of our peak zone catastrophe exposure, and our modeled peak zone international exposure (UK windstorm) was substantially less than both our peak zone windstorm and earthquake exposures.

Effective July 1, 2021, our insurance operations had in effect a reinsurance program which provided coverage for certain property-catastrophe related losses equal to $276 million in excess of various retentions per occurrence.

We also have significant exposure to losses due to mortgage defaults resulting from severe economic events in the future. For our U.S. mortgage insurance business, we have developed a proprietary risk model (“Realistic Disaster Scenario” or “RDS”) that simulates the maximum loss resulting from a severe economic downturn impacting the housing market. The RDS models the collective impact of adverse conditions for key economic indicators, the most significant of which is a decline in home prices. The RDS model projects paths of future home prices, unemployment rates, income levels and interest rates and assumes correlation across states and geographic regions. The resulting future performance of our in-force portfolio is then estimated under the economic stress scenario, reflecting loan and borrower information.

Currently, we seek to limit our modeled RDS loss from a severe economic event to approximately 25% of tangible shareholders’ equity available to Arch. We reserve the right to change this threshold at any time. Based on in-force


ARCH CAPITAL			63			2022 THIRD QUARTER FORM 10-Q

Table of Contents

exposure estimated as of October 1, ~~2021,~~2022, our modeled RDS loss was approximately 6%10% of tangible shareholders’ equity available to Arch.

Net probable maximum loss estimates are net of expected reinsurance recoveries, before income tax and before excess reinsurance reinstatement premiums. RDS loss estimates are net of expected reinsurance recoveries and before income tax. Catastrophe loss estimates are reflective of the zone indicated and not the entire portfolio. Since hurricanes and windstorms can affect more than one zone and make multiple landfalls, our catastrophe loss estimates include clash estimates from


~~ARCH CAPITAL~~			66			~~2021 THIRD QUARTER FORM 10-Q~~

~~Table of Contents~~

other zones. Our catastrophe loss estimates and RDS loss estimates do not represent our maximum exposures and it is highly likely that our actual incurred losses would vary materially from the modeled estimates. There can be no assurances that we will not suffer pre-tax losses greater than 25% of our tangible shareholders’ equity from one or more catastrophic events or severe economic events due to several factors. These factors include the inherent uncertainties in estimating the frequency and severity of such events and the margin of error in making such determinations resulting from potential inaccuracies and inadequacies in the data provided by clients and brokers, the modeling techniques and the application of such techniques or as a result of a decision to change the percentage of shareholders' equity exposed to a single catastrophic event or severe economic event. In addition, actual losses may increase if our reinsurers fail to meet their obligations to us or the reinsurance protections purchased by us are exhausted or are otherwise unavailable. See “Risk Factors—Risks Relating to Our Industry” and “Management’s Discussion and Analysis of Financial Condition and Results of Operations—Catastrophic Events and Severe Economic Events” in our ~~2020 Form 10-K.~~

~~OFF-BALANCE SHEET ARRANGEMENTS~~

~~Off-balance sheet arrangements are discussed in Management’s Discussion and Analysis of Financial Condition and Results of Operations contained in our 2020~~2021 Form 10-K.

MARKET SENSITIVE INSTRUMENTS AND RISK MANAGEMENT

In accordance with the SEC’s Financial Reporting Release No. 48, we performed a sensitivity analysis to determine the effects that market risk exposures could have on the future earnings, fair values or cash flows of our financial instruments as of September 30, ~~2021.~~2022. Market risk represents the risk of changes in the fair value of a financial instrument and is comprised of several components, including liquidity, basis and price risks.

An analysis of material changes in market risk exposures at September 30, ~~2021~~2022 that affect the quantitative and qualitative disclosures presented in our ~~2020~~2021 Form 10-K (see section captioned “Management’s Discussion and Analysis of Financial Condition and Results of Operations—Market Sensitive Instruments and Risk Management”) were as follows:

Investment Market Risk

Fixed Income Securities. We invest in interest rate sensitive securities, primarily debt securities. We consider the effect of interest rate movements on the fair value of our fixed

maturities, ~~fixed maturities pledged under securities lending agreements,~~ short-term investments and certain of our other investments, equity securities and investment funds accounted for using the equity method which invest in fixed income securities (collectively, “Fixed Income Securities”) and the corresponding change in unrealized appreciation. As interest rates rise, the fair value of our Fixed Income Securities falls, and the converse is also true. Based on historical observations, there is a low probability that all interest rate yield curves would shift in the same direction at the same time. Furthermore, at times interest rate movements in certain credit sectors exhibit a much lower correlation to changes in U.S. Treasury yields. Accordingly, the actual effect of interest rate movements may differ materially from the amounts set forth in the following tables.

