~~Table of Contents~~

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 March 31, ~~2020~~2021

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 5.25% Series E preferred share

ACGLP

NASDAQ

Stock Market

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

ACGLO

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 ~~May 1, 2020,~~April 30, 2021, there were ~~405,649,506~~403,619,081 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			3937
Item 3.		Quantitative and Qualitative Disclosures About Market Risk			6261
Item 4.		Controls and Procedures			6261

		PART II
		Other Information			6362
Item 1.		Legal Proceedings			62
Item 1A.		Risk Factors			62
Item 1.2.		~~Legal Proceedings~~		63
~~Item 1A.~~	~~Risk Factors~~	63
~~Item 2.~~	Unregistered Sales of Equity Securities and Use of Proceeds		6663
Item 3.		Defaults Upon Senior Securities			6763
Item 4.		Mine Safety Disclosures			6763
Item 5.		Other Information			6763
Item 6.		Exhibits			6864
		Signatures			6965



ARCH CAPITAL	1	~~2020~~2021 FIRST QUARTER FORM 10-Q

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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 ~~integration of any businesses~~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 ~~(including the length and magnitude of the current “soft” market)~~ 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 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;

~~the effect~~


ARCH CAPITAL			2			2021 FIRST QUARTER FORM 10-Q

Table of ~~contagious disease (including COVID-19) on the Company’s business;~~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;



~~ARCH CAPITAL~~	2	~~2020 FIRST QUARTER FORM 10-Q~~

~~Table of Contents~~•

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;

•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 the Tax Cuts and Jobs Act of 2017; 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, 2019, ~~“ITEM 1A—Risk Factors”~~ ~~of this Form 10-Q~~

•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, 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 FIRST QUARTER FORM 10-Q

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~~ARCH CAPITAL~~			3	~~2020 FIRST QUARTER FORM 10-Q~~

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ITEM 1. CONSOLIDATED FINANCIAL STATEMENTS

	~~Page No.~~
			Page No.

Report of Independent Registered Public Accounting Firm			5

Consolidated Balance Sheets
March 31, ~~2020~~2021 (unaudited) and December 31, ~~2019~~2020			6

Consolidated Statements of Income
For the three month periods ended March 31, 2021 and 2020 ~~and 2019~~ (unaudited)			7

Consolidated Statements of Comprehensive Income
For the three month periods ended March 31, 2021 and 2020 ~~and 2019~~ (unaudited)			8

Consolidated Statements of Changes in Shareholders’ Equity
For the three month periods ended March 31, 2021 and 2020 ~~and 2019~~ (unaudited)			9

Consolidated Statements of Cash Flows
For the three month periods ended March 31, 2021 and 2020 ~~and 2019~~ (unaudited)			10

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

Note 2 - Share Transactions			1311
Note 3 - Earnings Per Common Share			1412
Note 4 - Segment Information			1513
Note 5 - Reserve for Losses and Loss Adjustment Expenses			1816
Note 6 - Allowance for Expected Credit Losses			2017
Note 7 - Investment Information			2119
Note 8 - Fair Value			2725
Note 9 - Derivative Instruments			3330
Note 10 - Commitments and Contingencies			3431
~~Note 11 - Leases~~			34
Note 1211 - Variable Interest Entities and Noncontrolling Interests			3431
Note 1312 - Other Comprehensive Income (Loss)			3735

Note 13 - Income Taxes			36
Note 14 - ~~Income Taxes~~Legal Proceedings			3836
Note 15 ~~- Legal Proceedings~~		38
~~Note 16~~ - Transactions with Related Parties		3836



ARCH CAPITAL	4	~~2020~~2021 FIRST QUARTER FORM 10-Q

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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 March 31, ~~2020,~~2021, and the related consolidated statements of income, comprehensive income, changes in shareholders’ equity, and the consolidated statements of cash flows for the three-month periods ended March 31, ~~2020~~2021 and ~~2019,~~2020, 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, ~~2019,~~2020, 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 ~~28, 2020,~~26, 2021, 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, ~~2019,~~2020, 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 ~~Public Company Accounting Oversight Board (United States) (PCAOB)~~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, NY

May ~~8, 2020~~

6, 2021



ARCH CAPITAL	5	~~2020~~2021 FIRST QUARTER FORM 10-Q

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ARCH CAPITAL GROUP LTD. AND SUBSIDIARIES

CONSOLIDATED BALANCE SHEETS

ARCH CAPITAL GROUP LTD. AND SUBSIDIARIES
CONSOLIDATED BALANCE SHEETS
(U.S. dollars in thousands, except share data)
(Unaudited)
March 31,
2020 December 31,
2019
Assets

Investments:

Fixed maturities available for sale, at fair value (amortized cost: $16,757,086 and $16,598,808); net of allowance for credit losses: $9,909 at March 31, 2020) $ 16,841,571
$ 16,894,526
Short-term investments available for sale, at fair value (amortized cost: $944,878 and $957,283); net of allowance for credit losses: $29 at March 31, 2020) 944,531
956,546
Collateral received under securities lending, at fair value (amortized cost: $182,274 and $388,366) 182,284
388,376
Equity securities, at fair value 1,181,903
838,925
Investments accounted for using the fair value option 3,310,517
3,663,477
Investments accounted for using the equity method 1,676,055
1,660,396
Total investments 24,136,861
24,402,246

Cash 882,284
726,230
Accrued investment income 118,089
117,937
Securities pledged under securities lending, at fair value (amortized cost: $175,218 and $378,738) 177,442
379,868
Premiums receivable (net of allowance for credit losses: $27,990 and $21,003) 2,155,204
1,778,717
Reinsurance recoverable on unpaid and paid losses and loss adjustment expenses (net of allowance for credit losses: $13,700 and $1,364) 4,303,135
4,346,816
Contractholder receivables (net of allowance for credit losses: $9,038 and $0) 2,140,724
2,119,460
Ceded unearned premiums 1,357,284
1,234,683
Deferred acquisition costs 708,848
633,400
Receivable for securities sold 221,573
24,133
Goodwill and intangible assets 705,450
738,083
Other assets 1,509,232
1,383,788
Total assets $ 38,416,126
$ 37,885,361

Liabilities
Reserve for losses and loss adjustment expenses $ 14,309,580
$ 13,891,842
Unearned premiums 4,817,191
4,339,549
Reinsurance balances payable 737,597
667,072
Contractholder payables 2,149,762
2,119,460
Collateral held for insured obligations 211,597
206,698
Senior notes 1,871,869
1,871,626
Revolving credit agreement borrowings 500,587
484,287
Securities lending payable 182,274
388,366
Payable for securities purchased 327,359
87,579
Other liabilities 1,392,905
1,513,330
Total liabilities 26,500,721
25,569,809

Commitments and Contingencies

Redeemable noncontrolling interests 55,376
55,404

Shareholders' Equity
Non-cumulative preferred shares 780,000
780,000
Common shares ($0.0011 par, shares issued: 577,386,799 and 574,617,195) 642
638
Additional paid-in capital 1,921,487
1,889,683
Retained earnings 11,132,268
11,021,006
Accumulated other comprehensive income (loss), net of deferred income tax 21,944
212,091
Common shares held in treasury, at cost (shares: 171,776,932 and 168,997,994) (2,489,097 ) (2,406,047 )
Total shareholders' equity available to Arch 11,367,244
11,497,371
Non-redeemable noncontrolling interests 492,785
762,777
Total shareholders' equity 11,860,029
12,260,148
Total liabilities, noncontrolling interests and shareholders' equity $ 38,416,126
$ 37,885,361

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


	(Unaudited)
	March 31, 2021		December 31, 2020
Assets
Investments:
Fixed maturities available for sale, at fair value (amortized cost: $18,447,720 and $18,143,305; net of allowance for credit losses: $3,830 and $2,397 )	$	18,723,035	$	18,717,825
Short-term investments available for sale, at fair value (amortized cost: $1,269,312 and $1,924,292; net of allowance for credit losses: $0 and $0)	1,269,631		1,924,922
Collateral received under securities lending, at fair value (amortized cost: $143,886 and $301,089)	143,894		301,096
Equity securities, at fair value	1,532,906		1,444,830

Other investments (portion measured at fair value: $3,935,354 and $3,824,796)	4,435,354		4,324,796
Investments accounted for using the equity method	2,256,327		2,047,889
Total investments	28,361,147		28,761,358

Cash	941,951		906,448
Accrued investment income	101,108		103,299
Securities pledged under securities lending, at fair value (amortized cost: $142,129 and $294,493)	140,949		294,912

Investment in operating affiliates	739,783		129,291
Premiums receivable (net of allowance for credit losses: $36,111 and $37,781)	2,618,175		2,064,586
Reinsurance recoverable on unpaid and paid losses and loss adjustment expenses (net of allowance for credit losses: $10,872 and $11,636)	4,041,076		4,500,802
Contractholder receivables (net of allowance for credit losses: $5,853 and $8,638)	1,919,655		1,986,924
Ceded unearned premiums	1,406,489		1,234,075
Deferred acquisition costs	919,740		790,708
Receivable for securities sold	199,424		92,743
Goodwill and intangible assets	679,509		692,863

Other assets	2,135,261		1,724,288
Total assets	$	44,204,267	$	43,282,297

Liabilities
Reserve for losses and loss adjustment expenses	$	16,443,952	$	16,513,929
Unearned premiums	5,549,127		4,838,965
Reinsurance balances payable	919,125		683,263
Contractholder payables	1,925,508		1,995,562
Collateral held for insured obligations	222,245		215,581
Senior notes	2,861,417		2,861,113
Revolving credit agreement borrowings	155,687		155,687
Securities lending payable	143,886		301,089
Payable for securities purchased	386,453		218,779
Other liabilities	1,565,861		1,510,888
Total liabilities	30,173,261		29,294,856

Commitments and Contingencies	0		0
Redeemable noncontrolling interests	57,670		58,548

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

Common shares ($0.0011 par, shares issued: 581,226,408 and 579,000,841)	645		643
Additional paid-in capital	2,014,741		1,977,794
Retained earnings	12,790,216		12,362,463
Accumulated other comprehensive income (loss), net of deferred income tax	205,827		488,895
Common shares held in treasury, at cost (shares: 177,913,031 and 172,280,199)	(2,694,957)		(2,503,909)
Total shareholders' equity available to Arch	13,096,472		13,105,886
Non-redeemable noncontrolling interests	876,864		823,007
Total shareholders' equity	13,973,336		13,928,893
Total liabilities, noncontrolling interests and shareholders' equity	$	44,204,267	$	43,282,297

See Notes to Consolidated Financial Statements



ARCH CAPITAL	6	~~2020~~2021 FIRST QUARTER FORM 10-Q

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ARCH CAPITAL GROUP LTD. AND SUBSIDIARIES

ARCH CAPITAL GROUP LTD. AND SUBSIDIARIES
CONSOLIDATED STATEMENTS OF INCOME
(U.S. dollars in thousands, except share data)
(Unaudited)
Three Months Ended
March 31,
2020 2019
Revenues

Net premiums written $ 2,137,246
$ 1,525,259
Change in unearned premiums (392,802 ) (156,393 )
Net premiums earned 1,744,444
1,368,866
Net investment income 145,153
156,949
Net realized gains (losses) (366,960 ) 140,256
Other underwriting income 6,852
8,825
Equity in net income (loss) of investment funds accounted for using the equity method (4,209 ) 46,867
Other income 8,548
1,083
Total revenues 1,533,828
1,722,846

Expenses
Losses and loss adjustment expenses 1,115,419
718,532
Acquisition expenses 247,283
197,848
Other operating expenses 234,544
201,163
Corporate expenses 20,796
17,962
Amortization of intangible assets 16,631
20,417
Interest expense 32,555
29,065
Net foreign exchange (gains) losses (72,671 ) (3,525 )
Total expenses 1,594,557
1,181,462

Income (loss) before income taxes (60,729 ) 541,384
Income tax expense (27,945 ) (45,886 )
Net income (loss) $ (88,674 ) $ 495,498
Net (income) loss attributable to noncontrolling interests 232,791
(46,970 )
Net income available to Arch 144,117
448,528
Preferred dividends (10,403 ) (10,403 )
Net income available to Arch common shareholders $ 133,714
$ 438,125

Net income per common share and common share equivalent

Basic $ 0.33
$ 1.09
Diluted $ 0.32
$ 1.07

Weighted average common shares and common share equivalents outstanding
Basic 403,892,161
400,184,404
Diluted 414,033,570
408,971,029
CONSOLIDATED STATEMENTS OF INCOME

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


	(Unaudited)
	Three Months Ended
	March 31,
	2021		2020
Revenues


Net premiums earned	$	1,948,422	$	1,744,444
Net investment income	98,856		145,153
Net realized gains (losses)	142,461		(366,960)





Other underwriting income	6,110		6,852
Equity in net income (loss) of investment funds accounted for using the equity method	71,686		(4,209)
Other income (loss)	(1,741)		32
Total revenues	2,265,794		1,525,312

Expenses
Losses and loss adjustment expenses	1,203,100		1,115,419
Acquisition expenses	304,481		247,283
Other operating expenses	261,033		234,544
Corporate expenses	25,384		20,796
Amortization of intangible assets	14,402		16,631
Interest expense	38,346		32,555
Net foreign exchange (gains) losses	(20,063)		(72,671)
Total expenses	1,826,683		1,594,557

Income (loss) before income taxes and income (loss) from operating affiliates	439,111		(69,245)
Income tax expense	(38,860)		(27,945)
Income (loss) from operating affiliates	75,457		8,516
Net income (loss)	$	475,708	$	(88,674)
Net (income) loss attributable to noncontrolling interests	(37,552)		232,791
Net income (loss) available to Arch	438,156		144,117
Preferred dividends	(10,403)		(10,403)

Net income (loss) available to Arch common shareholders	$	427,753	$	133,714

Net income per common share and common share equivalent
Basic	$	1.07	$	0.33
Diluted	$	1.05	$	0.32

Weighted average common shares and common share equivalents outstanding
Basic	400,807,895		403,892,161
Diluted	409,223,253		414,033,570

See Notes to Consolidated Financial Statements



ARCH CAPITAL	7	~~2020~~2021 FIRST QUARTER FORM 10-Q

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ARCH CAPITAL GROUP LTD. AND SUBSIDIARIES

ARCH CAPITAL GROUP LTD. AND SUBSIDIARIES
CONSOLIDATED STATEMENTS OF COMPREHENSIVE INCOME
(U.S. dollars in thousands)
(Unaudited)
Three Months Ended
March 31,
2020 2019
Comprehensive Income
Net income (loss) $ (88,674 ) $ 495,498
Other comprehensive income (loss), net of deferred income tax
Unrealized appreciation (decline) in value of available-for-sale investments:
Unrealized holding gains (losses) arising during period (57,287 ) 225,887
Reclassification of net realized (gains) losses, included in net income (loss) (121,229 ) (10,221 )
Foreign currency translation adjustments (44,689 ) 5,516
Comprehensive income (loss) (311,879 ) 716,680
Net (income) loss attributable to noncontrolling interests 232,791
(46,970 )
Other comprehensive (income) loss attributable to noncontrolling interests 33,058
(4,139 )
Comprehensive income (loss) available to Arch $ (46,030 ) $ 665,571
CONSOLIDATED STATEMENTS OF COMPREHENSIVE INCOME

(U.S. dollars in thousands)


	(Unaudited)
	Three Months Ended
	March 31,
	2021		2020
Comprehensive Income
Net income (loss)	$	475,708	$	(88,674)
Other comprehensive income (loss), net of deferred income tax
Unrealized appreciation (decline) in value of available-for-sale investments:
Unrealized holding gains (losses) arising during period	(261,750)		(57,287)

Reclassification of net realized (gains) losses, included in net income (loss)	2,697		(121,229)
Foreign currency translation adjustments	(28,584)		(44,689)
Comprehensive income (loss)	188,071		(311,879)
Net (income) loss attributable to noncontrolling interests	(37,552)		232,791
Other comprehensive (income) loss attributable to noncontrolling interests	4,570		33,058
Comprehensive income (loss) available to Arch	$	155,089	$	(46,030)

See Notes to Consolidated Financial Statements



ARCH CAPITAL	8	~~2020~~2021 FIRST QUARTER FORM 10-Q

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ARCH CAPITAL GROUP LTD. AND SUBSIDIARIES

ARCH CAPITAL GROUP LTD. AND SUBSIDIARIES
CONSOLIDATED STATEMENTS OF CHANGES IN SHAREHOLDERS’ EQUITY
(U.S. dollars in thousands)
(Unaudited)
Three Months Ended
March 31,
2020 2019
Non-cumulative preferred shares
Balance at beginning and end of period 780,000
780,000

Common shares
Balance at beginning of period 638
634
Common shares issued, net 4
2
Balance at end of period 642
636

Additional paid-in capital
Balance at beginning of period 1,889,683
1,793,781
Amortization of share-based compensation 28,602
25,908
Other changes 3,202

(84 )
Balance at end of period 1,921,487
1,819,605

Retained earnings
Balance at beginning of period 11,021,006
9,426,299
Cumulative effect of an accounting change (1) (22,452 ) —
Balance at beginning of period, as adjusted 10,998,554
9,426,299
Net income (loss) (88,674 ) 495,498
Net (income) loss attributable to noncontrolling interests 232,791
(46,970 )
Preferred share dividends (10,403 ) (10,403 )
Balance at end of period 11,132,268
9,864,424

Accumulated other comprehensive income (loss), net of deferred income tax
Balance at beginning of period 212,091
(178,720 )
Unrealized appreciation (decline) in value of available-for-sale investments, net of deferred income tax:
Balance at beginning of period 258,486
(114,178 )
Unrealized holding gains (losses) during period, net of reclassification adjustment (178,516 ) 215,666
Unrealized holding gains (losses) during period attributable to noncontrolling interests 33,179
(4,286 )
Balance at end of period 113,149
97,202
Foreign currency translation adjustments, net of deferred income tax:
Balance at beginning of period (46,395 ) (64,542 )
Foreign currency translation adjustments (44,689 ) 5,516
Foreign currency translation adjustments attributable to noncontrolling interests (121 ) 147
Balance at end of period (91,205 ) (58,879 )
Balance at end of period 21,944
38,323

Common shares held in treasury, at cost
Balance at beginning of period (2,406,047 ) (2,382,167 )
Shares repurchased for treasury (83,050 ) (6,225 )
Balance at end of period (2,489,097 ) (2,388,392 )

Total shareholders’ equity available to Arch 11,367,244
10,114,596
Non-redeemable noncontrolling interests 492,785
838,081
Total shareholders’ equity $ 11,860,029
$ 10,952,677
CONSOLIDATED STATEMENTS OF CHANGES IN SHAREHOLDERS’ EQUITY

(U.S. dollars in thousands)


	(Unaudited)
	Three Months Ended
	March 31,
	2021		2020
Non-cumulative preferred shares



Balance at beginning and end of period	$	780,000	$	780,000







Common shares
Balance at beginning of period	643		638
Common shares issued, net	2		4
Balance at end of period	645		642

Additional paid-in capital
Balance at beginning of period	1,977,794		1,889,683



Amortization of share-based compensation	40,573		28,050



Other changes	(3,626)		3,754
Balance at end of period	2,014,741		1,921,487

Retained earnings
Balance at beginning of period	12,362,463		11,021,006
Cumulative effect of an accounting change (1)	0		(22,452)
Balance at beginning of period, as adjusted	12,362,463		10,998,554
Net income (loss)	475,708		(88,674)
Net (income) loss attributable to noncontrolling interests	(37,552)		232,791
Preferred share dividends	(10,403)		(10,403)

Balance at end of period	12,790,216		11,132,268

Accumulated other comprehensive income (loss), net of deferred income tax
Balance at beginning of period	488,895		212,091
Unrealized appreciation (decline) in value of available-for-sale investments, net of deferred income tax:
Balance at beginning of period	501,295		258,486


Unrealized holding gains (losses) during period, net of reclassification adjustment	(259,053)		(178,516)
Unrealized holding gains (losses) during period attributable to noncontrolling interests	4,469		33,179

Balance at end of period	246,711		113,149
Foreign currency translation adjustments, net of deferred income tax:
Balance at beginning of period	(12,400)		(46,395)
Foreign currency translation adjustments	(28,584)		(44,689)
Foreign currency translation adjustments attributable to noncontrolling interests	100		(121)
Balance at end of period	(40,884)		(91,205)
Balance at end of period	205,827		21,944

Common shares held in treasury, at cost
Balance at beginning of period	(2,503,909)		(2,406,047)
Shares repurchased for treasury	(191,048)		(83,050)
Balance at end of period	(2,694,957)		(2,489,097)

Total shareholders’ equity available to Arch	13,096,472		11,367,244
Non-redeemable noncontrolling interests	876,864		492,785
Total shareholders’ equity	$	13,973,336	$	11,860,029

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

See Notes to Consolidated Financial Statements



ARCH CAPITAL	9	~~2020~~2021 FIRST QUARTER FORM 10-Q

Table of Contents

ARCH CAPITAL GROUP LTD. AND SUBSIDIARIES
CONSOLIDATED STATEMENTS OF CASH FLOWS
(U.S. dollars in thousands)
(Unaudited)
Three Months Ended
March 31,
2020 2019
Operating Activities

Net income (loss) $ (88,674 ) $ 495,498
Adjustments to reconcile net income (loss) to net cash provided by operating activities:
Net realized (gains) losses 362,964
(144,091 )
Equity in net income or loss of investment funds accounted for using the equity method and other income or loss 29,034
(29,752 )
Amortization of intangible assets 16,631
20,417
Share-based compensation 28,549
25,891
Changes in:
Reserve for losses and loss adjustment expenses, net of unpaid losses and loss adjustment expenses recoverable 506,057
(6,005 )
Unearned premiums, net of ceded unearned premiums 392,802
156,393
Premiums receivable (418,457 ) (285,137 )
Deferred acquisition costs (75,135 ) (23,168 )
Reinsurance balances payable 79,807
62,605
Other items, net (223,124 ) (37,253 )
Net cash provided by (used for) operating activities 610,454
235,398
Investing Activities