The following table summarizes the effect that an immediate, parallel shift in the interest rate yield curve would have had on our Fixed Income Securities:


(U.S. dollars in billions)	(U.S. dollars in billions)	Interest Rate Shift in Basis Points														(U.S. dollars in billions)	Interest Rate Shift in Basis Points
		-100			-50			—		+50			+100				-100			-50			—		+50			+100
Sept. 30, 2021
September 30, 2022																September 30, 2022
Total fair value	Total fair value	$	25.29		$	25.00		$	24.67	$	24.35		$	24.06		Total fair value	$	25.75		$	25.40		$	25.05	$	24.70		$	24.37
Change from base	Change from base	2.5		%	1.3		%			(1.3)		%	(2.5)		%	Change from base	2.8		%	1.4		%			(1.4)		%	(2.7)		%
Change in unrealized value	Change in unrealized value	$	0.62		$	0.32				$	(0.32)		$	(0.62)		Change in unrealized value	$	0.70		$	0.35				$	(0.35)		$	(0.68)

Dec. 31, 2020
December 31, 2021																December 31, 2021
Total fair value	Total fair value	$	25.82		$	25.44		$	25.07	$	24.69		$	24.31		Total fair value	$	25.79		$	25.44		$	25.21	$	24.75		$	24.43
Change from base	Change from base	3.0		%	1.5		%			(1.5)		%	(3.0)		%	Change from base	2.3		%	0.9		%			(1.8)		%	(3.1)		%
Change in unrealized value	Change in unrealized value	$	0.75		$	0.38				$	(0.38)		$	(0.75)		Change in unrealized value	$	0.58		$	0.23				$	(0.45)		$	(0.78)

In addition, we consider the effect of credit spread movements on the market value of our Fixed Income Securities and the corresponding change in unrealized value. As credit spreads widen, the fair value of our Fixed Income Securities falls, and the converse is also true. In periods where the spreads on our Fixed Income Securities are much higher than their historical average due to short-term market dislocations, a parallel shift in credit spread levels would result in a much more pronounced change in unrealized value.


ARCH CAPITAL			6764			~~2021~~2022 THIRD QUARTER FORM 10-Q

Table of Contents

The following table summarizes the effect that an immediate, parallel shift in credit spreads in a static interest rate environment would have had on our Fixed Income Securities:


(U.S. dollars in billions)	(U.S. dollars in billions)	Credit Spread Shift in Percentage Points														(U.S. dollars in billions)	Credit Spread Shift in Percentage Points
		-100			-50			—		+50			+100				-100			-50			—		+50			+100
Sept. 30, 2021
September 30, 2022																September 30, 2022
Total fair value	Total fair value	$	25.24		$	24.97		$	24.67	$	24.38		$	24.11		Total fair value	$	26.03		$	25.54		$	25.05	$	24.56		$	24.07
Change from base	Change from base	2.3		%	1.2		%			(1.2)		%	(2.3)		%	Change from base	3.9		%	2.0		%			(2.0)		%	(3.9)		%
Change in unrealized value	Change in unrealized value	$	0.57		$	0.30				$	(0.30)		$	(0.57)		Change in unrealized value	$	0.98		$	0.49				$	(0.49)		$	(0.98)

Dec. 31, 2020
December 31, 2021																December 31, 2021
Total fair value	Total fair value	$	25.54		$	25.32		$	25.07	$	24.82		$	24.59		Total fair value	$	26.17		$	25.69		$	25.21	$	24.72		$	24.24
Change from base	Change from base	1.9		%	1.0		%			(1.0)		%	(1.9)		%	Change from base	3.8		%	1.9		%			(1.9)		%	(3.8)		%
Change in unrealized value	Change in unrealized value	$	0.48		$	0.25				$	(0.25)		$	(0.48)		Change in unrealized value	$	0.97		$	0.48				$	(0.48)		$	(0.97)

Another method that attempts to measure portfolio risk is Value-at-Risk (“VaR”). VaR measures the worst expected loss under normal market conditions over a specific time interval at a given confidence level. The 1-year 95th percentile parametric VaR reported herein estimates that 95% of the time, the portfolio loss in a one-year horizon would be less than or equal to the calculated number, stated as a percentage of the measured portfolio’s initial value. The VaR is a variance-covariance based estimate, based on linear sensitivities of a portfolio to a broad set of systematic market risk factors and idiosyncratic risk factors mapped to the portfolio exposures. The relationships between the risk factors are estimated using historical data, and the most recent data points are generally given more weight. As of September 30, ~~2021,~~2022, our portfolio’s VaR was estimated to be ~~3.2%~~7.9% compared to an estimated ~~4.3%~~4.8% at December 31, ~~2020.~~2021. In periods where the volatility of the risk factors mapped to our portfolio’s exposures is higher due to market conditions, the resulting VaR is higher than in other periods.

Equity Securities. At September 30, ~~2021~~2022 and December 31, ~~2020,~~2021, the fair value of our investments in equity securities ~~(excluding securities included in Fixed Income Securities above)~~and certain investments accounted for using the equity method with underlying equity strategies totaled ~~$1.5~~$0.8 billion and ~~$1.1~~$1.4 billion, respectively. These investments are exposed to price risk, which is the potential loss arising from decreases in fair value. An immediate hypothetical 10% decline in the value of each position would reduce the fair value of such investments by approximately ~~$146.7~~$81.9 million and ~~$109.5~~$137.5 million at September 30, ~~2021~~2022 and December 31, ~~2020,~~2021, respectively, and would have decreased book value per share by approximately ~~$0.38~~$0.22 and ~~$0.27,~~$0.36, respectively. An immediate hypothetical 10% increase in the value of each position would increase the fair value of such investments by approximately ~~$146.7~~$81.9 million and ~~$109.5~~$137.5 million at September 30, ~~2021~~2022 and December 31, ~~2020,~~2021, respectively, and would have increased book value per share by approximately ~~$0.38~~$0.22 and ~~$0.27,~~$0.36, respectively.

Investment-Related Derivatives. At September 30, ~~2021,~~2022, the notional value of all derivative instruments (excluding ~~to-be-announced mortgage backed securities which are included in the fixed income securities analysis above and~~ foreign currency forward contracts which are included in the foreign currency exchange risk analysis below) was ~~$6.8~~$5.9 billion, compared to ~~$8.6~~$6.4 billion at December 31, ~~2020.~~2021. If the underlying exposure of each investment-related derivative held at September 30, ~~2021~~2022 depreciated by 100 basis points, it would have resulted in a reduction in net income of approximately ~~$68.2~~$58.6 million, and a decrease in book value per share of approximately ~~$0.18~~$0.16 per share, compared to ~~$85.7~~$63.8 million and ~~$0.21~~$0.17 per share, respectively, on investment-related derivatives held at December 31, ~~2020.~~2021. If the underlying exposure of each investment-related derivative held at September 30, ~~2021~~2022 appreciated by 100 basis points, it would have resulted in an increase in net income of approximately ~~$68.2~~$58.6 million, and an increase in book value per share of approximately ~~$0.18~~$0.16 per share, compared to ~~$85.7~~$63.8 million and ~~$0.21~~$0.17 per share, respectively, on investment-related derivatives held at December 31, ~~2020.~~2021. See note ~~10,~~9, “Derivative Instruments,” to our consolidated financial statements for additional disclosures concerning derivatives.

For further discussion on investment activity, please refer to “Financial Condition—Investable Assets.”


ARCH CAPITAL			65			2022 THIRD QUARTER FORM 10-Q

Table of Contents

Foreign Currency Exchange Risk

Foreign currency rate risk is the potential change in value, income and cash flow arising from adverse changes in foreign currency exchange rates. Through our subsidiaries and branches located in various foreign countries, we conduct our insurance and reinsurance operations in a variety of local currencies other than the U.S. Dollar. We generally hold investments in foreign currencies which are intended to mitigate our exposure to foreign currency fluctuations in our net insurance liabilities. We may also utilize foreign currency forward contracts and currency options as part of our investment strategy. See note ~~10,~~9, “Derivative Instruments,” to our consolidated financial statements for additional information.