Purchases of fixed maturity investments (11,965,995 ) (7,444,470 )
Purchases of equity securities (760,683 ) (203,810 )
Purchases of other investments (228,471 ) (324,593 )
Proceeds from sales of fixed maturity investments 11,723,123
7,076,590
Proceeds from sales of equity securities 266,301
95,017
Proceeds from sales, redemptions and maturities of other investments 216,131
216,483
Proceeds from redemptions and maturities of fixed maturity investments 198,356
100,424
Net settlements of derivative instruments 195,488
29,737
Net (purchases) sales of short-term investments (11,777 ) 292,601
Change in cash collateral related to securities lending 55,001
(29,618 )
Purchases of fixed assets (8,470 ) (9,423 )
Other 42,500
(93,731 )
Net cash provided by (used for) investing activities (278,496 ) (294,793 )
Financing Activities

Purchases of common shares under share repurchase program (75,486 ) (2,871 )
Proceeds from common shares issued, net (4,527 ) (1,901 )
Proceeds from borrowings 16,300
59,000
Repayments of borrowings —
(26,038 )
Change in cash collateral related to securities lending (55,001 ) 29,618
Third party investment in non-redeemable noncontrolling interests (2,867 ) —
Dividends paid to redeemable noncontrolling interests (1,181 ) (4,497 )
Other (1,331 ) (1,389 )
Preferred dividends paid (10,403 ) (10,403 )
Net cash provided by (used for) financing activities (134,496 ) 41,519

Effects of exchange rate changes on foreign currency cash and restricted cash (30,723 ) 3,449

Increase (decrease) in cash and restricted cash 166,739
(14,427 )
Cash and restricted cash, beginning of year 903,698
724,643
Cash and restricted cash, end of period $ 1,070,437
$ 710,216

ARCH CAPITAL GROUP LTD. AND SUBSIDIARIES

CONSOLIDATED STATEMENTS OF CASH FLOWS

(U.S. dollars in thousands)


	(Unaudited)
	Three Months Ended
	March 31,
	2021		2020
Operating Activities
Net income (loss)	$	475,708	$	(88,674)
Adjustments to reconcile net income (loss) to net cash provided by operating activities:
Net realized (gains) losses	(161,007)		362,964

Equity in net (income) or loss of investment funds accounted for using the equity method and other income or loss	(135,939)		29,034
Amortization of intangible assets	14,402		16,631
Share-based compensation	40,812		28,549
Changes in:
Reserve for losses and loss adjustment expenses, net of unpaid losses and loss adjustment expenses recoverable	560,153		506,057
Unearned premiums, net of ceded unearned premiums	560,035		392,802
Premiums receivable	(608,250)		(418,457)
Deferred acquisition costs	(126,701)		(75,135)
Reinsurance balances payable	240,206		79,807
Other items, net	(96,574)		(223,124)
Net cash provided by (used for) operating activities	762,845		610,454
Investing Activities
Purchases of fixed maturity investments	(11,530,968)		(11,965,995)
Purchases of equity securities	(309,419)		(760,683)
Purchases of other investments	(430,961)		(228,471)
Proceeds from sales of fixed maturity investments	10,917,134		11,723,123
Proceeds from sales of equity securities	284,986		266,301
Proceeds from sales, redemptions and maturities of other investments	323,591		216,131
Proceeds from redemptions and maturities of fixed maturity investments	421,042		198,356
Net settlements of derivative instruments	47,660		195,488

Net (purchases) sales of short-term investments	589,175		(11,777)
Change in cash collateral related to securities lending	0		55,001

Purchase of operating affiliate	(546,349)		0
Purchases of fixed assets	(12,490)		(8,470)
Other	(246,590)		42,500
Net cash provided by (used for) investing activities	(493,189)		(278,496)
Financing Activities


Purchases of common shares under share repurchase program	(179,266)		(75,486)
Proceeds from common shares issued, net	(10,008)		(4,527)
Proceeds from borrowings	0		16,300

Change in cash collateral related to securities lending	0		(55,001)
Third party investment in non-redeemable noncontrolling interests	15,971		(2,867)

Dividends paid to redeemable noncontrolling interests	(948)		(1,181)
Other	(1,948)		(1,331)
Preferred dividends paid	(10,403)		(10,403)
Net cash provided by (used for) financing activities	(186,602)		(134,496)

Effects of exchange rate changes on foreign currency cash and restricted cash	(6,084)		(30,723)

Increase (decrease) in cash and restricted cash	76,970		166,739
Cash and restricted cash, beginning of year	1,290,544		903,698
Cash and restricted cash, end of period	$	1,367,514	$	1,070,437

See Notes to Consolidated Financial Statements



ARCH CAPITAL	10	~~2020~~2021 FIRST 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 ~~public limited liability~~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 include the results of Watford Holdings Ltd. and its wholly owned subsidiaries (“Watford”). Watford is a multi-line Bermuda reinsurance company. Watford’s own management and board of directors are responsible for its results and profitability. 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, ~~2019~~2020 (“~~2019~~2020 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.~~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’. 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 7. Tabular amounts are in U.S. Dollars in thousands, except share amounts, unless otherwise noted.

Recent Accounting Pronouncements

Recently Issued Accounting Standards Adopted

The Company adopted ASU ~~2018-13, “Fair Value Measurement (Topic 820): Disclosure Framework - Changes to~~2019-12, “Simplifying the ~~Disclosure Requirements~~Accounting for ~~Fair Value Measurement,~~Income Taxes.” ~~which was issued~~This ASU eliminates certain exceptions for recognizing deferred taxes for investments, performing intraperiod tax allocations and calculating income taxes in ~~August, 2018.~~interim periods. The ASU ~~modifies~~also clarifies the ~~disclosure requirements on fair value measurement as part of the disclosure framework project with the objective to improve the effectiveness of disclosures~~accounting for transactions that result in a step-up in the ~~notes to the financial statements. The amendments in this update allow for removal~~tax basis of (1) the amount and reasons for transfer between Level 1 and Level 2 of the fair value hierarchy; (2) the policy for transfers between levels; and (3) the valuation processes for Level 3 fair value measurements. The ASU is effective for fiscal years beginning after December 15, 2019 and interim periods within those fiscal years.goodwill. The adoption of this guidance did not have a material effect on the Company’s consolidated financial statements.

~~The~~For information regarding additional accounting standards that the Company has not yet adopted, ~~ASU 2018-15, “Intangibles - Goodwill and Other - Internal Use Software (Subtopic 350-40)~~see note 3(r), “Significant Accounting Policies—Recent Accounting Pronouncements,” which was issued in the 2018 third quarter. This ASU aligns the requirements for capitalizing certain implementation costs incurred in a cloud computing arrangement that is a service contract with the requirements for capitalizing implementation costs incurred to develop or obtain internal-use software. The standard is effective for financial statements issued for fiscal years, and interim periods within those fiscal years, beginning after December 15, 2019, with early adoption permitted. The guidance provides flexibility in adoption, allowing for either retrospective adjustment or prospective adjustment for all implementation costs incurred after the date of adoption. The Company adopted this guidance prospectively, which did not have a material effect on the Company’s consolidated financial statements.

In March 2020, the SEC amended Rule 3-10 of Regulation S-X regarding financial disclosure requirements for registered debt offerings involving subsidiaries as either issuers or guarantors and affiliates whose securities are pledged as collateral. This new guidance narrows the circumstances that require separate financial statements of subsidiary issuers and guarantors and streamlines the alternative disclosures required in lieu of those statements. The amendment is effective on January 4, 2021 with early adoption permitted. The Company elected to apply the amended requirements for the quarter ended March 31, 2020, and is no longer providing condensed consolidating financial information that resulted from the registered debt obligations of its subsidiaries, Arch Capital Group (US) Inc. and Arch Capital Finance LLC. that were disclosed in Note 26 of the notes to consolidated financial statements in the Company’s ~~2019~~2020 Form 10-K.

2. Share Transactions

Share-Based Compensation

During the 2021 first quarter, the Company granted 1,218,465 stock options, 685,104 performance share awards (“PSAs”) and units (“PSUs”) and 1,168,577 restricted shares and units to certain employees. The stock options were valued at the grant date using the Black-Scholes option pricing model. The weighted average grant-date fair value of the stock options, PSAs/PSUs and restricted shares and units granted during the 2021 first quarter were approximately $9.20, $37.38 and $35.82 per share, respectively. Such values are being amortized over the respective substantive vesting period.

During the 2020 first quarter, the Company ~~adopted ASU 2016-13, “Financial Instruments - Credit Losses (Topic 326),” which was issued in June 2016.~~granted 1,116,073 stock options, 557,204 PSAs and PSUs and 910,879 restricted shares and units to certain employees. The stock options were valued at the grant date using the Black-Scholes option pricing model. The weighted average grant-date fair value of the stock options, PSAs/PSUs and restricted shares and units granted during the 2020 first quarter were approximately $8.14, $44.17 and $42.36 per share, respectively. Such values are being amortized over the respective substantive vesting period.



ARCH CAPITAL	11	~~2020~~2021 FIRST QUARTER FORM 10-Q

Table of Contents

ARCH CAPITAL GROUP LTD. AND SUBSIDIARIES

NOTES TO CONSOLIDATED FINANCIAL STATEMENTS (UNAUDITED)

Share Repurchases

under the share repurchase program with an aggregate purchase price of $75.5 million during the three months ended March 31, 2020. At March 31, 2021, $737.3 million of share repurchases were available under the program, which may be effected from time to time in open market or privately negotiated transactions through December 31, 2021. 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.

3. Earnings Per Common Share

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


	Three Months Ended
	March 31,
	2021		2020
Numerator:
Net income (loss)	$	475,708	$	(88,674)
Amounts attributable to noncontrolling interests	(37,552)		232,791
Net income (loss) available to Arch	438,156		144,117
Preferred dividends	(10,403)		(10,403)

Net income (loss) available to Arch common shareholders	$	427,753	$	133,714

Denominator:


Weighted average common shares and common share equivalents outstanding — basic	400,807,895		403,892,161
Effect of dilutive common share equivalents:
Nonvested restricted shares	2,230,794		2,275,473
Stock options (1)	6,184,564		7,865,936
Weighted average common shares and common share equivalents outstanding — diluted	409,223,253		414,033,570

Earnings per common share:
Basic	$	1.07	$	0.33
Diluted	$	1.05	$	0.32

(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 first quarter and 2020 first quarter, the number of stock options excluded were 2,400,082 and 1,155,088, respectively.


ARCH CAPITAL			12			2021 FIRST QUARTER FORM 10-Q

Table of Contents

ARCH CAPITAL GROUP LTD. AND SUBSIDIARIES

NOTES TO CONSOLIDATED FINANCIAL STATEMENTS (UNAUDITED)

4. Segment Information

The ~~ASU applies a new credit loss model (current expected credit losses) for determining credit~~Company classifies its businesses into 3 underwriting segments — insurance, reinsurance and mortgage — and 2 other operating segments — ‘other’ and corporate (non-underwriting). The Company determined its reportable segments using the management approach described in accounting guidance regarding disclosures about segments of an enterprise and related impairments for financial instruments measured at amortized cost, including reinsurance recoverable, contractholder receivables, and premiums receivable, and requires an entity to estimate its lifetime “expected credit loss” and record an allowance that, when deducted from the amortized cost basisinformation. The accounting policies of the segments are the same as those used for the preparation of the Company’s consolidated financial ~~asset, presents~~statements. Intersegment business is allocated to the ~~net amount expected~~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 ~~be collected~~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 three underwriting segments based on underwriting income or loss. The Company does not manage its assets by underwriting segment, with the ~~financial asset.~~ exception of goodwill and intangible assets, and, accordingly, investment income is not allocated to each underwriting segment.

The ~~estimate~~insurance segment consists of ~~expected credit losses should consider historical information, current information,~~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. and international mortgage insurance and reinsurance operations as well as ~~reasonable~~government sponsored enterprise (“GSE”) credit-risk sharing transactions. Arch Mortgage Insurance Company and ~~supportable forecasts, including estimates of prepayments.~~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 ASU also amends the previous other-than-temporary impairment model for available-for-sale debt securities by requiring the recognition of impairments relating to credit losses through an allowance accountcorporate (non-underwriting) segment results include net investment income, other income (loss), corporate expenses, transaction costs and ~~limits the amount of credit loss~~other, interest expense, items related to the ~~difference between a security’s amortized cost basis and its fair value. In addition, the length of time a security has been~~Company’s non-cumulative preferred shares, net realized gains or losses (which includes changes in ~~an unrealized loss position will no longer impact the determination of whether a credit loss exists.~~

The Company adopted the ASU for the quarter ending March 31, 2020 by recognizing an after-tax cumulative effect adjustment of $22.5 million to the opening balance of retained earnings as of January 1, 2020. The cumulative effect adjustment decreased retained earnings and increased the allowance for credit ~~losses.~~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, income or loss from operating affiliates and income taxes. Such amounts exclude the results of the ‘other’ segment.

~~Significant Accounting Policies~~The ‘other’ segment includes the results of Watford (see note 11). For the ‘other’ segment, performance is measured based on net income or loss.


ARCH CAPITAL			13			2021 FIRST QUARTER FORM 10-Q

Table of Contents

ARCH CAPITAL GROUP LTD. AND SUBSIDIARIES

NOTES TO CONSOLIDATED FINANCIAL STATEMENTS (UNAUDITED)

The following ~~accounting policies~~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
	March 31, 2021
	Insurance			Reinsurance			Mortgage			Sub-Total			Other			Total

Gross premiums written (1)	$	1,415,886		$	1,471,060		$	391,246		$	3,277,293		$	216,523		$	3,397,206
Premiums ceded	(421,047)			(471,948)			(56,051)			(948,147)			(37,212)			(888,749)
Net premiums written	994,839			999,112			335,195			2,329,146			179,311			2,508,457
Change in unearned premiums	(175,365)			(354,212)			1,122			(528,455)			(31,580)			(560,035)
Net premiums earned	819,474			644,900			336,317			1,800,691			147,731			1,948,422
Other underwriting income (loss)	0			(1,198)			6,897			5,699			411			6,110
Losses and loss adjustment expenses	(535,747)			(484,870)			(63,689)			(1,084,306)			(118,794)			(1,203,100)
Acquisition expenses	(128,222)			(118,025)			(30,082)			(276,329)			(28,152)			(304,481)
Other operating expenses	(137,113)			(60,514)			(49,131)			(246,758)			(14,275)			(261,033)
Underwriting income (loss)	$	18,392		$	(19,707)		$	200,312		198,997			(13,079)			185,918

Net investment income										78,729			20,127			98,856
Net realized gains (losses)										101,336			41,125			142,461

Equity in net income (loss) of investment funds accounted for using the equity method										71,686			0			71,686
Other income (loss)										(1,741)			0			(1,741)
Corporate expenses (2)										(23,468)			0			(23,468)
Transaction costs and other (2)										(1,201)			(715)			(1,916)
Amortization of intangible assets										(14,402)			0			(14,402)
Interest expense										(34,197)			(4,149)			(38,346)
Net foreign exchange gains (losses)										21,505			(1,442)			20,063
Income (loss) before income taxes and income (loss) from operating affiliates										397,244			41,867			439,111
Income tax (expense) benefit										(38,852)			(8)			(38,860)
Income (loss) from operating affiliates										75,457			0			75,457
Net income (loss)										433,849			41,859			475,708
Amounts attributable to redeemable noncontrolling interests										117			(972)			(855)
Amounts attributable to nonredeemable noncontrolling interests										0			(36,697)			(36,697)
Net income (loss) available to Arch										433,966			4,190			438,156
Preferred dividends										(10,403)			0			(10,403)

Net income (loss) available to Arch common shareholders										$	423,563		$	4,190		$	427,753

Underwriting Ratios
Loss ratio	65.4		%	75.2		%	18.9		%	60.2		%	80.4		%	61.7		%
Acquisition expense ratio	15.6		%	18.3		%	8.9		%	15.3		%	19.1		%	15.6		%
Other operating expense ratio	16.7		%	9.4		%	14.6		%	13.7		%	9.7		%	13.4		%
Combined ratio	97.7		%	102.9		%	42.4		%	89.2		%	109.2		%	90.7		%

Goodwill and intangible assets	$	276,211		$	17,807		$	377,841		$	671,859		$	7,650		$	679,509

(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 ~~updated~~excluded from ‘corporate expenses’ and reflected in ‘transaction costs and other.’


ARCH CAPITAL			14			2021 FIRST QUARTER FORM 10-Q

Table of Contents

ARCH CAPITAL GROUP LTD. AND SUBSIDIARIES

NOTES TO CONSOLIDATED FINANCIAL STATEMENTS (UNAUDITED)


	Three Months Ended
	March 31, 2020
	Insurance			Reinsurance			Mortgage			Sub-Total			Other			Total

Gross premiums written (1)	$	1,207,645		$	1,122,519		$	368,945		$	2,698,537		$	234,902		$	2,832,830
Premiums ceded	(378,897)			(325,339)			(44,327)			(747,991)			(48,202)			(695,584)
Net premiums written	828,748			797,180			324,618			1,950,546			186,700			2,137,246
Change in unearned premiums	(112,829)			(253,720)			20,408			(346,141)			(46,661)			(392,802)
Net premiums earned	715,919			543,460			345,026			1,604,405			140,039			1,744,444
Other underwriting income (loss)	0			2,120			4,599			6,719			133			6,852
Losses and loss adjustment expenses	(507,108)			(430,069)			(67,566)			(1,004,743)			(110,676)			(1,115,419)
Acquisition expenses	(107,337)			(79,606)			(38,536)			(225,479)			(21,804)			(247,283)
Other operating expenses	(129,649)			(45,297)			(45,896)			(220,842)			(13,702)			(234,544)
Underwriting income (loss)	$	(28,175)		$	(9,392)		$	197,627		160,060			(6,010)			154,050

Net investment income										113,028			32,125			145,153
Net realized gains (losses)										(72,109)			(294,851)			(366,960)

Equity in net income (loss) of investment funds accounted for using the equity method										(4,209)			0			(4,209)
Other income (loss)										32			0			32
Corporate expenses (2)										(18,201)			0			(18,201)
Transaction costs and other (2)										(2,595)			0			(2,595)
Amortization of intangible assets										(16,631)			0			(16,631)
Interest expense										(25,245)			(7,310)			(32,555)
Net foreign exchange gains (losses)										63,307			9,364			72,671
Income (loss) before income taxes and income (loss) from operating affiliates										197,437			(266,682)			(69,245)
Income tax (expense) benefit										(27,945)			0			(27,945)
Income (loss) from operating affiliates										8,516			0			8,516
Net income (loss)										178,008			(266,682)			(88,674)
Amounts attributable to redeemable noncontrolling interests										(57)			(1,096)			(1,153)
Amounts attributable to nonredeemable noncontrolling interests										0			233,944			233,944
Net income (loss) available to Arch										177,951			(33,834)			144,117
Preferred dividends										(10,403)			0			(10,403)

Net income (loss) available to Arch common shareholders										$	167,548		$	(33,834)		$	133,714

Underwriting Ratios
Loss ratio	70.8		%	79.1		%	19.6		%	62.6		%	79.0		%	63.9		%
Acquisition expense ratio	15.0		%	14.6		%	11.2		%	14.1		%	15.6		%	14.2		%
Other operating expense ratio	18.1		%	8.3		%	13.3		%	13.8		%	9.8		%	13.4		%
Combined ratio	103.9		%	102.0		%	44.1		%	90.5		%	104.4		%	91.5		%

Goodwill and intangible assets	$	268,296		$	2,516		$	426,988		$	697,800		$	7,650		$	705,450

(1) Certain amounts included in the gross premiums written of each segment are related to ~~reflect~~intersegment transactions. Accordingly, the ~~Company's adoption~~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.’


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ARCH CAPITAL GROUP LTD. AND SUBSIDIARIES

NOTES TO CONSOLIDATED FINANCIAL STATEMENTS (UNAUDITED)

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 ~~new accounting guidance on credit losses.~~beginning and ending reserve for losses and loss adjustment expenses:

~~Investments~~


	Three Months Ended
	March 31,
	2021		2020
Reserve for losses and loss adjustment expenses at beginning of period	$	16,513,929	$	13,891,842
Unpaid losses and loss adjustment expenses recoverable	4,314,855		4,082,650
Net reserve for losses and loss adjustment expenses at beginning of period	12,199,074		9,809,192

Net incurred losses and loss adjustment expenses relating to losses occurring in:
Current year	1,244,772		1,134,442
Prior years	(41,672)		(19,023)
Total net incurred losses and loss adjustment expenses	1,203,100		1,115,419

Retroactive reinsurance transactions (1)	(183,893)		60,635

Net foreign exchange (gains) losses	(46,877)		(142,573)

Net paid losses and loss adjustment expenses relating to losses occurring in:
Current year	(58,984)		(41,260)
Prior years	(585,118)		(561,947)
Total net paid losses and loss adjustment expenses	(644,102)		(603,207)

Net reserve for losses and loss adjustment expenses at end of period	12,527,302		10,239,466
Unpaid losses and loss adjustment expenses recoverable	3,916,650		4,070,114
Reserve for losses and loss adjustment expenses at end of period	$	16,443,952	$	14,309,580

~~The~~(1) During 2021 first quarter, the Company ~~conducts~~entered into a ~~periodic review~~reinsurance to ~~identify~~close and ~~evaluate credit based impairments~~other related agreements with Premia Managing Agency Limited (“Premia”), in connection with the 2018 and prior years of account related to the ~~Company’s available for sale investments. The~~acquisition of Barbican Group Holdings Limited (“Barbican”). During the 2020 first quarter, the Company ~~derives estimated credit losses by comparing expected future cash flows~~entered into a reinsurance to ~~be collected to the amortized cost~~close agreement of the ~~security. Estimates~~2017 and prior years of ~~expected future cash flows consider among other things, macroeconomic conditions as well as~~account previously covered by a third party arrangement.