~~ARCH CAPITAL~~			68			~~2021 THIRD QUARTER FORM 10-Q~~

~~Table of Contents~~

The following table provides a summary of our net foreign currency exchange exposures, as well as foreign currency derivatives in place to manage these exposures:


(U.S. dollars in thousands, except per share data)	(U.S. dollars in thousands, except per share data)	September 30, 2021		December 31, 2020		(U.S. dollars in thousands, except per share data)	September 30, 2022		December 31, 2021
Net assets (liabilities), denominated in foreign currencies, excluding shareholders’ equity and derivatives	Net assets (liabilities), denominated in foreign currencies, excluding shareholders’ equity and derivatives	$	(813,451)	$	(309,968)	Net assets (liabilities), denominated in foreign currencies, excluding shareholders’ equity and derivatives	$	(366,136)	$	(825,371)
Shareholders’ equity denominated in foreign currencies (1)	Shareholders’ equity denominated in foreign currencies (1)	1,088,134		695,355		Shareholders’ equity denominated in foreign currencies (1)	978,889		1,095,706
Net foreign currency forward contracts outstanding (2)	Net foreign currency forward contracts outstanding (2)	39,171		1,108,161		Net foreign currency forward contracts outstanding (2)	8,369		15,151
Net exposures denominated in foreign currencies	Net exposures denominated in foreign currencies	$	313,854	$	1,493,548	Net exposures denominated in foreign currencies	$	621,122	$	285,486

Pre-tax impact of a hypothetical 10% appreciation of the U.S. Dollar against foreign currencies:	Pre-tax impact of a hypothetical 10% appreciation of the U.S. Dollar against foreign currencies:					Pre-tax impact of a hypothetical 10% appreciation of the U.S. Dollar against foreign currencies:
Shareholders’ equity	Shareholders’ equity	$	(31,385)	$	(149,355)	Shareholders’ equity	$	(62,112)	$	(28,549)
Book value per share	Book value per share	$	(0.08)	$	(0.37)	Book value per share	$	(0.17)	$	(0.08)

Pre-tax impact of a hypothetical 10% decline of the U.S. Dollar against foreign currencies:	Pre-tax impact of a hypothetical 10% decline of the U.S. Dollar against foreign currencies:					Pre-tax impact of a hypothetical 10% decline of the U.S. Dollar against foreign currencies:
Shareholders’ equity	Shareholders’ equity	$	31,385	$	149,355	Shareholders’ equity	$	62,112	$	28,549
Book value per share	Book value per share	$	0.08	$	0.37	Book value per share	$	0.17	$	0.08

(1) Represents capital contributions held in the foreign currencies of our operating units.

(2) Represents the net notional value of outstanding foreign currency forward contracts.

Although we generally attempt to match the currency of our projected liabilities with investments in the same currencies, from time to time we may elect to over or underweight one or more currencies, which could increase our exposure to foreign currency fluctuations and increase the volatility of our shareholders’ equity. Historical observations indicate a low probability that all foreign currency exchange rates would shift against the U.S. Dollar in the same direction and at the same time and, accordingly, the actual effect of foreign currency rate movements may differ materially from the

amounts set forth above. For further discussion on foreign exchange activity, please refer to “Results of Operations.”

Effects of Inflation

~~We do not believe that~~General economic inflation has ~~had a material effect on our consolidated results~~increased in recent quarters and may continue to remain at elevated levels for an extended period of ~~operations, except insofar as inflation may affect our reserve for losses and loss adjustment expenses and interest rates.~~time. The potential also exists, after a catastrophe loss or pandemic events like COVID-19, for the development of inflationary pressures in a local economy. This may have a material effect on the adequacy of our reserves for losses and loss adjustment expenses, especially in longer-tailed lines of business, and on the market value of our investment portfolio through rising interest rates. The anticipated effects of inflation ~~on us~~ are considered in our pricing models, reserving processes and exposure management, across all lines of business and types of loss including natural catastrophe ~~loss models.~~events. The actual effects of inflation on our results cannot be accurately known until claims are ultimately ~~settled.~~settled and will vary by the specific type of inflation affecting each line of business.

OTHER FINANCIAL INFORMATION

The consolidated financial statements as of September 30, ~~2021~~2022 have been reviewed by PricewaterhouseCoopers LLP, the registrant's independent public accountants, whose report is included as an exhibit to this filing. The report of PricewaterhouseCoopers LLP states that they did not audit and they do not express an opinion on that unaudited financial information. Accordingly, the degree of reliance on their report on such information should be restricted in light of the limited nature of the review procedures applied. PricewaterhouseCoopers LLP is not subject to the liability provisions of Section 11 of the Securities Act of 1933 for their report on the unaudited financial information because that report is not a "report" or a "part" of the registration statement prepared or certified by PricewaterhouseCoopers LLP within the meaning of Sections 7 and 11 of the Securities Act of 1933.

ITEM 3. QUANTITATIVE AND QUALITATIVE DISCLOSURES ABOUT MARKET RISK

Reference is made to the information appearing above under the subheading “Market Sensitive Instruments and Risk Management” under the caption “Management’s Discussion and Analysis of Financial Condition and Results of Operations,” which information is hereby incorporated by reference.


ARCH CAPITAL			66			2022 THIRD QUARTER FORM 10-Q

Table of Contents

ITEM 4. CONTROLS AND PROCEDURES

Evaluation of Disclosure Controls and Procedures

In connection with the filing of this Form 10-Q, our management, including the Chief Executive Officer and Chief Financial Officer, conducted an evaluation, ~~of the effectiveness of disclosure controls and procedures pursuant to applicable Exchange Act Rules~~ as of the end of the period covered by this ~~report.~~report, for the purposes set forth in the applicable rules under the Securities and Exchange Act of 1934, as amended (the “Exchange Act”). Based on that evaluation, the Chief Executive Officer and Chief Financial Officer concluded that the disclosure controls and procedures were effective as of the end of and during the period covered by this report with respect to information being recorded, processed, summarized and reported within time periods specified in the SEC’s rules and forms and with respect to timely communication to them and other members of management responsible for preparing periodic reports of all material information required to be disclosed in this report as it relates to Arch Capital and its consolidated subsidiaries.

We continue to enhance our operating procedures and internal controls to effectively support our business and our regulatory and reporting requirements. Our management does


~~ARCH CAPITAL~~			69			~~2021 THIRD QUARTER FORM 10-Q~~

~~Table of Contents~~

not expect that our disclosure controls or our internal controls will prevent all errors and all fraud. A control system, no matter how well conceived and operated, can provide only reasonable, not absolute, assurance that the objectives of the control system are met. Further, the design of a control system must reflect the fact that there are resource constraints, and the benefits of controls must be considered relative to their costs. As a result of the inherent limitations in all control systems, no evaluation of controls can provide absolute assurance that all control issues and instances of fraud, if any, within the company have been detected. These inherent limitations include the realities that judgments in decision-making can be faulty, and that breakdowns can occur because of simple error or mistake. Additionally, controls can be circumvented by the individual acts of some persons or by collusion of two or more people. The design of any system of controls also is based in part upon certain assumptions about the likelihood of future events, and there can be no assurance that any design will succeed in achieving its stated goals under all potential future conditions; over time, controls may become inadequate because of changes in conditions, or the degree of compliance with the policies or procedures may deteriorate. As a result of the inherent limitations in a cost-effective control system, misstatement due to error or fraud may occur and not be detected. Accordingly, our disclosure controls and procedures are designed to provide reasonable, not absolute, assurance that the disclosure controls and procedures are met.

Changes in Internal Controls Over Financial Reporting

There have been no changes in internal control over financial reporting that occurred during the quarter ended September 30, ~~2021~~2022 that have materially affected, or are reasonably likely to materially affect, internal control over financial reporting. We have not experienced any material impact to our internal controls over financial reporting despite the fact that most of our employees are working remotely due to the COVID-19. We are continually monitoring and assessing COVID-19 situation on our internal controls to minimize the impact on their design and operating effectiveness.reporting.

PART II. OTHER INFORMATION

ITEM 1. LEGAL PROCEEDINGS

We, in common with the insurance industry in general, are subject to litigation and arbitration in the normal course of our business. As of September 30, ~~2021,~~2022, we were not a party to any litigation or arbitration which is expected by management to have a material adverse effect on our results of operations and financial condition and liquidity.

ITEM 1A. RISK FACTORS

There were no material changes from the risk factors previously disclosed in our Annual Report on Form 10-K for the year ended December 31, ~~2020.~~2021.