Development on Prior Year Loss Reserves

2021 First Quarter

During the ~~financial condition, near-term~~2021 first quarter, the Company recorded net favorable development on prior year loss reserves of $41.7 million, which consisted of $4.1 million favorable development from the insurance segment, $26.8 million from the reinsurance segment and ~~long-term prospects~~$10.9 million from the mortgage segment, partially offset by $0.1 million unfavorable from the ‘other’ segment.

The insurance segment’s net favorable development of $4.1 million, or 0.5 loss ratio points, for the ~~issuer,~~2021 first quarter consisted of $25.0 million of net favorable development in short-tailed and $20.9 million of net adverse development in medium-tailed lines. Net favorable development in short-tailed lines reflected $14.6 million of favorable development from property (excluding marine), primarily from the ~~likelihood~~2019 and 2020 accident years (i.e., the year in which a loss occurred), $8.0 million of favorable development in lenders products, primarily from the ~~recoverability~~2020 accident year, and $2.5

million of ~~principal~~favorable development in travel and ~~interest. Effective January 1,~~accident, primarily from the 2020 ~~credit~~accident year. Net adverse development in medium-tailed lines included $10.8 million of adverse development in program business, primarily from the 2016 to 2020 accident years, $6.0 million of adverse development in professional liability business, primarily from the 2019 accident year, and $5.0 million of adverse development in surety, primarily from the 2019 accident year.

The reinsurance segment’s net favorable development of $26.8 million, or 4.2 loss ratio points, for the 2021 first quarter consisted of net favorable development in short-tailed, medium-tailed and long-tailed lines. Net favorable development of $17.5 million in short-tailed lines reflected $23.3 million of favorable development related to property other than property catastrophe business, primarily from the 2016 to 2019 underwriting years (i.e., all premiums and losses ~~are recognized through an allowance account subject to reversal, rather than a reduction in amortized cost. Declines in value~~ attributable to ~~factors~~contracts having an inception or renewal date within the given twelve-month period), and $16.6 million of favorable development from other specialty,


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NOTES TO CONSOLIDATED FINANCIAL STATEMENTS (UNAUDITED)

primarily from the 2018 and 2019 underwriting years, partially offset by $22.5 million of net adverse development related to property catastrophe, primarily from the 2020 underwriting year. Net favorable development of $9.3 million in medium and long-tailed lines reflected favorable development in casualty across most underwriting years.

The mortgage segment’s net favorable development was $10.9 million, or 3.2 loss ratio points, for the 2021 first quarter, primarily driven by favorable development in the credit risk transfer and international portfolios. Subrogation recoveries on second lien and student loan business also contributed.

2020 First Quarter

During the 2020 first quarter, the Company recorded net favorable development on prior year loss reserves of $19.0 million, which consisted of $1.1 million from the insurance segment, $11.6 million from the reinsurance segment, $6.1 million from the mortgage segment and $0.2 million from the ‘other’ segment.

The insurance segment’s net favorable development of $1.1 million, or 0.2 loss ratio points, for the 2020 first quarter consisted of $3.9 million of net favorable development in short-tailed lines, $7.9 million of net adverse development in medium-tailed lines and $5.2 million of net favorable development in long-tailed lines. Net favorable development in short-tailed lines primarily resulted from lenders products and property (including special risk other than ~~credit are reported~~marine) reserves across 2018 and prior accident years. Net adverse development in medium-tailed lines included $13.2 million of adverse development in contract binding business across most accident years, partially offset by $5.1 million of favorable development in professional liability business. Net favorable development in longer-tailed lines primarily related to construction business driven by the 2017 accident year.

~~For available for sale investments that the Company intends to sell or for which it is more likely~~2019 underwriting years. Such amounts were partially offset by $4.3 million of adverse development in property other than ~~not that the Company would be required to sell before an anticipated recovery in value, the full amount of the impairment is included in net~~

~~realized gains (losses). The new cost basis of the investment is the previous amortized cost basis reduced~~property catastrophe business, driven by the ~~impairment recognized~~2018 underwriting year. Adverse development in long-tailed lines reflected an increase in casualty reserves from various underwriting years.

The mortgage segment’s net ~~realized gains (losses).~~favorable development was $6.1 million, or 1.8 loss ratio points, for the 2020 first quarter. The ~~new cost basis is not adjusted~~2020 first quarter development was primarily driven by subrogation recoveries on second lien and student loan business.

6. Allowance for ~~any subsequent recoveries in fair value.~~Expected Credit Losses

Premiums Receivable

The ~~Company reports accrued investment income separately from investment balances and has elected not to measure an allowance for credit losses for accrued investment income~~. ~~Any uncollectible accrued interest income is written off in the period it is deemed uncollectible.~~

~~Reinsurance Recoverables~~

~~In the normal course~~following table provides a roll forward of business, the Company’s subsidiaries cede a portion of their premium and losses through pro rata and excess of loss reinsurance agreements on a treaty or facultative basis. Reinsurance recoverables are recorded as assets, predicated on the reinsurers’ ability to meet their obligations under the reinsurance agreements. In certain instances, the Company obtains collateral, including letters of credit and trust accounts to further reduce the credit exposure on its reinsurance recoverables. The Company reports its reinsurance recoverables net of an allowance for expected credit loss. The allowance is based upon the Company’s ongoing review of amounts outstanding, the financial condition of its reinsurers, amounts and form of collateral obtained and other relevant factors. A ratings based probability-of-default and loss-given-default methodology is used to estimate the allowance for expected credit ~~loss. Any~~losses of the Company’s premium receivables:



	Premium Receivables, Net of Allowance		Allowance for Expected Credit Losses
March 31, 2021
Balance at beginning of period	$	2,064,586	$	37,781

Change for provision of expected credit losses (1)			(1,670)


Balance at end of period	$	2,618,175	$	36,111

December 31, 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)			10,239
Balance at end of period	$	2,064,586	$	37,781

(1)Amounts deemed uncollectible are written-off in operating expenses. For the March 31, 2021 and as of December 31, 2020, amounts written off were $0.1 million and $2.8 million, respectively.

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

Reinsurance Recoverables

The following table provides a roll forward of the allowance for ~~credit losses is charged to net realized gains (losses) in the period the recoverable is recorded and revised in subsequent periods to reflect changes in the Company’s estimate of~~ expected credit losses of the Company’s reinsurance recoverables:



	Reinsurance Recoverables, Net of Allowance		Allowance for Expected Credit Losses
March 31, 2021
Balance at beginning of period	$	4,500,802	$	11,636

Change for provision of expected credit losses			(764)


Balance at end of period	$	4,041,076	$	10,872

December 31, 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			(1,738)
Balance at end of period	$	4,500,802	$	11,636

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


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ARCH CAPITAL GROUP LTD. AND SUBSIDIARIES

NOTES TO CONSOLIDATED FINANCIAL STATEMENTS (UNAUDITED)

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


	March 31,			December 31
	2021			2020
Reinsurance recoverable on unpaid and paid losses and loss adjustment expenses	$	4,041,076		$	4,500,802
% due from carriers with A.M. Best rating of “A-” or better	64.5		%	63.9		%
% due from all other carriers with no A.M. Best rating (1)	35.5		%	36.1		%
Largest balance due from any one carrier as % of total shareholders’ equity	1.7		%	1.8		%

(1) At March 31, 2021 and December 31, 2020 over 92% and 94% of such amount were collateralized through reinsurance trusts, funds withheld arrangements, letters of credit or other, respectively.

~~Contractholder Receivables~~Premiums Receivable

~~Certain insurance policies written by the Company’s U.S. insurance operations feature large deductibles, primarily in its construction and national accounts line~~The following table provides a roll forward of business. Under such contracts, the Company is obligated to pay the claimant for the full amount of the claim. The Company is subsequently reimbursed by the policy holder for the deductible amount. These amounts are included on a gross basis in the consolidated balance sheet as contractholder payables and contractholder receivables. In the event that the Company is unable to collect from the policyholder, the Company would be liable for such defaulted amounts. Collateral, primarily in the form of letters of credit, cash and trusts, is obtained from the policyholder to mitigate the Company’s credit risk.

Contractholder receivables are reported net of an allowance for expected credit losses. The allowance is based upon the Company’s ongoing review of amounts outstanding, changes in policyholder credit standing, amounts and form of collateral obtained, and other relevant factors. A ratings based probability-of-default and loss-given-default methodology is used to estimate the allowance for expected credit ~~losses.~~ losses of the Company’s premium receivables:



	Premium Receivables, Net of Allowance		Allowance for Expected Credit Losses
March 31, 2021
Balance at beginning of period	$	2,064,586	$	37,781

Change for provision of expected credit losses (1)			(1,670)


Balance at end of period	$	2,618,175	$	36,111

December 31, 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)			10,239
Balance at end of period	$	2,064,586	$	37,781

(1)~~Any~~Amounts deemed uncollectible are written-off in operating expenses. For the March 31, 2021 and as of December 31, 2020, amounts written off were $0.1 million and $2.8 million, respectively.

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

Reinsurance Recoverables

The following table provides a roll forward of the allowance for expected credit losses ~~is charged to net realized gains~~of the Company’s reinsurance recoverables:



	Reinsurance Recoverables, Net of Allowance		Allowance for Expected Credit Losses
March 31, 2021
Balance at beginning of period	$	4,500,802	$	11,636

Change for provision of expected credit losses			(764)


Balance at end of period	$	4,041,076	$	10,872

December 31, 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			(1,738)
Balance at end of period	$	4,500,802	$	11,636

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



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ARCH CAPITAL GROUP LTD. AND SUBSIDIARIES

NOTES TO CONSOLIDATED FINANCIAL STATEMENTS (UNAUDITED)

~~(losses) in the period the receivable is recorded and revised in subsequent periods to reflect changes in~~The following table summarizes the Company’s ~~estimate of expected credit~~reinsurance recoverables on paid and unpaid losses. (not including ceded unearned premiums):

~~Premiums Receivable~~


	March 31,			December 31
	2021			2020
Reinsurance recoverable on unpaid and paid losses and loss adjustment expenses	$	4,041,076		$	4,500,802
% due from carriers with A.M. Best rating of “A-” or better	64.5		%	63.9		%
% due from all other carriers with no A.M. Best rating (1)	35.5		%	36.1		%
Largest balance due from any one carrier as % of total shareholders’ equity	1.7		%	1.8		%

Premiums receivable include amounts receivable from agents, brokers and insured that are both currently due and amounts not yet due on insurance, reinsurance and mortgage insurance policies. Premiums receivable balances are reported net of an allowance for expected credit losses. The Company monitors credit risk associated with premiums receivable through its ongoing review of amounts outstanding, aging of the receivable, historical loss data, and counterparty financial strength measures. The allowance also includes estimated uncollectible amounts related to dispute risk. Amounts deemed to be uncollectible are written off against the allowance. In certain instances, credit risk may be reduced by the Company’s right to offset loss obligations or unearned premiums against premiums receivable. Any allowance for credit losses is charged to net realized gains (losses) in the period the receivable is recorded and revised in subsequent periods to reflect changes in the Company’s estimate of expected credit losses.

~~Recently Issued Accounting Standards Not Yet Adopted~~

In March 2020, the FASB issued ASU 2020-04, “Facilitation of the Effects of Reference Rate Reform on Financial Reporting.” This ASU provides optional expedients and exceptions for applying GAAP to investments, derivatives, or other transactions that reference the London Interbank Offered Rate (LIBOR) or another reference rate ~~expected~~ to be discontinued because of reference rate reform. Along with the optional expedients, the amendments include a general principle that permits an entity to consider contract modifications due to reference reform to be an event that does not require contract re-measurement at the modification date or reassessment of a previous accounting determination. Additionally, a company may make a one-time election to sell, transfer, or both sell and transfer debt securities classified as held to maturity that reference a rate affected by reference rate reform and that were classified as held to maturity before January 1, 2020. This standard may be elected over time through December 31, 2022 as reference rate reform activities occur. We are currently assessing the effect of adopting this guidance on our financial condition and results of operations.

~~For~~ information regarding additional accounting standards that the Company has not yet adopted, see note 3(r), “Significant Accounting Policies—Recent Accounting Pronouncements,” of the notes to consolidated financial statements in the Company’s 2019 Form 10-K.

~~2. Share Transactions~~

~~Share-Based Compensation~~

During the 2020 first quarter, the Company granted 1,116,073 stock options, 557,204 performance share awards (“PSAs”) and units (“PSUs”) and 910,879 restricted shares and units to certain employees. The stock options were valued at the grant date using the Black-Scholes option pricing model. The weighted average grant-date fair value of the stock options, PSAs/PSUs and restricted shares and units granted during the 2020 first quarter were approximately $8.14, $44.17 and $42.36 per share, respectively. Such values are being amortized over the respective substantive vesting period.

During the 2019 first quarter, the Company granted 1,182,264 stock options, 672,768 PSAs and PSUs and 1,099,125 restricted shares and units to certain employees. The stock options were valued at the grant date using the Black-Scholes option pricing model. The weighted average grant-date fair value of the stock options, PSAs/PSUs and restricted shares and units granted during the 2019 first quarter were approximately $7.90, $35.83 and $32.64 per share, respectively. Such values are being amortized over the respective substantive vesting period.

~~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 388.9 million common shares for an aggregate purchase price of $4.04 billion. For the three months ended March 31, 2020, Arch Capital repurchased 2.6 million shares under the share repurchase program with an aggregate purchase price of $75.5 million. Arch Capital repurchased 0.1 million shares under the share repurchase program with an aggregate purchase price of $2.9 million during the three months ended March 31, 2019.(1) At March 31, ~~2020, $924.5 million of share repurchases were available under the program, which may be effected from time to time in open market or privately negotiated transactions through~~2021 and December 31, ~~2021. The timing~~2020 over 92% and 94% of such amount were collateralized through reinsurance trusts, funds withheld arrangements, letters of ~~the repurchase transactions under this program will depend on a variety of factors, including market conditions and corporate and regulatory considerations.~~

credit or other, respectively.



~~ARCH CAPITAL~~	13	~~2020 FIRST QUARTER FORM 10-Q~~

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~~ARCH CAPITAL GROUP LTD. AND SUBSIDIARIES~~

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

~~3. Earnings Per Common Share~~

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

Three Months Ended
March 31,
2020 2019
Numerator:
Net income (loss) $ (88,674 ) $ 495,498
Amounts attributable to noncontrolling interests 232,791
(46,970 )
Net income available to Arch 144,117
448,528
Preferred dividends (10,403 ) (10,403 )
Net income available to Arch common shareholders $ 133,714
$ 438,125

Denominator:
Weighted average common shares and common share equivalents outstanding — basic 403,892,161
400,184,404
Effect of dilutive common share equivalents:
Nonvested restricted shares 2,275,473
1,807,488
Stock options (1) 7,865,936
6,979,137
Weighted average common shares and common share equivalents outstanding — diluted 414,033,570
408,971,029

Earnings per common share:
Basic $ 0.33
$ 1.09
Diluted $ 0.32
$ 1.07

~~(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 2020 first quarter and 2019 first quarter, the number of stock options excluded were 1,155,088 and 5,577,724, respectively.



~~ARCH CAPITAL~~	14	~~2020 FIRST QUARTER FORM 10-Q~~

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~~ARCH CAPITAL GROUP LTD. AND SUBSIDIARIES~~

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

~~4. Segment Information~~

The Company classifies its businesses into 3 underwriting segments — insurance, reinsurance and mortgage — and 2 other operating segments — ‘other’ and corporate (non-underwriting). 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 President and Chief Executive Officer of Arch Capital, and the Chief Financial 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 three 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 mortgage segment includes the Company’s U.S. and international mortgage insurance and reinsurance operations as well as government sponsored enterprise (“GSE”) credit-risk sharing transactions. 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.

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 accounted for using the equity method, net foreign exchange gains or losses and income taxes. Such amounts exclude the results of the ‘other’ segment.

~~The ‘other’ segment includes the results of Watford (see~~ ~~note 12). For the ‘other’ segment, performance is measured based on net income or loss.~~



~~ARCH CAPITAL~~	15	~~2020 FIRST QUARTER FORM 10-Q~~

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~~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
March 31, 2020
Insurance Reinsurance Mortgage Sub-Total Other Total

Gross premiums written (1) $ 1,207,645
$ 1,122,519
$ 368,945
$ 2,698,537
$ 234,902
$ 2,832,830
Premiums ceded (378,897 ) (325,339 ) (44,327 ) (747,991 ) (48,202 ) (695,584 )
Net premiums written 828,748
797,180
324,618
1,950,546
186,700
2,137,246
Change in unearned premiums (112,829 ) (253,720 ) 20,408
(346,141 ) (46,661 ) (392,802 )
Net premiums earned 715,919
543,460
345,026
1,604,405
140,039
1,744,444
Other underwriting income (loss) —
2,120
4,599
6,719
133
6,852
Losses and loss adjustment expenses (507,108 ) (430,069 ) (67,566 ) (1,004,743 ) (110,676 ) (1,115,419 )
Acquisition expenses (107,337 ) (79,606 ) (38,536 ) (225,479 ) (21,804 ) (247,283 )
Other operating expenses (129,649 ) (45,297 ) (45,896 ) (220,842 ) (13,702 ) (234,544 )
Underwriting income (loss) $ (28,175 ) $ (9,392 ) $ 197,627
160,060
(6,010 ) 154,050

Net investment income 113,028
32,125
145,153
Net realized gains (losses) (72,109 ) (294,851 ) (366,960 )
Equity in net income (loss) of investment funds accounted for using the equity method (4,209 ) —
(4,209 )
Other income (loss) 8,548
—
8,548
Corporate expenses (2) (18,201 ) —
(18,201 )
Transaction costs and other (2) (2,595 ) —
(2,595 )
Amortization of intangible assets (16,631 ) —
(16,631 )
Interest expense (25,245 ) (7,310 ) (32,555 )
Net foreign exchange gains (losses) 63,307
9,364
72,671
Income (loss) before income taxes 205,953
(266,682 ) (60,729 )
Income tax expense (27,945 ) —
(27,945 )
Net income (loss) 178,008
(266,682 ) (88,674 )
Amounts attributable to redeemable noncontrolling interests (57 ) (1,096 ) (1,153 )
Amounts attributable to nonredeemable noncontrolling interests —
233,944
233,944
Net income (loss) available to Arch 177,951
(33,834 ) 144,117
Preferred dividends (10,403 ) —
(10,403 )
Net income (loss) available to Arch common shareholders $ 167,548
$ (33,834 ) $ 133,714

Underwriting Ratios
Loss ratio 70.8 % 79.1 % 19.6 % 62.6 % 79.0 % 63.9 %
Acquisition expense ratio 15.0 % 14.6 % 11.2 % 14.1 % 15.6 % 14.2 %
Other operating expense ratio 18.1 % 8.3 % 13.3 % 13.8 % 9.8 % 13.4 %
Combined ratio 103.9 % 102.0 % 44.1 % 90.5 % 104.4 % 91.5 %

Goodwill and intangible assets $ 268,296
$ 2,516
$ 426,988
$ 697,800
$ 7,650
$ 705,450


~~(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~~	16	~~2020 FIRST QUARTER FORM 10-Q~~

~~Table of Contents~~

~~ARCH CAPITAL GROUP LTD. AND SUBSIDIARIES~~

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

Three Months Ended
March 31, 2019
Insurance Reinsurance Mortgage Sub-Total Other Total

Gross premiums written (1) $ 941,954
$ 682,855
$ 356,050
$ 1,980,453
$ 186,689
$ 2,077,879
Premiums ceded (320,622 ) (231,567 ) (48,798 ) (600,581 ) (41,302 ) (552,620 )
Net premiums written 621,332
451,288
307,252
1,379,872
145,387
1,525,259
Change in unearned premiums (67,827 ) (104,923 ) 15,650
(157,100 ) 707
(156,393 )
Net premiums earned 553,505
346,365
322,902
1,222,772
146,094
1,368,866
Other underwriting income (loss) —
4,377
3,856
8,233
592
8,825
Losses and loss adjustment expenses (356,723 ) (239,810 ) (11,149 ) (607,682 ) (110,850 ) (718,532 )
Acquisition expenses (82,824 ) (54,326 ) (31,672 ) (168,822 ) (29,026 ) (197,848 )
Other operating expenses (113,396 ) (35,704 ) (39,875 ) (188,975 ) (12,188 ) (201,163 )
Underwriting income (loss) $ 562
$ 20,902
$ 244,062
265,526
(5,378 ) 260,148

Net investment income 121,249
35,700
156,949
Net realized gains (losses) 111,124
29,132
140,256
Equity in net income (loss) of investment funds accounted for using the equity method 46,867
—
46,867
Other income (loss) 1,083
—
1,083
Corporate expenses (2) (16,772 ) —
(16,772 )
Transaction costs and other (2) (1,190 ) —
(1,190 )
Amortization of intangible assets (20,417 ) —
(20,417 )
Interest expense (23,482 ) (5,583 ) (29,065 )
Net foreign exchange gains (losses) 5,175
(1,650 ) 3,525
Income before income taxes 489,163
52,221
541,384
Income tax expense (45,886 ) —
(45,886 )
Net income 443,277
52,221
495,498
Amounts attributable to redeemable noncontrolling interests —
(4,588 ) (4,588 )
Amounts attributable to nonredeemable noncontrolling interests —
(42,382 ) (42,382 )
Net income available to Arch 443,277
5,251
448,528
Preferred dividends (10,403 ) —
(10,403 )
Net income available to Arch common shareholders $ 432,874
$ 5,251
$ 438,125

Underwriting Ratios

Loss ratio 64.4 % 69.2 % 3.5 % 49.7 % 75.9 % 52.5 %
Acquisition expense ratio 15.0 % 15.7 % 9.8 % 13.8 % 19.9 % 14.5 %
Other operating expense ratio 20.5 % 10.3 % 12.3 % 15.5 % 8.3 % 14.7 %
Combined ratio 99.9 % 95.2 % 25.6 % 79.0 % 104.1 % 81.7 %

Goodwill and intangible assets $ 156,735
$ —
$ 494,830
$ 651,565
$ 7,650
$ 659,215


~~(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~~	17	~~2020 FIRST QUARTER FORM 10-Q~~

~~Table of Contents~~

~~ARCH CAPITAL GROUP LTD. AND SUBSIDIARIES~~

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

~~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
March 31,
2020 2019
Reserve for losses and loss adjustment expenses at beginning of period $ 13,891,842
$ 11,853,297
Unpaid losses and loss adjustment expenses recoverable 4,082,650
2,814,291
Net reserve for losses and loss adjustment expenses at beginning of period 9,809,192
9,039,006

Net incurred losses and loss adjustment expenses relating to losses occurring in:
Current year 1,134,442
757,964
Prior years (19,023 ) (39,432 )
Total net incurred losses and loss adjustment expenses 1,115,419
718,532

Retroactive reinsurance transactions (1) 60,635
(225,500 )

Net foreign exchange (gains) losses and other (142,573 ) (504 )

Net paid losses and loss adjustment expenses relating to losses occurring in:
Current year (41,260 ) (64,340 )
Prior years (561,947 ) (427,312 )
Total net paid losses and loss adjustment expenses (603,207 ) (491,652 )

Net reserve for losses and loss adjustment expenses at end of period 10,239,466
9,039,882
Unpaid losses and loss adjustment expenses recoverable 4,070,114
2,970,159
Reserve for losses and loss adjustment expenses at end of period $ 14,309,580
$ 12,010,041

~~(1)~~

During 2020 first quarter, a subsidiary of the Company entered into a reinsurance to close agreement of the 2017 and prior years of account previously covered by a third party arrangement, while in the 2019 first quarter, a subsidiary of the Company entered into a retroactive reinsurance transaction with third party reinsurer to reinsure run-off liabilities associated with certain U.S. insurance exposures.

~~Development on Prior Year Loss Reserves~~

~~2020 First Quarter~~

During the 2020 first quarter, the Company recorded net favorable development on prior year loss reserves of $19.0 million, which consisted of $1.1 million of favorable development from the insurance segment, $11.6 million from the reinsurance segment, $6.1 million from the mortgage segment and $0.2 million from the ‘other’ segment.

The insurance segment’s net favorable development of $1.1 million, or 0.2 loss ratio points, for the 2020 first quarter consisted of $3.9 million of net favorable development in short-tailed lines, $7.9 million of net adverse development in medium-tailed lines and $5.2 million of net favorable development in long-tailed lines. Net favorable development in short-tailed lines primarily resulted from lenders products and property (including special risk other than marine) reserves across 2018 and prior accident years (~~i.e.~~, the year in which a loss occurred). Net adverse development in medium-tailed lines included $13.2 million of adverse development in contract binding business across most accident years, partially offset by

~~$5.1 million of favorable development in professional liability business. Net favorable development in longer-tailed lines primarily related to construction business driven by the 2017 accident year.~~

The reinsurance segment’s net favorable development of $11.6 million, or 2.1 loss ratio points, for the 2020 first quarter consisted of $21.5 million of net favorable development in short-tailed and medium-tailed lines and net adverse development of $9.9 million in long-tailed lines. Net favorable development in short-tailed and medium-tailed lines reflected $11.9 million of favorable development in other specialty lines across most underwriting years (~~i.e.~~, all premiums and losses attributable to contracts having an inception or renewal date within the given twelve-month period) and $10.5 million of favorable development from property catastrophe business, primarily from the 2015 to 2019 underwriting years. Such amounts were partially offset by $4.3 million of adverse development in property other than property catastrophe business, driven by the 2018 underwriting year. Adverse development in long-tailed lines reflected an increase in casualty reserves from various underwriting years.



~~ARCH CAPITAL~~	18	~~2020 FIRST QUARTER FORM 10-Q~~

~~Table of Contents~~

~~ARCH CAPITAL GROUP LTD. AND SUBSIDIARIES~~

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

The mortgage segment’s net favorable development was $6.1 million, or 1.8 loss ratio points, for the 2020 first quarter. The 2020 first quarter development was primarily driven by subrogation recoveries on second lien business and student loan business.

~~2019 First Quarter~~

During the 2019 first quarter, the Company recorded net favorable development on prior year loss reserves of $39.4 million, which consisted of $4.4 million of favorable development from the insurance segment, $36.6 million from the mortgage segment and $0.1 million from the ‘other’ segment, partially offset by $1.7 million of adverse development from the reinsurance segment.

The insurance segment’s net favorable development of $4.4 million, or 0.8 loss ratio points, for the 2019 first quarter consisted of $9.7 million of net favorable development in short- tailed lines, $7.0 million of net adverse development in medium-tailed lines and $1.7 million of net favorable development in long-tailed lines. Net favorable development in short-tailed lines primarily resulted from property (including special risk other than marine) reserves from the 2017 accident year (i.e., the year in which a loss occurred). Net adverse development in medium-tailed lines primarily resulted from $7.7 million of adverse development on program business and $6.0 million of adverse development on contract binding business. Such amounts were partially offset by $6.7 million of net favorable development in other medium-tailed lines, including professional liability and surety business, across most accident years.

The reinsurance segment’s net adverse development of $1.7 million, or 0.5 loss ratio points, for the 2019 first quarter consisted of $6.2 million of net adverse development from short-tailed lines, partially offset by $4.5 million of net favorable development from long-tailed and medium-tailed lines. Net adverse development in short-tailed lines included $13.8 million from property catastrophe and property other than property catastrophe reserves, primarily due to an increase in reserves on Typhoon Jebi of $16.0 million based on receipt of updated information from cedents and additional updated industry data. Such amounts were partially offset by net favorable development of $9.6 million from other specialty reserves, primarily from the 2016 and 2018 underwriting years (i.e., all premiums and losses attributable to contracts having an inception or renewal date within the given twelve-month period). Favorable development in long-tailed and medium tailed lines reflected reductions in casualty and marine reserves from most underwriting years.

The mortgage segment’s net favorable development was $36.6 million, or 11.3 loss ratio points, for the 2019 first quarter. The 2019 first quarter development was primarily driven by continued favorable claim rates on first lien business and subrogation recoveries on second lien business.



~~ARCH CAPITAL~~	19	~~2020 FIRST QUARTER FORM 10-Q~~

~~Table of Contents~~

~~ARCH CAPITAL GROUP LTD. AND SUBSIDIARIES~~

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

~~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.~~receivables:

March 31, 2020
Premium Receivables, Net of Allowance Allowance for Expected Credit Losses
Balance at beginning of period $ 1,778,717
$ 21,003
Cumulative effect of accounting change (1) 6,539
Change for provision for expected credit losses 448
Write-offs charged against the allowance —
Balance at end of period $ 2,155,204
$ 27,990



	Premium Receivables, Net of Allowance		Allowance for Expected Credit Losses
March 31, 2021
Balance at beginning of period	$	2,064,586	$	37,781

Change for provision of expected credit losses (1)			(1,670)


Balance at end of period	$	2,618,175	$	36,111

December 31, 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)			10,239
Balance at end of period	$	2,064,586	$	37,781

(1)Amounts deemed uncollectible are written-off in operating expenses. For the March 31, 2021 and as of December 31, 2020, amounts written off were $0.1 million and $2.8 million, respectively.

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

Reinsurance Recoverables

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

March 31, 2020
Reinsurance Recoverables, Net of Allowance Allowance for Expected Credit Losses
Balance at beginning of period $ 4,346,816
$ 1,364
Cumulative effect of accounting change (1) 12,010
Additions for current-period provision for expected credit losses 326
Write-offs charged against the allowance —
Balance at end of period $ 4,303,135
$ 13,700



	Reinsurance Recoverables, Net of Allowance		Allowance for Expected Credit Losses
March 31, 2021
Balance at beginning of period	$	4,500,802	$	11,636

Change for provision of expected credit losses			(764)


Balance at end of period	$	4,041,076	$	10,872

December 31, 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			(1,738)
Balance at end of period	$	4,500,802	$	11,636

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

~~At March 31, 2020 and December 31, 2019, approximately 60.8% and 61.2%~~


ARCH CAPITAL			17			2021 FIRST QUARTER FORM 10-Q

Table of Contents

ARCH CAPITAL GROUP LTD. AND SUBSIDIARIES

NOTES TO CONSOLIDATED FINANCIAL STATEMENTS (UNAUDITED)

The following table summarizes the Company’s reinsurance recoverables on paid and unpaid losses (not including ceded unearned premiums) ~~of $4.32 billion~~:


	March 31,			December 31
	2021			2020
Reinsurance recoverable on unpaid and paid losses and loss adjustment expenses	$	4,041,076		$	4,500,802
% due from carriers with A.M. Best rating of “A-” or better	64.5		%	63.9		%
% due from all other carriers with no A.M. Best rating (1)	35.5		%	36.1		%
Largest balance due from any one carrier as % of total shareholders’ equity	1.7		%	1.8		%

(1) At March 31, 2021 and ~~$4.35 billion, respectively, were due from carriers which had an A.M. Best rating of “A-” or better while 38.4%~~December 31, 2020 over 92% and ~~38.8%, respectively, were from companies not rated. For items not rated, over 90%~~94% of such amount ~~was~~were collateralized through reinsurance trusts, orfunds withheld arrangements, letters of credit at March 31, 2020 and December 31, 2019. The largest reinsurance recoverables from any one carrier were approximately 1.9% and 1.7%, of total shareholders’ equity available to Arch at March 31, 2020 and December 31, 2019,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.~~receivables:


						Contract-holder Receivables, Net of Allowance		Allowance for Expected Credit Losses
March 31, 2021					March 31, 2021
Balance at beginning of period					Balance at beginning of period	$	1,986,924	$	8,638

Change for provision of expected credit losses					Change for provision of expected credit losses			(2,785)

Balance at end of period					Balance at end of period	$	1,919,655	$	5,853

December 31, 2020					December 31, 2020
Balance at beginning of period					Balance at beginning of period	$	2,119,460	$	0
Cumulative effect of accounting change (1)					Cumulative effect of accounting change (1)			6,663
Change for provision of expected credit losses					Change for provision of expected credit losses			1,975
Balance at end of period					Balance at end of period	$	1,986,924	$	8,638

	March 31, 2020
	Contractholder Receivables, Net of Allowance		Allowance for Expected Credit Losses
Balance at beginning of period	$	2,119,460	$	—
Cumulative effect of accounting change (1)			6,663
Additions for current-period provision for expected credit losses			2,375
Write-offs charged against the allowance			—
Balance at end of period	$	2,140,724	$	9,038

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



ARCH CAPITAL	2018	~~2020~~2021 FIRST QUARTER FORM 10-Q

Table of Contents

ARCH CAPITAL GROUP LTD. AND SUBSIDIARIES

NOTES TO CONSOLIDATED FINANCIAL STATEMENTS (UNAUDITED)

7. Investment Information

At March 31, ~~2020,~~2021, total investable assets of ~~$24.88~~$29.1 billion included ~~$22.38~~$26.3 billion held by the Company and ~~$2.50~~$2.7 billion attributable to Watford.

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
March 31, 2021
Fixed maturities (1):
Corporate bonds	$	8,072,883	$	242,832	$	(83,961)	$	(2,569)	$	7,916,581
Mortgage backed securities	571,071		7,066		(11,165)		(325)		575,495
Municipal bonds	457,329		19,942		(4,814)		(2)		442,203
Commercial mortgage backed securities	255,373		2,755		(1,721)		(5)		254,344
U.S. government and government agencies	5,042,208		15,102		(30,545)		0		5,057,651
Non-U.S. government securities	2,425,882		127,886		(19,267)		(51)		2,317,314
Asset backed securities	2,028,441		18,817		(4,962)		(878)		2,015,464
Total	18,853,187		434,400		(156,435)		(3,830)		18,579,052

Short-term investments	1,269,631		920		(601)		0		1,269,312
Total	$	20,122,818	$	435,320	$	(157,036)	$	(3,830)	$	19,848,364

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)		0		5,547,076
Non-U.S. government securities	2,433,733		153,891		(8,060)		0		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)		0		1,924,292
Total	$	20,921,530	$	657,620	$	(79,654)	$	(2,397)	$	20,345,961

Estimated
Fair
Value

Gross
Unrealized
Gains

Gross
Unrealized
Losses

Allowance for Expected Credit Losses ⁽²⁾

Cost or
Amortized
Cost
March 31, 2020
Fixed maturities (1):
Corporate bonds $ 6,552,825
$ 176,246
$ (118,340 ) $ (7,233 ) $ 6,502,152
Mortgage backed securities 466,045
16,006
(6,208 ) (208 ) 456,455
Municipal bonds 862,415
27,287
(7,550 ) (23 ) 842,701
Commercial mortgage backed securities 780,358
11,657
(18,410 ) (306 ) 787,417
U.S. government and government agencies 4,574,630
143,987
(300 ) —
4,430,943
Non-U.S. government securities 2,035,459
57,289
(105,533 ) —
2,083,703
Asset backed securities 1,747,281
12,155
(91,668 ) (2,139 ) 1,828,933
Total 17,019,013
444,627
(348,009 ) (9,909 ) 16,932,304
Short-term investments 944,531
2,461
(2,779 ) (29 ) 944,878
Total $ 17,963,544
$ 447,088
$ (350,788 ) $ (9,938 ) $ 17,877,182

December 31, 2019
Fixed maturities (1):
Corporate bonds $ 6,406,591
$ 191,889
$ (12,793 ) $ 6,227,495
Mortgage backed securities 562,309
9,669
(931 ) 553,571
Municipal bonds 881,926
24,628
(2,213 ) 859,511
Commercial mortgage backed securities 733,108
14,951
(2,330 ) 720,487
U.S. government and government agencies 4,916,592
36,600
(10,134 ) 4,890,126
Non-U.S. government securities 2,078,757
48,549
(20,330 ) 2,050,538
Asset backed securities 1,683,753
24,017
(4,724 ) 1,664,460
Total 17,263,036
350,303
(53,455 ) 16,966,188
Short-term investments 956,546
811
(1,548 ) 957,283
Total $ 18,219,582
$ 351,114
$ (55,003 ) $ 17,923,471
(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.”


~~(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.”


~~(2)~~	(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. ~~See~~ ~~note 1.~~



ARCH CAPITAL	2119	~~2020~~2021 FIRST 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
March 31, 2021
Fixed maturities (1):
Corporate bonds	$	3,253,030	$	(82,735)	$	15,894	$	(1,226)	$	3,268,924	$	(83,961)
Mortgage backed securities	383,760		(10,271)		20,648		(894)		404,408		(11,165)
Municipal bonds	90,634		(4,737)		1,827		(77)		92,461		(4,814)
Commercial mortgage backed securities	39,863		(759)		23,421		(962)		63,284		(1,721)
U.S. government and government agencies	3,920,377		(30,545)		0		0		3,920,377		(30,545)
Non-U.S. government securities	911,609		(18,433)		16,841		(834)		928,450		(19,267)
Asset backed securities	502,300		(2,391)		142,331		(2,571)		644,631		(4,962)
Total	9,101,573		(149,871)		220,962		(6,564)		9,322,535		(156,435)

Short-term investments	95,579		(601)		0		0		95,579		(601)
Total	$	9,197,152	$	(150,472)	$	220,962	$	(6,564)	$	9,418,114	$	(157,036)

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)		0		0		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)		0		0		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)		0		0		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
March 31, 2020
Fixed maturities (1):
Corporate bonds $ 2,377,206
$ (116,795 ) $ 7,865
$ (1,545 ) $ 2,385,071
$ (118,340 )
Mortgage backed securities 99,108
(6,183 ) 116
(25 ) 99,224
(6,208 )
Municipal bonds 278,557
(7,550 ) —
—
278,557
(7,550 )
Commercial mortgage backed securities 419,028
(18,075 ) 2,342
(335 ) 421,370
(18,410 )
U.S. government and government agencies 216,620
(300 ) 2,000
—
218,620
(300 )
Non-U.S. government securities 1,484,987
(105,533 ) —
—
1,484,987
(105,533 )
Asset backed securities 1,003,251
(86,283 ) 28,724
(5,385 ) 1,031,975
(91,668 )
Total 5,878,757
(340,719 ) 41,047
(7,290 ) 5,919,804
(348,009 )
Short-term investments 83,196
(2,779 ) —
—
83,196
(2,779 )
Total $ 5,961,953
$ (343,498 ) $ 41,047
$ (7,290 ) $ 6,003,000
$ (350,788 )

December 31, 2019
Fixed maturities (1):
Corporate bonds $ 675,131
$ (12,350 ) $ 37,671
$ (443 ) $ 712,802
$ (12,793 )
Mortgage backed securities 102,887
(927 ) 203
(4 ) 103,090
(931 )
Municipal bonds 220,296
(2,213 ) —
—
220,296
(2,213 )
Commercial mortgage backed securities 147,290
(2,302 ) 2,683
(28 ) 149,973
(2,330 )
U.S. government and government agencies 1,373,127
(10,089 ) 32,058
(45 ) 1,405,185
(10,134 )
Non-U.S. government securities 1,224,243
(20,163 ) 37,610
(167 ) 1,261,853
(20,330 )
Asset backed securities 441,522
(3,334 ) 48,313
(1,390 ) 489,835
(4,724 )
Total 4,184,496
(51,378 ) 158,538
(2,077 ) 4,343,034
(53,455 )
Short-term investments 95,777
(1,548 ) —
—
95,777
(1,548 )
Total $ 4,280,273
$ (52,926 ) $ 158,538
$ (2,077 ) $ 4,438,811
$ (55,003 )
(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.”


~~(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.”

At March 31, ~~2020,~~2021, on a lot level basis, approximately ~~5,420~~4,610 security lots out of a total of approximately ~~9,960~~11,360 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 ~~$6.3~~$1.1 million. At December 31, ~~2019,~~2020, on a lot level basis, approximately ~~2,230~~2,320 security lots out of a total of approximately ~~9,590~~11,180 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 million.



ARCH CAPITAL	2220	~~2020~~2021 FIRST 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.


	March 31, 2021				December 31, 2020
Maturity	Estimated Fair Value		Amortized Cost		Estimated Fair Value		Amortized Cost
Due in one year or less	$	381,212	$	370,798	$	348,200	$	339,951
Due after one year through five years	11,124,344		10,918,279		10,629,959		10,340,819
Due after five years through 10 years	4,052,472		4,008,520		4,881,564		4,654,754
Due after 10 years	440,274		436,152		482,180		448,139
	15,998,302		15,733,749		16,341,903		15,783,663
Mortgage backed securities	571,071		575,495		630,001		626,368
Commercial mortgage backed securities	255,373		254,344		389,900		384,254
Asset backed securities	2,028,441		2,015,464		1,634,804		1,627,384
Total (1)	$	18,853,187	$	18,579,052	$	18,996,608	$	18,421,669

March 31, 2020 December 31, 2019
Maturity
Estimated
Fair
Value

Amortized
Cost
Estimated
Fair
Value
Amortized
Cost
Due in one year or less $ 445,134
$ 445,701
$ 428,659
$ 423,617
Due after one year through five years 9,622,046
9,558,975
10,126,403
9,996,206
Due after five years through 10 years 3,435,903
3,358,574
3,317,535
3,219,567
Due after 10 years 522,246
496,249
411,269
388,280
14,025,329
13,859,499
14,283,866
14,027,670
Mortgage backed securities 466,045
456,455
562,309
553,571
Commercial mortgage backed securities 780,358
787,417
733,108
720,487
Asset backed securities 1,747,281
1,828,933
1,683,753
1,664,460
Total (1) $ 17,019,013
$ 16,932,304
$ 17,263,036
$ 16,966,188


~~(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.

(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.”

Securities Lending Agreements

The Company enters into securities lending agreements with financial institutions to enhance investment income whereby it loans certain of its securities to third parties, primarily major brokerage firms, for short periods of time through a lending agent. The Company maintains legal control over the securities it lends (shown as ‘Securities pledged under securities lending, at fair value’ on the Company’s balance sheet), retains the earnings and cash flows associated with the loaned securities and receives a fee from the borrower for the temporary use of the securities. An indemnification agreement with the lending agent protects the Company in the event a borrower becomes insolvent or fails to return any of the securities on loan from the Company.