ARCH CAPITAL			7067			~~2021~~2022 THIRD QUARTER FORM 10-Q

Table of Contents

ITEM 2. UNREGISTERED SALES OF EQUITY SECURITIES AND USE OF PROCEEDS

Issuer’s Repurchases of Equity Securities

The following table summarizes our purchases of common shares for the ~~2021~~2022 third quarter:

Issuer Purchases of Equity Securities
Period Total Number of Shares
Purchased (1) Average Price Paid per Share Total Number of Shares Purchased as Part of
Publicly Announced
Plans or Programs Approximate Dollar
Value of Shares that
May Yet be Purchased
Under the Plan or
Programs (2)
7/1/2021-7/31/2021 729,925 $ 39.01 727,778 $ 402,822
8/1/2021-8/31/2021 4,173,006 40.66 4,130,776 $ 234,886
9/1/2021-9/30/2021 4,864,398 39.32 4,846,402 $ 44,331
Total 9,767,329 $ 39.87 9,704,956


Period	Total Number of Shares Purchased (1)	Average Price Paid per Share		Total Number of Shares Purchased as Part of Publicly Announced Plans or Programs	Approximate Dollar Value of Shares that May Yet be Purchased Under the Plan or Programs ($000’s) (2)
7/1/2022-7/31/2022	235,544	$	42.97	233,177	$	596,541
8/1/2022-8/31//2022	24,798	45.56		3,017	$	596,411
9/1/2022-9/30/2022	10,739	46.31		—	$	596,411
Total	271,081	$	43.34	236,194

(1)~~Represents~~This column represents open market share repurchases, including an aggregate of 2,367, 21,781, and 10,739 shares repurchased by Arch Capital ofduring July, August and September, respectively, other than through publicly announced plans or programs. We repurchased these shares ~~from time to time,~~ from employees in order to facilitate the payment of withholding taxes on restricted shares granted and the exercise of stock appreciation ~~rights. We purchased these shares~~rights, in each case at their fair value as determined by reference to the closing price of our common shares on the day the restricted shares vested or the stock appreciation rights were exercised.

(2)~~Remaining~~This column represents the remaining approximate dollar amount available at ~~September 30, 2021~~the end of each applicable period under Arch Capital’s $1.5 billion share repurchase authorization ~~under which repurchases may be effected~~ from ~~time to time in open market or privately negotiated transactions. On~~ October 8, ~~2021, the board of directors of ACGL increased the aggregate purchase amount authorized under the share repurchase program to $1.5 billion.~~2021. Repurchases ~~under this authorization~~ may be effected from time to time in open market or privately negotiated transactions through December 31, 2022.

ITEM 3. DEFAULTS UPON SENIOR SECURITIES

None.

ITEM 4. MINE SAFETY DISCLOSURES

Not applicable.

ITEM 5. OTHER INFORMATION

In accordance with Section 10a(i)(2) of the Securities and Exchange Act of 1934, as amended, we are responsible for disclosing non-audit services to be provided by our independent auditor, PricewaterhouseCoopers LLP, which are approved by the Audit Committee of our board of directors. During the ~~2021~~2022 third quarter, the Audit Committee approved engagements of PricewaterhouseCoopers LLP for permitted non-audit services, which consisted of tax consulting services, tax compliance services and other accounting consulting services.


ARCH CAPITAL			7168			~~2021~~2022 THIRD QUARTER FORM 10-Q

Table of Contents

ITEM 6. EXHIBITS

Incorporated by Reference

Exhibit Number

Exhibit Description

Form

Original Number

Date Filed

Filed Herewith

~~10.1~~

~~First Amendment to Third Amended and Restated Credit Agreement, dated as of August 12, 2020by and among~~ ~~Arch Capital Group Ltd. (~~“~~ACGL~~”), ~~the other Loan Parties party hereto, the Lenders party hereto, and Bank of America, N.A., as Administrative Agent(“Third Amended and Restated Credit Agreement”).~~

~~10.2~~

~~The LIBOR Transition Amendment to the Third Amended and Restated Credit Agreement, dated as of~~ ~~September 29, 2021~~.