The Company receives 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 March 31, 2021, the fair value of the cash collateral received on securities lending was NaN and the fair value of security collateral received was $143.9 million. At December 31, 2020, the fair value of the cash collateral received on securities lending was ~~$26.2 million~~NaN, and the fair value of security collateral received was ~~$156.1~~$301.1 million. ~~At December 31, 2019, the fair value of the cash collateral received on securities lending was $81.2 million, and the fair value of security collateral received was $307.2 million.~~



~~ARCH CAPITAL~~	23	~~2020 FIRST QUARTER FORM 10-Q~~

~~Table of Contents~~

~~ARCH CAPITAL GROUP LTD. AND SUBSIDIARIES~~

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

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 is as follows:


	Remaining Contractual Maturity of the Agreements
	Overnight and Continuous		Less than 30 Days		30-90 Days		90 Days or More		Total
March 31, 2021
U.S. government and government agencies	$	16,397	$	0	$	102,743	$	0	$	119,140
Corporate bonds	13,724		0		0		0		13,724
Equity securities	11,022		0		0		0		11,022
Total	$	41,143	$	0	$	102,743	$	0	$	143,886
Gross amount of recognized liabilities for securities lending in offsetting disclosure in note 9									$	0
Amounts related to securities lending not included in offsetting disclosure in note 9									$	143,886

December 31, 2020
U.S. government and government agencies	$	142,317	$	0	$	139,290	$	0	$	281,607
Corporate bonds	3,021		0		0		0		3,021
Equity securities	16,461		0		0		0		16,461
Total	$	161,799	$	0	$	139,290	$	0	$	301,089
Gross amount of recognized liabilities for securities lending in offsetting disclosure in note 9									$	0
Amounts related to securities lending not included in offsetting disclosure in note 9									$	301,089

Remaining Contractual Maturity of the Agreements
Overnight and Continuous Less than 30 Days 30-90 Days 90 Days or More Total
March 31, 2020
U.S. government and government agencies $ 144,375
$ —
$ 14,316
$ —
$ 158,691
Corporate bonds 11,715
—
—
—
11,715
Equity securities 11,868
—
—
—
11,868
Total $ 167,958
$ —
$ 14,316
$ —
$ 182,274
Gross amount of recognized liabilities for securities lending in offsetting disclosure in note 9 $ —
Amounts related to securities lending not included in offsetting disclosure in note 9 $ 182,274

December 31, 2019
U.S. government and government agencies $ 240,332
$ —
$ 115,973
$ —
$ 356,305
Corporate bonds 2,570
—
—
—
2,570
Equity securities 29,491
—
—
—
29,491
Total $ 272,393
$ —
$ 115,973
$ —
$ 388,366
Gross amount of recognized liabilities for securities lending in offsetting disclosure in note 9
$ —
Amounts related to securities lending not included in offsetting disclosure in note 9
$ 388,366


ARCH CAPITAL			21			2021 FIRST QUARTER FORM 10-Q

Table of Contents

ARCH CAPITAL GROUP LTD. AND SUBSIDIARIES

NOTES TO CONSOLIDATED FINANCIAL STATEMENTS (UNAUDITED)

Equity Securities, at Fair Value

At March 31, ~~2020,~~2021, the Company held ~~$1.18~~$1.5 billion of equity securities, at fair value, compared to ~~$838.9 million~~$1.4 billion at December 31, ~~2019.~~2020. Such holdings include publicly traded common stocks primarily in the consumer cyclical and non-cyclical, technology, communication and financial sectors and exchange-traded funds in fixed income, equity and other sectors.

Other Investments

The following table summarizes the Company’s other investments ~~which are included~~and other investable assets:


	March 31, 2021		December 31, 2020
Fixed maturities	$	900,304	$	843,354
Other investments	2,318,185		2,331,885
Short-term investments	623,930		557,008
Equity securities	92,935		92,549
Investments accounted for using the fair value option	$	3,935,354	$	3,824,796

Other investable assets (1)	500,000		500,000
Total other investments	$	4,435,354	$	4,324,796

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

The following table summarizes the Company’s other investments, ~~accounted for using~~as detailed in the ~~fair value option,~~previous table, by strategy:


	March 31, 2020		December 31, 2019			March 31, 2021		December 31, 2020
Term loan investments	$	1,135,584	$	1,326,018	Term loan investments	$	1,187,752	$	1,231,731
Lending	544,308		602,841		Lending	606,207		572,636
Credit related funds	111,874		123,020		Credit related funds	79,355		90,780
Energy	63,057		97,402		Energy	78,500		65,813
Investment grade fixed income	137,370		151,594		Investment grade fixed income	142,630		138,646
Infrastructure	33,644		61,786		Infrastructure	152,352		165,516
Private equity	51,284		49,376		Private equity	52,064		48,750
Real estate	14,296		17,279		Real estate	19,325		18,013
Total	$	2,091,417	$	2,429,316	Total	$	2,318,185	$	2,331,885

Investments Accounted For Using the Equity Method

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


	March 31, 2021		December 31, 2020
Credit related funds	$	818,344	$	740,060
Equities	357,641		343,058
Real estate	292,424		258,518
Lending	199,913		179,629
Private equity	288,657		235,289
Infrastructure	179,225		175,882
Energy	120,123		115,453
Total	$	2,256,327	$	2,047,889

March 31,
2020 December 31,
2019
Credit related funds $ 421,943
$ 428,437
Equities 256,249
293,686
Real estate 254,957
246,851
Lending 194,132
202,690
Private equity 154,322
144,983
Infrastructure 283,147
235,033
Energy 111,305
108,716
Total $ 1,676,055
$ 1,660,396

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



~~ARCH CAPITAL~~	24	~~2020 FIRST QUARTER FORM 10-Q~~

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~~ARCH CAPITAL GROUP LTD. AND SUBSIDIARIES~~

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

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

~~Fair Value Option~~

~~The following table summarizes the Company’s assets which are accounted for using the fair value option:~~

March 31,
2020 December 31,
2019
Fixed maturities $ 734,694
$ 754,452
Other investments 2,091,417
2,429,316
Short-term investments 396,409
377,014
Equity securities 87,997
102,695
Investments accounted for using the fair value option $ 3,310,517
$ 3,663,477

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 unfundedcommitment.

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


	March 31, 2021		December 31, 2020
Investments accounted for using the equity method (1)	2,256,327		2,047,889
Investments accounted for using the fair value option (2)	196,087		184,720
Total	$	2,452,414	$	2,232,609

(1) Aggregate unfunded commitments were $2.0 billion at March 31, 2021, compared to $1.8 billion at December 31, 2020.

(2) Aggregate unfunded commitments were $36.1 million at March 31, 2021, compared to $35.6 million at December 31, 2020.

March 31,
2020 December 31,
2019
Investments accounted for using the equity method (1) 1,676,055
1,660,396
Investments accounted for using the fair value option (2) 170,515
188,283
Total $ 1,846,570
$ 1,848,679


~~(1)~~ARCH CAPITAL			~~Aggregate unfunded commitments were $1.30 billion at March 31, 2020, compared to $1.36 billion at December 31, 2019.~~

22
~~(2)~~	~~Aggregate unfunded commitments were $40.2 million at March 31, 2020, compared to $41.7 million at December 31, 2019.~~2021 FIRST 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:


	March 31,
	2021		2020
Three Months Ended
Fixed maturities	$	90,626	$	114,847
Term loans	14,728		23,170
Equity securities	5,650		6,007
Short-term investments	607		4,896
Other (1)	14,355		19,406
Gross investment income	125,966		168,326
Investment expenses	(27,110)		(23,173)
Net investment income	$	98,856	$	145,153

March 31,
2020 2019
Three Months Ended
Fixed maturities $ 114,847
$ 129,799
Term loans 23,170
24,616
Equity securities 6,007
2,988
Short-term investments 4,896
4,179
Other (1) 19,406
21,196
Gross investment income 168,326
182,778
Investment expenses (23,173 ) (25,829 )
Net investment income $ 145,153
$ 156,949
(1) Includes income distributions from investment funds and other items.


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

Net Realized Gains (Losses)

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


	March 31,
	2021		2020
Three Months Ended
Available for sale securities:
Gross gains on investment sales	$	65,002	$	178,200
Gross losses on investment sales	(62,998)		(31,968)
Change in fair value of assets and liabilities accounted for using the fair value option:
Fixed maturities	16,553		(127,666)
Other investments	46,855		(307,800)
Equity securities	2,065		(4,909)
Short-term investments	736		(8,681)
Equity securities, at fair value:
Net realized gains (losses) on sales during the period	37,849		(539)
Net unrealized gains (losses) on equity securities still held at reporting date	19,708		(175,566)
Allowance for credit losses:
Investments related	(1,648)		(9,320)
Underwriting related	5,268		(3,270)
Net impairment losses	0		(533)
Derivative instruments (1)	36,116		127,189
Other	(23,045)		(2,097)
Net realized gains (losses)	$	142,461	$	(366,960)

March 31,
2020 2019
Three Months Ended
Available for sale securities:

Gross gains on investment sales $ 178,200
$ 43,365
Gross losses on investment sales (31,968 ) (31,656 )
Change in fair value of assets and liabilities accounted for using the fair value option:
Fixed maturities (127,666 ) 31,148
Other investments (307,800 ) 18,195
Equity securities (4,909 ) 4,266
Short-term investments (8,681 ) 720
Equity securities, at fair value:
Net realized gains (losses) on sales during the period (539 ) 10,930
Net unrealized gains (losses) on equity securities still held at reporting date (175,566 ) 37,136
Allowance for credit losses:
Investments related (9,320 ) —
Underwriting related (3,270 ) —
Net impairment losses (533 ) (1,309 )
Derivative instruments (1) 127,189
35,871
Other (2,097 ) (8,410 )
Net realized gains (losses) $ (366,960 ) $ 140,256
(1) See note 9 for information on the Company’s derivative instruments.


~~(1)~~	~~See~~ ~~note 9~~ ~~for information on the Company’s derivative instruments.~~

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

The Company recorded ~~a loss~~$71.7 million of ~~$4.2 million~~equity in net income related to investment funds accounted for using the equity method in the ~~2020~~2021 first quarter, compared to ~~an income~~loss of ~~$46.9~~$4.2 million for the ~~2019~~2020 first quarter. 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



~~ARCH CAPITAL~~	25	~~2020 FIRST QUARTER FORM 10-Q~~

~~Table of Contents~~

~~ARCH CAPITAL GROUP LTD. AND SUBSIDIARIES~~

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

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 and Premia Holdings Ltd. (“Premia”) and are generally recorded on a three month 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 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. At March 31, 2021 the Company’s carrying value in Coface was $604.6 million.


ARCH CAPITAL			23			2021 FIRST 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
March 31, 2021
Balance at beginning of period	$	1,490	$	11	$	896	$	2,397

Additions for current-period provision for expected credit losses	182		0		2,421		2,603
Additions (reductions) for previously recognized expected credit losses	(382)		(9)		(540)		(931)
Reductions due to disposals	(83)		0		(156)		(239)
Write-offs charged against the allowance	0		0		0		0
Balance at end of period	$	1,207	$	2	$	2,621	$	3,830

December 31, 2020
Balance at beginning of period	$	0	$	0	$	0	$	0
Cumulative effect of accounting change (2)	517		0		117		634
Additions for current-period provision for expected credit losses	2,942		67		7,644		10,653
Additions (reductions) for previously recognized expected credit losses	(1,398)		6		(5,638)		(7,030)
Reductions due to disposals	(571)		(62)		(1,227)		(1,860)
Write-offs charged against the allowance	0		0		0		0
Balance at end of period	$	1,490	$	11	$	896	$	2,397

March 31, 2020
Structured Securities (1)
Municipal
Bonds

Corporate
Bonds
Short Term Investments Total
Three Months Ended
Balance at beginning of period $ —
$ —
$ —
$ —
$ —
Cumulative effect of accounting change 517
—
117
—
634
Additions for current-period provision for expected credit losses 2,146
23
7,151
29
9,349
Additions (reductions) for previously recognized expected credit losses (2 ) —
(21 ) —
(23 )
Reductions due to disposals (7 ) —
(15 ) —
(22 )
Write-offs charged against the allowance —
—
—
—
—
Balance at end of period $ 2,654
$ 23
$ 7,232
$ 29
$ 9,938


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

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

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 ~~17,~~18, “Commitments and Contingencies,” of the notes to consolidated financial statements in the Company’s ~~2019~~2020 Form 10-K.

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


	March 31, 2021		December 31, 2020
Assets used for collateral or guarantees:
Affiliated transactions	$	4,815,120	$	4,643,334
Third party agreements	3,366,016		3,083,324
Deposits with U.S. regulatory authorities	819,444		827,552
Deposits with non-U.S. regulatory authorities	330,197		179,099

Total restricted assets	$	9,330,777	$	8,733,309

March 31,
2020 December 31,
2019
Assets used for collateral or guarantees:

Affiliated transactions $ 4,540,455
$ 4,526,761
Third party agreements 2,277,298
2,278,248
Deposits with U.S. regulatory authorities 831,411
797,371
Deposits with non-U.S. regulatory authorities 162,336
119,238
Total restricted assets $ 7,811,500
$ 7,721,618

In addition, Watford maintains a secured credit ~~facility~~facilities to provide borrowing capacity for investment purposes and a total return swap agreement and maintains assets pledged as collateral for such purposes. The Company does not guarantee or provide credit support for Watford, and the Company’s financial exposure to Watford is limited to its investment in Watford’s senior notes, common and preferred shares and counterparty credit risk (mitigated by collateral) arising from reinsurance transactions. As of March 31, ~~2020~~2021 and December 31, ~~2019,~~2020, Watford held ~~$1.06~~$1.0 billion and ~~$1.0 billion,~~$954.6 million, respectively, in pledged assets to collateralize the credit facility mentioned above.

Reconciliation of Cash and Restricted Cash

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


	March 31, 2021		December 31, 2020
Cash	$	941,951	$	906,448
Restricted cash (included in ‘other assets’)	$	425,563	$	384,096
Cash and restricted cash	$	1,367,514	$	1,290,544

March 31,
2020 December 31,
2019
Cash $ 882,284
$ 726,230
Restricted cash (included in ‘other assets’) $ 188,153
$ 177,468
Cash and restricted cash $ 1,070,437
$ 903,698



ARCH CAPITAL	2624	~~2020~~2021 FIRST QUARTER FORM 10-Q

Table of Contents

ARCH CAPITAL GROUP LTD. AND SUBSIDIARIES

NOTES TO CONSOLIDATED FINANCIAL STATEMENTS (UNAUDITED)

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 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 March 31, ~~2020.~~2021.

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 ~~$22.70~~$25.9 billion of financial assets and liabilities measured at fair value at March 31, ~~2020,~~2021, approximately ~~$195.5~~$146.9 million, or ~~0.9%~~0.6%, were priced using non-binding broker-dealer ~~quotes.~~quotes or modeled valuations. Of the ~~$22.90~~$26.5 billion of financial assets and liabilities measured at fair value at December 31, ~~2019,~~2020, approximately ~~$179.6~~$150.1 million, or ~~0.8%~~0.6%, were priced using non-binding broker-dealer ~~quotes.~~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


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NOTES TO CONSOLIDATED FINANCIAL STATEMENTS (UNAUDITED)

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.



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~~ARCH CAPITAL GROUP LTD. AND SUBSIDIARIES~~

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

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.

•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-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


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NOTES TO CONSOLIDATED FINANCIAL STATEMENTS (UNAUDITED)

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.



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~~ARCH CAPITAL GROUP LTD. AND SUBSIDIARIES~~

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

Other investments

The ~~Company determined that exchange-traded~~Company’s other investments ~~in mutual funds would be included in Level 1 as their fair values are based on quoted market prices in active markets. Other investments also~~ 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.

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 future payments using an income approach based on modeled inputs which include a weighted average cost of capital. The Company determined that contingent consideration liabilities would be included within Level 3.



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NOTES TO CONSOLIDATED FINANCIAL STATEMENTS (UNAUDITED)

The following table presents the Company’s financial assets and liabilities measured at fair value by level at March 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 (1):
Available for sale securities:												Available for sale securities:
Fixed maturities:												Fixed maturities:
Corporate bonds	$	6,552,825		$	—	$	6,550,845		$	1,980		Corporate bonds	$	8,072,883	$	0	$	8,072,870	$	13
Mortgage backed securities	466,045			—		465,821			224			Mortgage backed securities	571,071		0		571,071		0
Municipal bonds	862,415			—		862,415			—			Municipal bonds	457,329		0		457,329		0
Commercial mortgage backed securities	780,358			—		780,358			—			Commercial mortgage backed securities	255,373		0		255,373		0
U.S. government and government agencies	4,574,630			4,480,074		94,556			—			U.S. government and government agencies	5,042,208		4,949,217		92,991		0
Non-U.S. government securities	2,035,459			—		2,035,459			—			Non-U.S. government securities	2,425,882		0		2,425,882		0
Asset backed securities	1,747,281			—		1,743,659			3,622			Asset backed securities	2,028,441		0		2,024,969		3,472
Total	17,019,013			4,480,074		12,533,113			5,826			Total	18,853,187		4,949,217		13,900,485		3,485

Short-term investments	944,531			884,527		60,004			—			Short-term investments	1,269,631		1,252,535		17,096		0

Equity securities, at fair value	1,181,903			1,122,694		3,577			55,632			Equity securities, at fair value	1,543,703		1,476,504		24,087		43,112


Derivative instruments (4)	92,052			—		92,052			—			Derivative instruments (4)	156,160		0		156,160		0

Residential mortgage loans												Residential mortgage loans	5,693		0		5,693		0

Fair value option:												Fair value option:
Corporate bonds	493,639			—		492,674			965			Corporate bonds	724,316		0		723,327		989
Non-U.S. government bonds	79,209			—		79,209			—			Non-U.S. government bonds	23,996		0		23,996		0
Mortgage backed securities	13,293			—		13,293			—			Mortgage backed securities	2,828		0		2,828		0
Municipal bonds	251			—		251			—

Commercial mortgage backed securities	1,059			—		1,059			—			Commercial mortgage backed securities	1,225		0		1,225		0
Asset backed securities	146,646			—		146,646			—			Asset backed securities	147,666		0		147,666		0
U.S. government and government agencies	597			484		113			—			U.S. government and government agencies	273		164		109		0
Short-term investments	396,409			321,401		75,008			—			Short-term investments	623,930		482,869		141,061		0
Equity securities	87,997			27,825		157			60,015			Equity securities	92,935		21,512		247		71,176
Other investments	1,177,508			24,930		1,097,958			54,620			Other investments	1,078,505		31,268		979,307		67,930
Other investments measured at net asset value (2)	913,909											Other investments measured at net asset value (2)	1,239,680
Total	3,310,517			374,640		1,906,368			115,600			Total	3,935,354		535,813		2,019,766		140,095

Total assets measured at fair value	$	22,548,016		$	6,861,935	$	14,595,114		$	177,058		Total assets measured at fair value	$	25,763,728	$	8,214,069	$	16,123,287	$	186,692

Liabilities measured at fair value:												Liabilities measured at fair value:
Contingent consideration liabilities	$	(7,967	)	$	—	$	—		$	(7,967	)	Contingent consideration liabilities	$	(465)	$	0	$	0	$	(465)
Securities sold but not yet purchased (3)	(30,076		)	—		(30,076		)	—			Securities sold but not yet purchased (3)	(34,097)		0		(34,097)		0
Derivative instruments (4)	(116,572		)	—		(116,572		)	—			Derivative instruments (4)	(98,103)		0		(98,103)		0
Total liabilities measured at fair value	$	(154,615	)	$	—	$	(146,648	)	$	(7,967	)	Total liabilities measured at fair value	$	(132,665)	$	0	$	(132,200)	$	(465)

~~(1)~~

(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 7, “—Securities Lending Agreements.”

(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) See note 9~~note 7, “—Securities Lending Agreements.”~~

~~(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)~~	~~See~~ ~~note 9~~.



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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, ~~2019:~~2020:


			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)
Assets measured at fair value (1):
Available for sale securities:
Fixed maturities:
Corporate bonds	$	7,856,571	$	0	$	7,856,558	$	13
Mortgage backed securities	630,001		0		630,001		0
Municipal bonds	494,522		0		494,522		0
Commercial mortgage backed securities	389,900		0		389,900		0
U.S. government and government agencies	5,557,077		5,463,356		93,721		0
Non-U.S. government securities	2,433,733		0		2,433,733		0
Asset backed securities	1,634,804		0		1,631,378		3,426
Total	18,996,608		5,463,356		13,529,813		3,439

Short-term investments	1,924,922		1,920,565		4,357		0

Equity securities, at fair value	1,460,959		1,401,653		17,291		42,015





Derivative instruments (4)	177,383		0		177,383		0

Fair value option:
Corporate bonds	651,294		0		650,309		985
Non-U.S. government bonds	35,263		0		35,263		0
Mortgage backed securities	3,282		0		3,282		0

Commercial mortgage backed securities	1,090		0		1,090		0
Asset backed securities	152,151		0		152,151		0
U.S. government and government agencies	274		164		110		0
Short-term investments	557,008		420,131		136,877		0
Equity securities	92,549		23,373		188		68,988
Other investments	1,134,229		51,149		1,015,977		67,103
Other investments measured at net asset value (2)	1,197,656
Total	3,824,796		494,817		1,995,247		137,076

Total assets measured at fair value	$	26,384,668	$	9,280,391	$	15,724,091	$	182,530

Liabilities measured at fair value:
Contingent consideration liabilities	$	(461)	$	0	$	0	$	(461)
Securities sold but not yet purchased (3)	(21,679)		0		(21,679)		0
Derivative instruments (4)	(108,705)		0		(108,705)		0
Total liabilities measured at fair value	$	(130,845)	$	0	$	(130,384)	$	(461)

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)
Assets measured at fair value (1):
Available for sale securities:
Fixed maturities:
Corporate bonds $ 6,406,591
$ —
$ 6,397,740
$ 8,851
Mortgage backed securities 562,309
—
562,055
254
Municipal bonds 881,926
—
881,926
—
Commercial mortgage backed securities 733,108
—
733,108
—
U.S. government and government agencies 4,916,592
4,805,581
111,011
—
Non-U.S. government securities 2,078,757
—
2,078,757
—
Asset backed securities 1,683,753
—
1,678,791
4,962
Total 17,263,036
4,805,581
12,443,388
14,067

Equity securities 850,283
789,596
4,798
55,889

Short-term investments 956,546
904,804
51,742
—

Derivative instruments (4) 48,946
—
48,946
—

Fair value option:
Corporate bonds 488,402
—
487,470
932
Non-U.S. government bonds 50,465
—
50,465
—
Mortgage backed securities 11,947
—
11,947
—
Municipal bonds 377
—
377
—
Commercial mortgage backed securities 1,134
—
1,134
—
Asset backed securities 200,163
—
200,163
—
U.S. government and government agencies 1,962
1,852
110
—
Short-term investments 377,014
333,320
43,694
—
Equity securities 102,697
43,962
641
58,094
Other investments 1,418,273
53,287
1,296,169
68,817
Other investments measured at net asset value (2) 1,011,043

Total 3,663,477
432,421
2,092,170
127,843

Total assets measured at fair value $ 22,782,288
$ 6,932,402
$ 14,641,044
$ 197,799

Liabilities measured at fair value:
Contingent consideration liabilities $ (7,998 ) $ —
$ —
$ (7,998 )
Securities sold but not yet purchased (3) (66,257 ) —
(66,257 ) —
Derivative instruments (4) (39,750 ) —
(39,750 ) —
Total liabilities measured at fair value $ (114,005 ) $ —
$ (106,007 ) $ (7,998 )


~~(1)~~	(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 7~~note 7~~, “—Securities Lending Agreements.”

~~(2)~~


~~(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)~~	~~See~~ ~~note 9~~.

(4) See note 9.



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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
s	Available For Sale				Fair Value Option						Fair Value
	Structured Securities (1)		Corporate Bonds		Corporate Bonds		Other Investments		Equity Securities		Equity Securities		Contingent Consideration Liabilities
Three Months Ended March 31, 2021
Balance at beginning of period	$	3,426	$	13	$	985	$	67,103	$	68,988	$	42,015	$	(461)
Total gains or (losses) (realized/unrealized)
Included in earnings (2)	(68)		0		4		248		2,188		904		0
Included in other comprehensive income	114		0		0		0		0		0		0
Purchases, issuances, sales and settlements
Purchases	0		0		0		7,365		0		193		0
Issuances	0		0		0		0		0		0		0
Sales	0		0		0		(6,786)		0		0		0
Settlements	0		0		0		0		0		0		(4)
Transfers in and/or out of Level 3	0		0		0		0		0		0		0
Balance at end of period	$	3,472	$	13	$	989	$	67,930	$	71,176	$	43,112	$	(465)

Three Months Ended March 31, 2020
Balance at beginning of period	$	5,216	$	8,851	$	932	$	68,817	$	58,094	$	55,889	$	(7,998)
Total gains or (losses) (realized/unrealized)
Included in earnings (2)	9		7		0		(27)		1,921		(3,721)		(54)
Included in other comprehensive income	(22)		(5,416)		0		0		0		0		0
Purchases, issuances, sales and settlements
Purchases	0		0		33		21		0		3,464		0
Issuances	0		0		0		0		0		0		0
Sales	0		0		0		(17,175)		0		0		0
Settlements	(1,357)		(1,462)		0		0		0		0		85
Transfers in and/or out of Level 3	0		0		0		2,984		0		0		0
Balance at end of period	$	3,846	$	1,980	$	965	$	54,620	$	60,015	$	55,632	$	(7,967)

Assets Liabilities
s Available For Sale Fair Value Option Fair Value
Structured Securities (1) Corporate
Bonds Corporate
Bonds
Other
Investments

Equity
Securities

Equity
Securities
Contingent Consideration Liabilities
Three Months Ended March 31, 2020

Balance at beginning of period $ 5,216
$ 8,851
$ 932
$ 68,817
$ 58,094
$ 55,889
$ (7,998 )
Total gains or (losses) (realized/unrealized)

Included in earnings (2) 9
7
—
(27 ) 1,921
(3,721 ) (54 )
Included in other comprehensive income (22 ) (5,416 ) —
—
—
—
—
Purchases, issuances, sales and settlements

Purchases —
—
33
21
—
3,464
—
Issuances —
—
—
—
—
—
—
Sales —
—
—
(17,175 ) —
—
—
Settlements (1,357 ) (1,462 ) —
—
—
—
85
Transfers in and/or out of Level 3 —
—
—
2,984
—
—
—
Balance at end of period $ 3,846
$ 1,980
$ 965
$ 54,620
$ 60,015
$ 55,632
$ (7,967 )

Three Months Ended March 31, 2019

Balance at beginning of period $ 313
$ 8,141
$ 5,758
$ 62,705
$ —
$ —
$ (66,665 )
Total gains or (losses) (realized/unrealized)

Included in earnings (2) 1,757
—
(290 ) 298
—
—
(908 )
Included in other comprehensive income 4
(118 ) —
—
—
—
—
Purchases, issuances, sales and settlements

Purchases —
—
—
—
—
—
—
Issuances —
—
—
—
—
—
(548 )
Sales (1,757 ) —
(3,235 ) (74 ) —
—
—
Settlements (15 ) (456 ) —
(600 ) —
—
—
Transfers in and/or out of Level 3 —
—
—
—
—
—
—
Balance at end of period $ 302
$ 7,567
$ 2,233
$ 62,329
$ —
$ —
$ (68,121 )
(1) Includes asset backed securities, mortgage backed securities and commercial mortgage backed securities.

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


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


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

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 March 31, ~~2020,~~2021, due to their respective short maturities. As these financial instruments are not actively traded, their respective fair values are classified within Level 2.

At March 31, 2021, 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 $3.4 billion. At December 31, 2020, the Company’s senior notes were carried at their cost, net of debt issuance costs, of ~~$1.87~~$2.9 billion and had a fair value of ~~$2.26 billion. At December 31, 2019, the Company’s senior notes were carried at their cost, net of debt issuance costs, of $1.87 billion and had a fair value of $2.34~~$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.

9. Derivative Instruments



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~~ARCH CAPITAL GROUP LTD. AND SUBSIDIARIES~~

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

~~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


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NOTES TO CONSOLIDATED FINANCIAL STATEMENTS (UNAUDITED)

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
	Asset Derivatives		Liability Derivatives		Notional Value (1)
March 31, 2021
Futures contracts (2)	$	85,379	$	(54,615)	$	7,116,745
Foreign currency forward contracts (2)	17,898		(29,887)		2,190,031
TBAs (3)	0		0		0
Other (2)	52,883		(13,601)		6,324,926
Total	$	156,160	$	(98,103)

December 31, 2020
Futures contracts (2)	$	11,046	$	(4,496)	$	3,099,796
Foreign currency forward contracts (2)	52,716		(6,202)		1,656,729
TBAs (3)	0		0		0
Other (2)	113,621		(98,007)		5,763,919
Total	$	177,383	$	(108,705)

Estimated Fair Value
Asset Derivatives Liability Derivatives
Notional
Value (1)
March 31, 2020
Futures contracts (2) $ 17,696
$ (24,714 ) $ 2,444,851
Foreign currency forward contracts (2) 12,164
(27,015 ) 1,490,266
TBAs (3) 14,403
—
13,483
Other (2) 62,192
(64,843 ) 3,062,419
Total $ 106,455
$ (116,572 )

December 31, 2019
Futures contracts (2) $ 10,065
$ (13,722 ) $ 4,104,559
Foreign currency forward contracts (2) 5,352
(5,327 ) 686,878
TBAs (3) 55,010
—
53,229
Other (2) 33,529
(20,701 ) 4,356,300
Total $ 103,956
$ (39,750 )
(1) Represents the absolute notional value of all outstanding contracts, consisting of long and short positions.


~~(1)~~	~~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.’~~

(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 March 31, ~~2020~~2021 or December 31, ~~2019.~~2020.

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. ~~The remaining derivatives included in the table above were not subject to a master netting agreement.~~

At March 31, ~~2020,~~2021, asset derivatives and liability derivatives of ~~$102.1~~$148.4 million and ~~$108.5~~$98.1 million, respectively, were subject to a master netting agreement, compared to ~~$97.8~~$138.8 million and ~~$37.8~~$93.0 million, respectively, at December 31, ~~2019.~~2020. The remaining derivatives included in the preceding table were not subject to a master netting agreement.

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 March 31,
hedging instruments: 2020 2019

Three Months Ended
Net realized gains (losses):
Futures contracts $ 95,944
$ 27,336
Foreign currency forward contracts (10,870 ) (13,709 )
TBAs 745
190
Other 41,370
22,054
Total $ 127,189
$ 35,871


Derivatives not designated as	March 31,
hedging instruments:	2021		2020

Three Months Ended
Net realized gains (losses):
Futures contracts	$	47,438	$	95,944
Foreign currency forward contracts	(22,071)		(10,870)
TBAs	0		745
Other (1)	10,749		41,370
Total	$	36,116	$	127,189

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

10. Commitments and Contingencies



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~~ARCH CAPITAL GROUP LTD. AND SUBSIDIARIES~~

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

~~10. Commitments and Contingencies~~

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 ~~$1.72~~$2.3 billion at March 31, ~~2020,~~2021, compared to ~~$1.69~~$2.1 billion at December 31, ~~2019.~~2020.

Interest Paid

Interest paid on the Company’s senior notes and other borrowings were ~~$6.6~~$1.0 million for the three months ended March 31, ~~2020, consistent with $6.2~~2021, compared to $6.6 million for the ~~2019~~2020 period.

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

In the ordinary course of business, the Company renews and enters into new leases for office property and equipment. At the lease inception date, the Company determines whether a contract contains a lease and its classification as a finance or operating lease. Primarily all of the Company’s leases are classified as operating leases. The Company’s operating leases have remaining lease terms of up to 11 years, some of which include options to extend the lease term. The Company considers these options when determining the lease term and measuring its lease liability and right-of-use asset. In addition, the Company’s lease agreements do not contain any material residual value guarantees or material restrictive covenants.

~~Short-term operating leases with an initial term of twelve months or less were excluded on the Company's consolidated balance sheet and represent an inconsequential amount of operating lease expense.~~

As most leases do not provide an implicit rate, the Company uses its incremental borrowing rate based on the information available at the lease commencement date in determining the present value of lease payments.

~~Additional information regarding the Company’s operating leases is as follows:~~

March 31,
Three Months Ended

2020 2019
Operating lease costs $ 7,992
$ 7,616
Cash payments included in the measurement of lease liabilities reported in operating cash flows $ 8,462
$ 6,900
Right-of-use assets obtained in exchange for new lease liabilities $ 3,560
$ —
Right-of-use assets (1) $ 127,766
$ 140,741
Operating lease liability (1) $ 145,956
$ 157,729
Weighted average discount rate 3.9 % 3.9 %
Weighted average remaining lease term 6.3 years
7.2 years


~~(1)~~			~~The right-of-use assets are included in ‘other assets’ while the operating lease liability is included in ‘other liabilities.’~~

~~The following table presents the contractual maturities of the Company's operating lease liabilities at March 31, 2020:~~

Years Ending December 31,
2020 (remainder) $ 23,994
2021 31,279
2022 28,198
2023 23,692
2024 17,473
2025 and thereafter 40,124
Total undiscounted lease liability $ 164,760
Less: present value adjustment (18,804 )
Operating lease liability $ 145,956


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

Watford

In March 2014, the Company invested $100.0 million and acquired 2,500,000 common shares, approximately 11% of Watford’s outstanding common equity. Watford’s common shares are listed on the Nasdaq Select Global Market under the ticker symbol “WTRE”. As of March 31, ~~2020,~~2021, the Company owns approximately ~~13%~~10.3% of Watford’s outstanding common equity.

~~In July 2019, Watford completed an offering of $175.0~~ The Company also owns $35.0 million in aggregate principal amount of ~~its~~Watford


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Holdings Ltd’s 6.5% senior notes, due July 2, 2029 ~~(“Watford Senior Notes”). Interest on the Watford Senior Notes is payable semi-annually in arrears on each January 2~~ and ~~July 2 commencing on January 2, 2020. The $172.4 million net proceeds from the offering were used to redeem a portion~~approximately 6.6% of Watford’s ~~outstanding~~ preference ~~shares (“Watford Preference Shares”). The Company purchased $35.0 million in aggregate principal amount of the Watford Senior Notes.~~shares.

Watford is considered a VIE and the Company concluded that it is the primary beneficiary of Watford. As such, the results of Watford are included in the Company’s consolidated financial statements.

The Company does not guarantee or provide credit support for Watford, and the Company’s financial exposure to Watford is limited to its investment in Watford’s senior notes, common and preferred shares and counterparty credit risk (mitigated by collateral) arising from reinsurance transactions.

In the 2020 fourth quarter, Arch Capital, Watford Holdings Ltd. and Greysbridge Ltd., a wholly-owned subsidiary of Arch Capital, entered into an Agreement and Plan of Merger (as amended, the “Merger Agreement”) pursuant to which, among other things, Arch Capital agreed to acquire all of the common shares of Watford Holdings Ltd. not owned by Arch for a cash purchase price of $35.00 per common share. Arch Capital has assigned its rights under the Merger Agreement to Greysbridge Holdings Ltd., a wholly-owned subsidiary of Arch Capital (“Greysbridge”). The transaction is expected to close in the second quarter of 2021 and remains subject to customary closing conditions. Shareholder approval has been obtained and regulatory approvals are ongoing. Upon closing of the transaction, Watford will be wholly owned by Greysbridge and Greysbridge will be owned 40% by Arch Re Bermuda, 30% by certain investment funds managed by Kelso & Company and 30% by certain investment funds managed by Warburg Pincus LLC.



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~~ARCH CAPITAL GROUP LTD. AND SUBSIDIARIES~~

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

The following table provides the carrying amount and balance sheet caption in which the assets and liabilities of Watford are reported:


	March 31,		December 31,
	2021		2020
Assets
Investments accounted for using the fair value option (1)	$	1,880,768	$	1,790,385
Fixed maturities available for sale, at fair value	627,387		655,249
Equity securities, at fair value	62,314		52,410
Cash	236,164		211,451
Accrued investment income	14,325		14,679
Premiums receivable	252,523		224,377
Reinsurance recoverable on unpaid and paid losses and LAE	291,485		286,590
Ceded unearned premiums	113,180		122,339
Deferred acquisition costs	62,224		53,705
Receivable for securities sold	68,076		37,423
Goodwill and intangible assets	7,650		7,650
Other assets	87,358		75,801
Total assets of consolidated VIE	$	3,703,454	$	3,532,059

Liabilities
Reserve for losses and loss adjustment expenses	$	1,568,243	$	1,519,583
Unearned premiums	426,975		407,714
Reinsurance balances payable	77,041		63,269
Revolving credit agreement borrowings	155,687		155,687
Senior notes	172,757		172,689
Payable for securities purchased	59,230		25,881
Other liabilities	214,103		193,494
Total liabilities of consolidated VIE	$	2,674,036	$	2,538,317

Redeemable noncontrolling interests	$	52,421	$	52,398

March 31, December 31,
2020 2019
Assets
Investments accounted for using the fair value option $ 1,732,086
$ 1,898,091
Fixed maturities available for sale, at fair value 717,552
745,708
Equity securities, at fair value 63,169
65,338
Cash 96,580
102,437
Accrued investment income 16,344
14,025
Premiums receivable 281,541
273,657
Reinsurance recoverable on unpaid and paid losses and LAE 197,458
170,973
Ceded unearned premiums 128,570
132,577
Deferred acquisition costs 71,402
64,044
Receivable for securities sold 26,789
16,287
Goodwill and intangible assets 7,650
7,650
Other assets 67,493
60,070
Total assets of consolidated VIE $ 3,406,634
$ 3,550,857

Liabilities
Reserve for losses and loss adjustment expenses $ 1,300,249
$ 1,263,628
Unearned premiums 478,663
438,907
Reinsurance balances payable 71,204
77,066
Revolving credit agreement borrowings 500,587
484,287
Senior notes 172,486
172,418
Payable for securities purchased 63,829
18,180
Other liabilities (1) 203,234
171,714
Total liabilities of consolidated VIE $ 2,790,252
$ 2,626,200

Redeemable noncontrolling interests $ 52,328
$ 52,305
(1) Includes in “other investments” on the Company’s balance sheet.


~~(1)~~	~~Includes certain borrowings related to investing activities.~~

For the three months ended March 31, ~~2020,~~2021, Watford generated $7.0 million of cash provided by operating activities, $21.4 million of cash provided by investing activities and $1.0 million of cash used for financing activities, compared to $24.6 million of cash provided by operating activities, $35.7 million of cash used for investing activities and $12.3 million of cash provided by financing activities ~~compared to $70.3 million of cash provided by operating activities, $105.9 million of cash used for investing activities and $28.1 million of cash provided by financing activities~~ for the three months ended March 31, ~~2019.~~2020.

Non-redeemable noncontrolling interests

The Company accounts for the portion of Watford’s common equity attributable to third party investors in the shareholders’ equity section of its consolidated balance sheets. The noncontrolling ownership in Watford’s common shares was approximately ~~87%~~90% at March 31, ~~2020.~~2021. The portion of Watford’s income or loss attributable to third party investors is recorded in the consolidated statements of income in ‘net (income) loss attributable to noncontrolling interests.’


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NOTES TO CONSOLIDATED FINANCIAL STATEMENTS (UNAUDITED)

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

March 31,
2020 2019
Three Months Ended
Balance, beginning of year $ 762,777
$ 791,560
Additional paid in capital attributable to noncontrolling interests (123 ) —
Repurchases attributable to non-redeemable noncontrolling interests ⁽¹⁾
(2,867 ) —
Amounts attributable to noncontrolling interests (233,944 ) 42,382
Other comprehensive income (loss) attributable to noncontrolling interests (33,058 ) 4,139
Balance, end of period $ 492,785
$ 838,081


	March 31,
	2021		2020
Three Months Ended
Balance, beginning of period	$	823,007	$	762,777
Additional paid in capital attributable to noncontrolling interests	21,730		(123)
Repurchases attributable to non-redeemable noncontrolling interests (1)	0		(2,867)
Amounts attributable to noncontrolling interests	36,697		(233,944)
Other comprehensive income (loss) attributable to noncontrolling interests	(4,570)		(33,058)
Balance, end of period	$	876,864	$	492,785

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

Redeemable noncontrolling interests

The Company accounts for redeemable noncontrolling interests in the mezzanine section of its consolidated balance sheets in accordance with applicable accounting guidance. Such redeemable noncontrolling interests primarily relate 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. Preferred dividends, including the accretion of the discount and issuance costs, are included in ‘net (income) loss attributable to noncontrolling interests’ in the Company’s consolidated statements of income.

In August 2019, Watford redeemed 6,919,998 of its 9,065,200 issued and outstanding Watford Preference Shares. The Watford Preference Shares were redeemed at a total redemption price of $25.19748 per share, inclusive of all declared and unpaid dividends, with accumulation of any undeclared dividends on or after June 30, 2019. In addition, the Company received $11.5 million pursuant to the redemption of Watford Preference Shares.

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


							March 31,
							2021		2020
Three Months Ended						Three Months Ended
Balance, beginning of period						Balance, beginning of period	$	58,548	$	55,404

Accretion of preference share issuance costs						Accretion of preference share issuance costs	23		23
Other						Other	(901)		(51)
Balance, end of period						Balance, end of period	$	57,670	$	55,376

	March 31,
	2020			2019
Three Months Ended
Balance, beginning of year	$	55,404		$	206,292
Accretion of preference share issuance costs	23			91
Other	(51		)	—
Balance, end of period	$	55,376		$	206,383



~~ARCH CAPITAL~~	35	~~2020 FIRST QUARTER FORM 10-Q~~

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~~ARCH CAPITAL GROUP LTD. AND SUBSIDIARIES~~

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

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:


	March 31,
	2021		2020
Three Months Ended
Amounts attributable to non-redeemable noncontrolling interests	$	(36,697)	$	233,944
Amounts attributable to redeemable noncontrolling interests	(855)		(1,153)
Net (income) loss attributable to noncontrolling interests	$	(37,552)	$	232,791

March 31,
2020 2019
Three Months Ended
Amounts attributable to non-redeemable noncontrolling interests $ 233,944
$ (42,382 )
Amounts attributable to redeemable noncontrolling interests (1,153 ) (4,588 )
Net (income) loss attributable to noncontrolling interests $ 232,791
$ (46,970 )


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NOTES TO CONSOLIDATED FINANCIAL STATEMENTS (UNAUDITED)

Bellemeade Re

The Company has entered into various 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 ~~one month LIBOR, the basis~~benchmark index for ~~the contractual payments to bond holders,~~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 agreement 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.