Accountants’ Awareness Letter (regarding unaudited interim financial information)

31.1

Certification of Chief Executive Officer pursuant to Section 302 of the Sarbanes-Oxley Act of 2002

31.2

Certification of Chief Financial Officer pursuant to Section 302 of the Sarbanes-Oxley Act of 2002

32.1

Certification of Chief Executive Officer pursuant to Section 906 of the Sarbanes-Oxley Act of 2002

32.2

Certification of Chief Financial Officer pursuant to Section 906 of the Sarbanes-Oxley Act of 2002

101.INS

XBRL Instance Document

101.SCH

XBRL Taxonomy Extension Schema Document

101.CAL

XBRL Taxonomy Extension Calculation Linkbase Document

101.DEF

XBRL Taxonomy Extension Definition Linkbase Document

101.LAB

XBRL Taxonomy Extension Label Linkbase Document

101.PRE

XBRL Taxonomy Extension Presentation Linkbase Document

104

Cover Page Interactive Data File (embedded within the Inline XBRL document)


ARCH CAPITAL			7269			~~2021~~2022 THIRD QUARTER FORM 10-Q

Table of Contents

SIGNATURES

Pursuant to the requirements of the Securities Exchange Act of 1934, the registrant has duly caused this report to be signed on its behalf by the undersigned thereunto duly authorized.


						ARCH CAPITAL GROUP LTD.
						(REGISTRANT)

						/s/ Marc Grandisson
Date: November ~~4, 2021~~3, 2022						Marc Grandisson
						Chief Executive Officer (Principal Executive Officer)

						/s/ François Morin
Date: November ~~4, 2021~~3, 2022						François Morin
						Executive Vice President, Chief Financial Officer (Principal Financial and Accounting Officer) and Treasurer


ARCH CAPITAL			7370			~~2021~~2022 THIRD QUARTER FORM 10-Q


	Remaining Contractual Maturity of the Agreements
	Overnight and Continuous		Less than 30 Days		30-90 Days		90 Days or More		Total








December 31, 2020
U.S. government and government agencies	$	142,317	$	—	$	139,290	$	—	$	281,607
Corporate bonds	3,021		—		—		—		3,021
Equity securities	16,461		—		—		—		16,461
Total	$	161,799	$	—	$	139,290	$	—	$	301,089
Gross amount of recognized liabilities for securities lending in offsetting disclosure in note 10									$	—
Amounts related to securities lending not included in offsetting disclosure in note 10									$	301,089


Investable assets (1):	Estimated Fair Value			% of Total
September 30, 2021
Fixed maturities (2)	$	17,182,370		63.0
Short-term investments (2)	3,185,646			11.7
Cash	1,137,721			4.2
Equity securities (2)	1,815,163			6.7
Other investments (2)	1,489,759			5.5
Other investable assets (3)	—			—
Investments accounted for using the equity method	2,741,293			10.0

Securities transactions entered into but not settled at the balance sheet date	(273,512)			(1.0)
Total investable assets held by Arch	$	27,278,440		100.0

Average effective duration (in years)	2.68
Average S&P/Moody’s credit ratings (4)	AA-/Aa3
Embedded book yield (5)	1.54		%

December 31, 2020
Fixed maturities (2)	$	18,771,296		69.9
Short-term investments (2)	2,063,240			7.7
Cash	694,997			2.6
Equity securities (2)	1,436,104			5.3
Other investments (2)	1,480,347			5.5
Other investable assets (3)	500,000			1.9
Investments accounted for using the equity method	2,047,889			7.6

Securities transactions entered into but not settled at the balance sheet date	(137,578)			(0.5)
Total investable assets held by Arch	$	26,856,295		100.0

Average effective duration (in years)	3.01
Average S&P/Moody’s credit ratings (4)	AA/Aa2
Embedded book yield (5)	1.56		%


	Issuer Purchases of Equity Securities
Period	Total Number of Shares Purchased (1)	Average Price Paid per Share		Total Number of Shares Purchased as Part of Publicly Announced Plans or Programs	Approximate Dollar Value of Shares that May Yet be Purchased Under the Plan or Programs (2)
7/1/2021-7/31/2021	729,925	$	39.01	727,778	$	402,822
8/1/2021-8/31/2021	4,173,006	40.66		4,130,776	$	234,886
9/1/2021-9/30/2021	4,864,398	39.32		4,846,402	$	44,331
Total	9,767,329	$	39.87	9,704,956