			March 31, 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	$	(306)	$	1,152	$	846	$	145,573	$	(245)	$	844	$	599
Bellemeade 2018-1 Ltd. (Apr-18)	250,095		(1,081)		2,885		1,804		250,095		(903)		2,245		1,342
Bellemeade 2018-2 Ltd. (Aug-18)	66,747		(32)		62		30		108,395		(138)		280		142
Bellemeade 2018-3 Ltd. (Oct-18)	302,563		(1,604)		4,277		2,673		302,563		(1,320)		3,262		1,942
Bellemeade 2019-1 Ltd. (Mar-19)	219,256		(1,117)		7,991		6,874		219,256		(1,361)		8,461		7,100
Bellemeade 2019-2 Ltd. (Apr-19)	398,316		(780)		6,577		5,797		398,316		(730)		5,201		4,471
Bellemeade 2019-3 Ltd. (Jul-19)	528,084		(898)		6,047		5,149		528,084		(861)		5,079		4,218
Bellemeade 2019-4 Ltd. (Oct-19)	468,737		(908)		8,034		7,126		468,737		(890)		6,676		5,786
Bellemeade 2020-1 Ltd. (Jun-20) (1)	132,881		(58)		294		236		275,068		(178)		1,012		834
Bellemeade 2020-2 Ltd. (Sep-20) (2)	368,797		(370)		6,077		5,707		423,420		(556)		6,839		6,283
Bellemeade 2020-3 Ltd. (Nov-20) (3)	418,158		(433)		9,527		9,094		418,158		(631)		9,605		8,974
Bellemeade 2020-4 Ltd. (Dec-20) (4)	321,393		(23)		5,969		5,946		321,393		(156)		6,816		6,660
Bellemeade 2021-1 Ltd. (Mar-21) (5)	579,717		0		4,767		4,767		0		0		0		0
Total	$	4,200,317	$	(7,610)	$	63,659	$	56,049	$	3,859,058	$	(7,969)	$	56,320	$	48,351

Maximum Exposure to Loss
Bellemeade Entities (Issue Date) Total VIE Assets On-Balance Sheet (Asset) Liability Off-Balance Sheet Total
Mar 31, 2020
Bellemeade 2017-1 Ltd. (Oct-17) $ 190,324
$ 204
$ 1,491
$ 1,695
Bellemeade 2018-1 Ltd. (Apr-18) 299,909
(132 ) 3,790
3,658
Bellemeade 2018-2 Ltd. (Aug-18) 380,986
83
2,787
2,870
Bellemeade 2018-3 Ltd. (Oct-18) 383,268
(116 ) 4,272
4,156
Bellemeade 2019-1 Ltd. (Mar-19) 228,940
396
3,072
3,468
Bellemeade 2019-2 Ltd. (Apr-19) 462,057
814
4,373
5,187
Bellemeade 2019-3 Ltd. (Jul-19)
603,465
1,033
8,449
9,482
Bellemeade 2019-4 Ltd. (Oct-19)

563,160
1,420
10,320
11,740
Total $ 3,112,109
$ 3,702
$ 38,554
$ 42,256
Dec 31, 2019
Bellemeade 2017-1 Ltd. (Oct-17) $ 216,429
$ (442 ) $ 2,794
$ 2,352
Bellemeade 2018-1 Ltd. (Apr-18) 328,482
(1,574 ) 5,757
4,183
Bellemeade 2018-2 Ltd. (Aug-18) 437,009
(877 ) 2,524
1,647
Bellemeade 2018-3 Ltd. (Oct-18) 426,806
(1,113 ) 3,937
2,824
Bellemeade 2019-1 Ltd. (Mar-19) 257,358
(226 ) 3,027
2,801
Bellemeade 2019-2 Ltd. (Apr-19) 525,959
(78 ) 2,579
2,501
Bellemeade 2019-3 Ltd. (Jul-19) 656,523
(585 ) 9,273
8,688
Bellemeade 2019-4 Ltd. (Oct-19) 577,267
(302 ) 12,193
11,891
Total $ 3,425,833
$ (5,197 ) $ 42,084
$ 36,887

(1) An additional $79 million capacity was provided directly to Arch MI U.S. by 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.



ARCH CAPITAL	3634	~~2020~~2021 FIRST 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
Consolidated Statement of Income Three Months Ended
Details About Line Item That Includes March 31,
AOCI Components Reclassification 2020 2019

Unrealized appreciation on available-for-sale investments
Net realized gains (losses) $ 146,232
$ 11,709
Provision for credit losses (9,320 )
Other-than-temporary impairment losses (533 ) (1,309 )
Total before tax 136,379
10,400
Income tax (expense) benefit (15,150 ) (179 )
Net of tax $ 121,229
$ 10,221


		Amounts Reclassified from AOCI
	Consolidated Statement of Income	Three Months Ended
Details About	Line Item That Includes	March 31,
AOCI Components	Reclassification	2021		2020

Unrealized appreciation on available-for-sale investments
	Net realized gains (losses)	$	2,004	$	146,232
	Provision for credit losses	(1,647)		(9,320)
	Other-than-temporary impairment losses	0		(533)
	Total before tax	357		136,379
	Income tax (expense) benefit	(3,054)		(15,150)
	Net of tax	$	(2,697)	$	121,229

Before Tax Amount Tax Expense (Benefit) Net of Tax Amount
Three Months Ended March 31, 2020
Unrealized appreciation (decline) in value of investments:
Unrealized holding gains (losses) arising during period $ (63,451 ) $ (6,164 ) $ (57,287 )
Less reclassification of net realized gains (losses) included in net income 136,379
15,150
121,229
Foreign currency translation adjustments (45,424 ) (735 ) (44,689 )
Other comprehensive income (loss) $ (245,254 ) $ (22,049 ) $ (223,205 )

Three Months Ended March 31, 2019
Unrealized appreciation (decline) in value of investments:
Unrealized holding gains (losses) arising during period $ 254,990
$ 29,103
$ 225,887
Less reclassification of net realized gains (losses) included in net income 10,400
179
10,221
Foreign currency translation adjustments 5,644
128
5,516
Other comprehensive income (loss) $ 250,234
$ 29,052
$ 221,182


	Before Tax Amount		Tax Expense (Benefit)		Net of Tax Amount
Three Months Ended March 31, 2021
Unrealized appreciation (decline) in value of investments:
Unrealized holding gains (losses) arising during period	$	(294,360)	$	(32,610)	$	(261,750)

Less reclassification of net realized gains (losses) included in net income	357		3,054		(2,697)
Foreign currency translation adjustments	(28,415)		169		(28,584)
Other comprehensive income (loss)	$	(323,132)	$	(35,495)	$	(287,637)

Three Months Ended March 31, 2020
Unrealized appreciation (decline) in value of investments:
Unrealized holding gains (losses) arising during period	$	(63,451)	$	(6,164)	$	(57,287)

Less reclassification of net realized gains (losses) included in net income	136,379		15,150		121,229
Foreign currency translation adjustments	(45,424)		(735)		(44,689)
Other comprehensive income (loss)	$	(245,254)	$	(22,049)	$	(223,205)



ARCH CAPITAL	3735	~~2020~~2021 FIRST 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 ~~(46.0%)~~7.6% for the three months ended March 31, ~~2020,~~2021, compared to an(46.0%) for the 2020 period. The Company’s prior year effective tax rate ~~of 8.5% for the 2019 period. The Company’s effective tax rate in the current year differed from the prior year period primarily due to the~~was impacted by significant ~~proportion~~portion of realized losses generated in lower tax jurisdictions.

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. For interim reporting purposes, the Company has calculated its annual effective tax rate for the full year 2020 by treating excess tax benefits in the U.S. that arise from the accounting for stock based compensation as a discrete item. The impact of the discrete item resulted in a benefit of 3.9% for the three months ended March 31, 2020.

The Company had a net deferred tax ~~liability~~asset of ~~$8.0~~$48.1 million at March 31, ~~2020,~~2021, compared to a net deferred tax ~~liability~~asset of ~~$53.5~~$15.7 million at December 31, ~~2019.~~2020. The change is primarily a result of ~~the decline~~market value fluctuations in the ~~fair value of the Company’s fixed maturities from December 31, 2019 to March 31, 2020.~~investment portfolio. In addition, the Company paid ~~$7.4~~$7.1 million and ~~recovered $32.7~~$7.4 million of income taxes for the three months ended March 31, ~~2020~~2021 and ~~2019,~~2020, 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 March 31, ~~2020,~~2021, 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 2017, the Company acquired approximately 25% of Premia Holdings Ltd. Premia Holdings Ltd. is the parent of Premia Reinsurance Ltd., a multi-line Bermuda reinsurance company (together with Premia Holdings Ltd., “Premia”). Premia’s strategy is to reinsure or acquire companies or reserve portfolios in the non-life property and casualty insurance and reinsurance run-off market. Arch Re Bermuda and certain Arch co-investors invested $100.0 million and acquired approximately 25% of Premia as well as warrants to purchase additional common equity. Arch has appointed 2 directors to serve on the 7 person board of directors of Premia. Arch Re Bermuda is providing a 25% quota share reinsurance treaty on certain business written by Premia.

In the 2019 fourth quarter, Barbican, ~~Group Holdings Limited (“Barbican”),~~ a wholly owned subsidiary of the Company, entered into certain reinsurance and related transactions with Premia pursuant to which Premia assumed a transfer of liability for the 2018 and prior years of account of Barbican as of July 1, 2019. Barbican recorded reinsurance recoverable on unpaid and paid losses and funds held liability of ~~$216.0 million~~NaN and ~~$210.2~~$275.0 million, respectively, at March 31, ~~2020,~~2021, compared to ~~$177.7~~$199.8 million and ~~$180.0~~$149.6 million, respectively, at December 31, ~~2019.~~2020.

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.

Certain directors and executive officers of the Company own common and preference shares of Watford. See note ~~12,~~11, “Variable Interest Entity and Noncontrolling Interests,” for information about Watford.


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~~ARCH CAPITAL~~			38	~~2020 FIRST QUARTER FORM 10-Q~~

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

~~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, ~~2019~~2020 (“~~2019~~2020 Form 10-K”). In addition, readers should review “Risk Factors” set forth in Item 1A of Part I of our ~~2019~~2020 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” or “us”) is a publicly listed Bermuda ~~public limited liability~~exempted company with approximately ~~$13.10~~$15.8 billion in capital at March 31, ~~2020~~2021 and, through operations in Bermuda, the United States, Europe, Canada, Australia and Hong Kong, writes insurance, reinsurance and mortgage insurance on a worldwide basis.

CURRENT OUTLOOK

~~The outbreak~~Our three primary areas of ~~COVID-19 began significantly impacting social and economic activity~~focus for 2021 are to continue our growth in the ~~U.S.~~sectors where rates allow for returns that are substantially more than our cost of capital, to optimize our mortgage insurance book as it transitions from forbearance to recovery on its way back to normalcy in the next few quarters, and ~~global markets during~~to actively manage our investments and capital to enhance our returns over the ~~2020~~long run.

From an operating perspective, the 2021 first ~~quarter. We are committed~~quarter reflected the benefits of attractive pricing in almost all of our insurance markets. As a result, we currently expect the next several quarters to continue to show improved underwriting margins, partially due to the ~~safety~~compounding of rate-on-rate increases and the rebalancing of our ~~employees, including restricting travel~~mix. Importantly, the market is showing discipline in maintaining its momentum and ~~instituting an extensive work from home policy. These actions~~the recent catastrophic losses are likely to keep upward pressure on rates.

Consequently, these rate improvements have ~~helped prevent a major disruption~~enabled us to our clients and operations. The impact of the spread of COVID-19, a developing recession and related levels of unemployment has changed some of our outlook for 2020, but we are entering this period with a strong capital base.

~~Recent investments~~continue to expand writings in our property ~~and~~ casualty ~~business are beginning to take form.~~segments. In the insurance segment, our rate increases for the first quarter averaged over 11%, representing the fifth consecutive quarter of rate increases in excess of loss cost trends. In reinsurance, we estimate that our effective rate change was roughly 8%. We ~~continue to look for opportunities to find acceptable books of business to underwrite without sacrificing underwriting discipline and~~ continue to write a portion of our overall book in catastrophe-exposed business, which has the potential to increase the volatility of our operating results.

The extent to which COVID-19 ~~impacts~~continues to impact our business, results of operations and financial results ~~will depend~~depends on numerous evolving factors including, but not limited ~~to:~~to the ~~magnitude and~~ duration of COVID-19, the extent to which it will impact macroeconomic conditions, the speed of the anticipated recovery and governmental, business and individual reactions to the pandemic. ~~Given~~During the ~~daily evolution~~first quarter of ~~the COVID-19 outbreak and the response to curb its spread, currently~~2021, we ~~are~~did not ~~able to estimate the effects of the COVID-19 outbreak~~make any significant changes to our ~~results of~~2020 COVID-19 related loss reserves.

For our U.S. primary mortgage operations, ~~financial condition, or liquidity.~~

~~Given the unusual circumstances and breadth of the pandemic, we have classified COVID-19 losses as a catastrophe.~~

~~We recorded approximately $87 million for COVID-19 losses~~

across our insurance and reinsurance segment, split 41% to insurance and 59% to reinsurance. While it is still very early and we have extremely limited information to accurately quantify our potential exposure to the pandemic, we believe it was prudent to establish a certain level of IBNR reserves for occurrences throughreported delinquencies were 3.86% at March 31, 2020, based on policy terms and conditions including limits, sub-limits, and deductibles. These reserves were recorded across a limited number of lines of business, such as trade credit and property where we have a very small number of policies that do not contain a specific pandemic exclusion and/or explicitly afford business interruption coverage under a pandemic.

~~We believe that the mortgage insurance industry enters this period of stress in a stronger position~~2021, compared to 4.19% at December 31, 2020. Delinquencies continue to be better than ~~it did back in 2007~~our expectations at the beginning of the ~~great financial crisis. Given~~COVID-19 pandemic but delinquency rates remain at elevated levels, reflecting the ~~financial stress due~~impact of the recession and forbearance programs under the CARES Act to ~~COVID-19 global pandemic, our~~borrowers experiencing a hardship. Forbearance allows for mortgage ~~segment’s combined ratio~~payments to be suspended for ~~the 2020 first quarter included 12.0 points~~up to 360 days or longer along with a suspension of ~~related losses.~~foreclosures and evictions. See “Results of Operations—Mortgage Segment” for further details on our mortgage operations.

~~As we look towards~~In the ~~remainder~~first quarter, our U.S. primary mortgage operations saw new insurance written of ~~2020,~~$27 billion, around 60% above the same period last year. The refinancing boom that began last year has resulted in ~~the U.S. we expect delinquency~~significant turnover in our insurance in force and lower persistency. However, if mortgage rates continue to increase progressively from the current level, as more borrowers request forbearance on their mortgage loans under the CARES Act. We expect to record loss reserves on these delinquencies, which will likely increase our levels of incurred losses over the coming quarters. Over time,rise, we would expect ~~many~~persistency to gradually return to the longer-term range of ~~these delinquencies to cure and revert back to performing loans~~75%. Outside of the U.S., we increased our writings in Australia as the ~~economy returns~~housing market remains strong there. We like the long-term opportunity in Australia as demonstrated by our announcement in March to ~~a less-stressed state. At this time,~~acquire Westpac's LMI business. The agreement allows us to free up capital even as we ~~do not have enough visibility to predictably forecast the rate~~build our Australian presence and diversify our earning streams at which forbearance delinquencies will be reported to us, cure or ultimately turn into claims on an annual, let alone a quarterly basis. That said, based on our current analysis which tells us that the pandemic will represent an earnings event for our mortgage segment and not a capital event, our current expectation is that our pre-tax underwriting income for the entire mortgage segment will be minimal for the remainder of 2020. However, there is likely to be variability in underwriting income between quarters based on the timing of receipt of notice of defaults. For further discussion of the potential impacts of COVID-19, see ~~“ITEM 1A—Risk Factors”~~.attractive risk-adjusted returns.

~~Arch remains~~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.” In addition, we enter into aggregate excess of loss mortgage reinsurance agreements with various special purpose reinsurance companies domiciled in Bermuda and issue mortgage insurance linked notes, increasing our protection for mortgage tail risk. The Bellemeade structures provide approximately $4.3 billion of aggregate reinsurance coverage at March 31, 2021.


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FINANCIAL MEASURES


~~ARCH CAPITAL~~			39	~~2020 FIRST QUARTER FORM 10-Q~~

~~Table of Contents~~

~~enterprises, or “GSEs.” Such programs have continued to generate business.~~

~~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 $30.54 at March 31, 2021, compared to $30.31 at December 31, 2020 and $26.10 at March 31, ~~2020, compared to $26.42 at December 31, 2019 and $23.12 at March 31, 2019.~~2020. The ~~1.2% decrease~~0.8% increase in book value per share for the ~~2020~~2021 first quarter reflected the impact of ~~negative total return~~a high level of catastrophic loss activity and the impact of rising interest rates on ~~investments and losses related to COVID-19 exposures, while~~our fixed income portfolio. Results for the ~~12.9%~~ 2021 first quarter reflected a one-time gain of $74.5 million realized from the Company’s recent acquisition of a 29.5% stake in Coface, a global trade credit insurer. The 17.0% increase in book value per share over the trailing twelve months reflected strong underwriting results and investment returns.

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 was 7.8% for the 2021 first quarter, compared to 7.1% for the 2020 first ~~quarter, compared to 12.3% for the 2019 first~~ quarter. The ~~2020 first quarter return~~ratios for

both periods reflected the impact of ~~losses related to COVID-19 exposures~~a high level of catastrophic loss activity and ~~lower investment income than in the 2019 first quarter.~~low yields on investments.

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, 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. 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 First Quarter	(0.18)	%	(0.51)	%
2020 First Quarter	(0.86)	%	(4.55)	%

Arch
Portfolio

Benchmark
Return
Pre-tax total return (before investment expenses):
2020 First Quarter (0.86 )% (4.55 )%
2019 First Quarter 2.70 % 2.82 %

Total return for the ~~2020~~2021 first quarter reflected the impact of ~~the COVID-19 global pandemic and the economic market conditions that followed, with negative returns~~rising interest rates on ~~equities and non-investment grade~~our fixed income ~~securities. This impact was partially offset by positive returns~~portfolio. We continue to maintain a short duration on ~~investment grade fixed income securities and derivatives which helped the Arch~~our portfolio ~~beat its benchmark return index in the 2020 first quarter.~~of 2.71 years at March 31, 2021.

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, 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 March 31, ~~2020,~~2021, the benchmark return index had an average credit quality of ~~“Aa3”~~“Aa1” by Moody’s Investors Service (“Moody’s”), and an estimated duration of ~~2.89~~3.14 years.



ARCH CAPITAL	4038	~~2020~~2021 FIRST QUARTER FORM 10-Q

Table of Contents

The benchmark return index included weightings to the following indices:



		%
ICE BoAML ~~1-10~~1-5 Year A - AAA U.S. Corporate Index		~~21.00~~13.00	%
ICE BoAML 5-10 Year A - AAA U.S. Corporate Index		11.00
ICE BoAML 1-5 Year U.S. Treasury Index		~~15.00~~11.00
MSCI ACWI Net Total Return USD Index		~~8.60~~9.30
~~ICE BoAML 3-5 Year Fixed Rate Asset Backed Securities Index~~		~~7.00~~
~~S&P Leveraged Loan Total Return Index~~	~~5.20~~
~~Bloomberg Barclays CMBS Invest Grade Aaa Total Return Index~~	~~5.00~~
ICE BoAML 1-10 Year BBB U.S. Corporate Index	~~4.00~~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 ~~Month~~Year U.S. Treasury ~~Bill~~ 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
~~ICE BoAML 5-10 Year U.S. Treasury~~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 ~~Total Return~~ Index		~~1.50~~1.38
~~Hedge Fund Research HFRX ED Distressed Restructuring Index~~		~~1.50~~
~~Dow Jones~~S&P DJ Global ex-US Select Real Estate Securities ~~Total Return~~ Net Index	~~0.90~~0.825
FTSE Nareit All Mortgage Capped Index Total Return USD		~~0.90~~0.825
Bloomberg Barclays CMBS: Erisa Eligible Unhedged USD		~~0.90~~0.825
ICE BoAML ~~20+~~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 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 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 and transaction costs and other 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 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 (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 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. 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 and transaction costs and other from the calculation of after-tax operating income available to Arch common shareholders.

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


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since we evaluate the performance of and manage our business to produce an underwriting profit. In addition to presenting net income



~~ARCH CAPITAL~~	41	~~2020 FIRST QUARTER FORM 10-Q~~

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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. 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 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, in accordance with Regulation G, is shown in note 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. For the ‘other’ segment, performance is measured based on net income or loss.

Along with consolidated underwriting income, we provide a subtotal of underwriting income or loss before the contribution from the ‘other’ segment. The ‘other’ segment includes the results of Watford Holdings Ltd. Watford Holdings Ltd. is the parent of Watford Re Ltd., a multi-line Bermuda reinsurance company (together with Watford Holdings Ltd., “Watford”). Pursuant to generally accepted accounting principles, Watford is considered a variable

interest entity and we concluded that we are the primary beneficiary of Watford. As such, we consolidate the results of Watford in our consolidated financial statements, although we only own approximately ~~13%~~10% of Watford’s common equity. Watford’s own management and board of directors are responsible for its results and profitability. In addition, we do not guarantee or provide credit support for

Watford. Since Watford is an independent company, the assets of Watford can be used only to settle obligations of Watford and Watford is solely responsible for its own liabilities and commitments. Our financial exposure to Watford is limited to our investment in Watford’s senior notes, common and preferred shares and counterparty credit risk (mitigated by collateral) arising from the reinsurance transactions. We believe that presenting certain information excluding the ‘other’ segment enables investors and other users of our financial information to analyze our performance in a manner similar to how our management analyzes performance.

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



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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. Each line item reflects the impact of our percentage ownership of Watford’s common equity during such period.


	Three Months Ended							Three Months Ended
	March 31,							March 31,
	2020			2019				2021		2020
Net income available to Arch common shareholders	$	133,714		$	438,125		Net income available to Arch common shareholders	$	427,753	$	133,714
Net realized (gains) losses	109,364			(114,335		)	Net realized (gains) losses	(105,551)		109,364

Equity in net (income) loss of investment funds accounted for using the equity method	4,209			(46,867		)	Equity in net (income) loss of investment funds accounted for using the equity method	(71,686)		4,209
Net foreign exchange (gains) losses	(64,491		)	(4,994		)	Net foreign exchange (gains) losses	(21,332)		(64,491)
Transaction costs and other	2,595			1,190			Transaction costs and other	1,274		2,595

Income tax expense (1)	4,365			2,778			Income tax expense (1)	9,311		4,365
After-tax operating income available to Arch common shareholders	$	189,756		$	275,897		After-tax operating income available to Arch common shareholders	$	239,769	$	189,756

Beginning common shareholders’ equity	$	10,717,371		$	8,659,827		Beginning common shareholders’ equity	$	12,325,886	$	10,717,371
Ending common shareholders’ equity	10,587,244			9,334,596			Ending common shareholders’ equity	12,316,472		10,587,244
Average common shareholders’ equity	$	10,652,308		$	8,997,212		Average common shareholders’ equity	$	12,321,179	$	10,652,308

Annualized return on average common equity %	5.0			19.5			Annualized return on average common equity %	13.9		5.0
Annualized operating return on average common equity %	7.1			12.3			Annualized operating return on average common equity %	7.8		7.1

(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.

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 ~~President and~~ Chief Executive Officer of Arch Capital, ~~and~~ 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~~

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 March 31,									Three Months Ended March 31,
	2020			2019			% Change			2021			2020			% Change
Gross premiums written	$	1,207,645		$	941,954		28.2		Gross premiums written	$	1,415,886		$	1,207,645		17.2
Premiums ceded	(378,897		)	(320,622		)			Premiums ceded	(421,047)			(378,897)
Net premiums written	828,748			621,332			33.4		Net premiums written	994,839			828,748			20.0
Change in unearned premiums	(112,829		)	(67,827		)			Change in unearned premiums	(175,365)			(112,829)
Net premiums earned	715,919			553,505			29.3		Net premiums earned	819,474			715,919			14.5
Other underwriting income (loss)									Other underwriting income (loss)	—			—
Losses and loss adjustment expenses	(507,108		)	(356,723		)			Losses and loss adjustment expenses	(535,747)			(507,108)
Acquisition expenses	(107,337		)	(82,824		)			Acquisition expenses	(128,222)			(107,337)
Other operating expenses	(129,649		)	(113,396		)			Other operating expenses	(137,113)			(129,649)
Underwriting income (loss)	$	(28,175	)	$	562		n/m		Underwriting income (loss)	$	18,392		$	(28,175)		165.3

Underwriting Ratios							% Point Change		Underwriting Ratios							% Point Change
Loss ratio	70.8		%	64.4		%	6.4		Loss ratio	65.4		%	70.8		%	(5.4)
Acquisition expense ratio	15.0		%	15.0		%	—		Acquisition expense ratio	15.6		%	15.0		%	0.6
Other operating expense ratio	18.1		%	20.5		%	(2.4	)	Other operating expense ratio	16.7		%	18.1		%	(1.4)
Combined ratio	103.9		%	99.9		%	4.0		Combined ratio	97.7		%	103.9		%	(6.2)

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.


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•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



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capital, real estate investment trust, limited partnership, financial institution and not-for-profit clients of all sizes and medical professional and general liability insurance coverages for the healthcare industry. The business is predominately written on a claims-made basis.

•Programs: primarily package policies, underwriting workers’ compensation and umbrella liability business in support of desirable package programs, targeting program managers with unique expertise and niche products offering general liability, commercial automobile, inland marine and property business with minimal catastrophe exposure.

•Property, energy, marine and aviation: primary and excess general property insurance coverages, including catastrophe-exposed property coverage, for commercial clients. Coverages for marine include hull, war, specie and liability. Aviation and ~~stand alone~~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 March 31,
	2021			2020
	Amount		%	Amount		%
Property, energy, marine and aviation	$	170,498	17.1	$	127,585	15.4
Professional lines	238,246		23.9	169,118		20.4
Programs	158,401		15.9	112,532		13.6
Construction and national accounts	134,792		13.5	115,999		14.0
Excess and surplus casualty	85,593		8.6	65,419		7.9
Travel, accident and health	92,306		9.3	126,046		15.2
Lenders products	34,860		3.5	33,292		4.0
Other	80,143		8.1	78,757		9.5
Total	$	994,839	100.0	$	828,748	100.0

Three Months Ended March 31,
2020 2019
Amount % Amount %
Professional lines $ 169,118
20.4
$ 129,234
20.8
Property, energy, marine and aviation 127,585
15.4
70,486
11.3
Travel, accident and health 126,046
15.2
88,104
14.2
Construction and national accounts 115,999
14.0
95,355
15.3
Programs 112,532
13.6
101,172
16.3
Excess and surplus casualty 65,419
7.9
45,165
7.3
Lenders products 33,292
4.0
22,415
3.6
Other 78,757
9.5
69,401
11.2
Total $ 828,748
100.0
$ 621,332
100.0

2021 First Quarter versus 2020 Period. Gross premiums written by the insurance segment in the ~~2020~~2021 first quarter were ~~28.2%~~17.2% higher than in the ~~2019~~2020 first quarter, while net premiums written were ~~33.4%~~20.0% higher. The higher level

of net premiums written reflected increases inacross most lines of business, ~~primarily~~ due in part to new business opportunities, rate increases and growth in existing ~~accounts.~~accounts, partially offset by a decrease in travel business, reflecting the ongoing impact of the COVID-19 global pandemic.

Net Premiums Earned.

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


	Three Months Ended March 31,
	2021			2020
	Amount		%	Amount		%
Property, energy, marine and aviation	$	157,259	19.2	$	111,183	15.5
Professional lines	199,671		24.4	151,700		21.2
Programs	112,840		13.8	108,878		15.2
Construction and national accounts	102,671		12.5	99,700		13.9
Excess and surplus casualty	75,367		9.2	65,097		9.1
Travel, accident and health	49,666		6.1	77,375		10.8
Lenders products	40,081		4.9	25,343		3.5
Other	81,919		10.0	76,643		10.7
Total	$	819,474	100.0	$	715,919	100.0

Three Months Ended March 31,
2020 2019
Amount % Amount %
Professional lines $ 151,700
21.2
$ 114,791
20.7
Property, energy, marine and aviation 111,183
15.5
59,638
10.8
Travel, accident and health 77,375
10.8
71,575
12.9
Construction and national accounts 99,700
13.9
75,931
13.7
Programs 108,878
15.2
97,486
17.6
Excess and surplus casualty 65,097
9.1
42,369
7.7
Lenders products 25,343
3.5
23,232
4.2
Other 76,643
10.7
68,483
12.4
Total $ 715,919
100.0
$ 553,505
100.0


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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 in the ~~2020~~2021 first quarter were ~~29.3%~~14.5% higher than in the ~~2019~~2020 first quarter. Net premiums earned reflect changes in net premiums written over the previous five quarters.

Losses and Loss Adjustment Expenses.

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


	Three Months Ended					Three Months Ended
	March 31,					March 31,
	2020		2019			2021		2020
Current year	71.0	%	65.2	%	Current year	65.9	%	71.0	%
Prior period reserve development	(0.2	)%	(0.8	)%	Prior period reserve development	(0.5)	%	(0.2)	%
Loss ratio	70.8	%	64.4	%	Loss ratio	65.4	%	70.8	%

Current Year Loss Ratio.

2021 First Quarter versus 2020 Period. The insurance segment’s current year loss ratio in the ~~2020~~2021 first quarter was ~~5.8~~5.1 points ~~higher~~lower than in the ~~2019~~2020 first quarter. The 2021 first quarter ~~and~~loss ratio reflected ~~6.9~~5.1 points of current year catastrophic activity, primarily from winter storms Uri and Viola, compared to 6.9 points of catastrophic activity for the 2020 first quarter, which included 5.0 points for exposure ~~through March 31, 2020~~ to the COVID-19 global pandemic. ~~The 2019 first quarter reflected minimal catastrophic activity.~~

Prior Period Reserve Development.

The insurance segment’s net favorable development was $4.1 million, or 0.5 points, for the 2021 first quarter, compared to $1.1 million, or 0.2 points, for the 2020 first ~~quarter, compared to $4.4 million, or 0.8 points, for the 2019 first~~ quarter. See note



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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 First Quarter versus 2020 Period. The insurance segment’s underwriting expense ratio was 32.3% in the 2021 first quarter, compared to 33.1% in the 2020 first quarter, ~~compared to 35.5% in the 2019 first quarter,~~ with the decrease primarily due ~~in part~~ to growth in net premiums earned.

Reinsurance Segment

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


	Three Months Ended March 31,									Three Months Ended March 31,
	2020			2019			% Change			2021			2020			% Change
Gross premiums written	$	1,122,519		$	682,855		64.4		Gross premiums written	$	1,471,060		$	1,122,519		31.0
Premiums ceded	(325,339		)	(231,567		)			Premiums ceded	(471,948)			(325,339)
Net premiums written	797,180			451,288			76.6		Net premiums written	999,112			797,180			25.3
Change in unearned premiums	(253,720		)	(104,923		)			Change in unearned premiums	(354,212)			(253,720)
Net premiums earned	543,460			346,365			56.9		Net premiums earned	644,900			543,460			18.7
Other underwriting income	2,120			4,377
Other underwriting income (loss)									Other underwriting income (loss)	(1,198)			2,120
Losses and loss adjustment expenses	(430,069		)	(239,810		)			Losses and loss adjustment expenses	(484,870)			(430,069)
Acquisition expenses	(79,606		)	(54,326		)			Acquisition expenses	(118,025)			(79,606)
Other operating expenses	(45,297		)	(35,704		)			Other operating expenses	(60,514)			(45,297)
Underwriting income	$	(9,392	)	$	20,902		(144.9	)
Underwriting income (loss)									Underwriting income (loss)	$	(19,707)		$	(9,392)		(109.8)

Underwriting Ratios							% Point Change		Underwriting Ratios							% Point Change
Loss ratio	79.1		%	69.2		%	9.9		Loss ratio	75.2		%	79.1		%	(3.9)
Acquisition expense ratio	14.6		%	15.7		%	(1.1	)	Acquisition expense ratio	18.3		%	14.6		%	3.7
Other operating expense ratio	8.3		%	10.3		%	(2.0	)	Other operating expense ratio	9.4		%	8.3		%	1.1
Combined ratio	102.0		%	95.2		%	6.8		Combined ratio	102.9		%	102.0		%	0.9

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

•Casualty: provides coverage to ceding company clients on third party liability and workers’ compensation exposures from ceding company clients, primarily on a treaty basis. Exposures include, among others, executive assurance, professional liability, workers’ compensation, excess and umbrella liability, excess motor and healthcare business.

•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 and other lines, including surety, accident and health, workers’ compensation catastrophe, agriculture, trade credit and political risk.

•Property catastrophe: provides protection for most 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 of loss basis 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.


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•Property excluding property catastrophe: provides coverage for both personal lines and commercial property exposures and principally covers buildings, structures, equipment and contents. The primary perils in this business include fire, explosion, collapse, riot, vandalism, wind, tornado, flood and earthquake. Business is assumed on both a proportional and excess of loss treaty basis and on a 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 March 31,
	2021			2020
	Amount		%	Amount		%
Property excluding property catastrophe	$	292,833	29.3	$	158,924	19.9
Property catastrophe	117,207		11.7	89,092		11.2
Other specialty	284,331		28.5	284,952		35.7
Casualty	218,256		21.8	190,880		23.9
Marine and aviation	61,638		6.2	49,785		6.2
Other	24,847		2.5	23,547		3.0
Total	$	999,112	100.0	$	797,180	100.0

Three Months Ended March 31,
2020 2019
Amount % Amount %
Other Specialty $ 284,952
35.7
$ 140,477
31.1
Casualty 190,880
23.9
168,484
37.3
Property excluding property catastrophe 158,924
19.9
102,740
22.8
Property catastrophe 89,092
11.2
3,383
0.7
Marine and aviation 49,785
6.2
15,958
3.5
Other 23,547
3.0
20,246
4.5
Total $ 797,180
100.0
$ 451,288
100.0

2021 First Quarter versus 2020 Period. Gross premiums written by the reinsurance segment in the ~~2020~~2021 first quarter were ~~64.4%~~31.0% higher than in the ~~2019~~2020 first quarter, while net premiums written were ~~76.6%~~25.3% higher. Premiums written for the reinsurance segment in the 2020 first quarter were affected by the presence of an $88 million loss portfolio transfer contract, written and fully earned in the period in the other specialty line of business. Absent this transaction, gross and net premiums written would have been ~~51.5% and 57.2%~~ higher than in the ~~2019~~2020 first quarter by 42.2% and 40.8%, respectively. The growth in net premiums written ~~also~~ reflected increases in most lines of business, ~~primarily~~mainly due to ~~growth in existing accounts,~~rate increases and new ~~business, including premiums written through Barbican which was acquired in the 2019 fourth quarter, and rate increases.~~

business.



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Net Premiums Earned.

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


								Three Months Ended March 31,
	Three Months Ended March 31,							2021			2020
	2020			2019				Amount		%	Amount		%
	Amount		%	Amount		%
Other Specialty	$	203,385	37.4	$	121,521	35.1
Casualty	135,071		24.9	91,624		26.5
Property excluding property catastrophe	112,652		20.7	83,792		24.2	Property excluding property catastrophe	$	187,782	29.1	$	112,652	20.7
Property catastrophe	53,000		9.8	18,732		5.4	Property catastrophe	88,011		13.6	53,000		9.8
Other specialty							Other specialty	163,898		25.4	203,385		37.4
Casualty							Casualty	149,031		23.1	135,071		24.9
Marine and aviation	24,858		4.6	11,059		3.2	Marine and aviation	40,108		6.2	24,858		4.6
Other	14,494		2.7	19,637		5.7	Other	16,070		2.5	14,494		2.7
Total	$	543,460	100.0	$	346,365	100.0	Total	$	644,900	100.0	$	543,460	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. Excluding the loss portfolio transfer contract, net premiums earned by the reinsurance segment in the ~~2020~~2021 first quarter were ~~31.6%~~41.5% higher than in the ~~2019~~2020 first ~~quarter.~~quarter, and reflect changes in net premiums written over the previous five quarters.

Other Underwriting Income (Loss).

Other underwriting income for the ~~2020~~2021 first quarter was ~~$2.1~~a loss of $1.2 million, compared to ~~$4.4~~a gain of $2.1 million for the ~~2019~~2020 first quarter.

Losses and Loss Adjustment Expenses.

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


	Three Months Ended					Three Months Ended
	March 31,					March 31,
	2020		2019			2021		2020
Current year	81.2	%	68.7	%	Current year	79.4	%	81.2	%
Prior period reserve development	(2.1	)%	0.5	%	Prior period reserve development	(4.2)	%	(2.1)	%
Loss ratio	79.1	%	69.2	%	Loss ratio	75.2	%	79.1	%

Current Year Loss Ratio.

2021 First Quarter versus 2020 Period. The reinsurance segment’s current year loss ratio in the ~~2020~~2021 first quarter was ~~12.5~~1.8 points ~~higher~~lower than in the ~~2019~~2020 first quarter. The 2021 first quarter ~~and~~loss ratio reflected ~~12.7~~24.7 points of current year catastrophic activity, ~~compared to 2.3 points in the 2019 first quarter. Catastrophic activity for the~~including winter storms Uri and Viola as well as other minor global events. The 2020 first quarter ~~ratio~~included 12.7 points of catastrophic activity, included 9.3 points for exposure ~~through March 31, 2020~~ to the COVID-19 ~~pandemic, while the 2019 first quarter ratio included an increase in reserves on Typhoon Jebi~~pandemic.


ARCH CAPITAL			44			2021 FIRST QUARTER FORM 10-Q

Table of ~~$16.0 million. The balance of the change in the 2020 loss ratios resulted, in part, from changes in mix of business and the level of attritional losses.~~Contents

Prior Period Reserve Development.

The reinsurance segment’s net favorable development was $26.8 million, or 4.2 points, for the 2021 first quarter, compared to $11.6 million, or 2.1 points, for the 2020 first ~~quarter, compared to $1.7 million, or 0.5 points of adverse development, for the 2019 first~~ quarter. Seenote 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 First Quarter versus 2020 Period. The underwriting expense ratio for the reinsurance segment was 27.7% in the 2021 first quarter, compared to 22.9% in the 2020 first ~~quarter, compared to 26.0% in the 2019~~quarter. The 2020 first quarter ~~reflecting growth~~ratio reflected a 4.4 point benefit related to the loss portfolio transfer contract and changes in ~~net premiums earned.~~mix of business.

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, ~~and~~ 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 ~~MI Europe”~~Insurance EU”) ~~and~~; in Hong Kong through Arch MI Asia Limited (“Arch MI Asia”); in Australia through Arch LMI Pty Ltd (“Arch LMI”) 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 March 31,
	2021			2020			% Change
Gross premiums written	$	391,246		$	368,945		6.0
Premiums ceded	(56,051)			(44,327)
Net premiums written	335,195			324,618			3.3
Change in unearned premiums	1,122			20,408
Net premiums earned	336,317			345,026			(2.5)
Other underwriting income	6,897			4,599
Losses and loss adjustment expenses	(63,689)			(67,566)
Acquisition expenses	(30,082)			(38,536)
Other operating expenses	(49,131)			(45,896)
Underwriting income	$	200,312		$	197,627		1.4

Underwriting Ratios							% Point Change
Loss ratio	18.9		%	19.6		%	(0.7)
Acquisition expense ratio	8.9		%	11.2		%	(2.3)
Other operating expense ratio	14.6		%	13.3		%	1.3
Combined ratio	42.4		%	44.1		%	(1.7)

Three Months Ended March 31,
2020 2019 % Change
Gross premiums written $ 368,945
$ 356,050
3.6
Premiums ceded (44,327 ) (48,798 )
Net premiums written 324,618
307,252
5.7
Change in unearned premiums 20,408
15,650

Net premiums earned 345,026
322,902
6.9
Other underwriting income 4,599
3,856

Losses and loss adjustment expenses (67,566 ) (11,149 )
Acquisition expenses (38,536 ) (31,672 )
Other operating expenses (45,896 ) (39,875 )
Underwriting income $ 197,627
$ 244,062
(19.0 )

Underwriting Ratios % Point
Change
Loss ratio 19.6 % 3.5 % 16.1
Acquisition expense ratio 11.2 % 9.8 % 1.4
Other operating expense ratio 13.3 % 12.3 % 1.0
Combined ratio 44.1 % 25.6 % 18.5



~~ARCH CAPITAL~~	46	~~2020 FIRST QUARTER FORM 10-Q~~

~~Table of Contents~~

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 March 31,
	2021			2020
	Amount		%	Amount		%
Underwriting location:
United States	$	247,529	73.8	$	264,108	81.4
Other	87,666		26.2	60,510		18.6
Total	$	335,195	100.0	$	324,618	100.0

Three Months Ended March 31,
2020 2019
Amount % Amount %
Underwriting location:
United States $ 264,108
81.4
$ 255,380
83.1
Other 60,510
18.6
51,872
16.9
Total $ 324,618
100.0
$ 307,252
100.0

2021 First Quarter versus 2020 Period. Gross premiums written by the mortgage segment in the ~~2020~~2021 first quarter were ~~3.6%~~6.0% higher than in the ~~2019~~2020 first quarter, while net premiums written were ~~5.7% higher. The~~3.3% higher, primarily reflecting growth in ~~net premiums written primarily reflected an increase in monthly~~Australian single premium ~~business due to growth in~~mortgage insurance, partially offset by a lower level of U.S. primary mortgage insurance in force ~~and lower ceded premiums.~~on monthly premium policies.

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, ofwas 54.1% for the Arch MI U.S. portfolio of mortgage ~~loans was 72.6%~~insurance policies at March 31, ~~2020,~~2021, reflecting the higher level of mortgage refinancing activity, compared to ~~75.7%~~58.7% at December 31, ~~2019.~~2020.

~~Arch MI U.S. generated $16.8 billion~~


ARCH CAPITAL			45			2021 FIRST QUARTER FORM 10-Q

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The following tables provide details on the new insurance written (“NIW”) ~~in the 2020 first quarter, compared to $11.2 billion in the 2019 first quarter.~~generated by Arch MI U.S. NIW represents the original principal balance of all loans that received coverage during the period. ~~Monthly premium policies contributed 93.5%~~


(U.S. Dollars in millions)	Three Months Ended March 31,
	2021			2020
	Amount		%	Amount		%
Total new insurance written (NIW) (1)	$	27,019		$	16,778

Credit quality (FICO):
>=740	$	17,818	65.9	$	10,069	60.0
680-739	8,418		31.2	5,787		34.5
620-679	783		2.9	922		5.5

Total	$	27,019	100.0	$	16,778	100.0

Loan-to-value (LTV):
95.01% and above	$	1,608	6.0	$	1,668	9.9
90.01% to 95.00%	12,288		45.5	7,199		42.9
85.01% to 90.00%	8,312		30.8	5,329		31.8
85.00% and below	4,811		17.8	2,582		15.4
Total	$	27,019	100.0	$	16,778	100.0

Monthly vs. single:
Monthly	$	24,989	92.5	$	15,692	93.5
Single	2,030		7.5	1,086		6.5
Total	$	27,019	100.0	$	16,778	100.0

Purchase vs. refinance:
Purchase	$	20,505	75.9	$	12,299	73.3
Refinance	6,514		24.1	4,479		26.7
Total	$	27,019	100.0	$	16,778	100.0

(1)Represents the original principal balance of ~~NIW in~~all loans that received coverage during the ~~2020 first quarter, compared to 91.6% for the 2019 first quarter.~~period.

~~The following tables provide details on the NIW generated by Arch MI U.S.:~~

(U.S. Dollars in millions) Three Months Ended March 31,
2020 2019
Amount % Amount %
Total new insurance written (NIW) (1) $ 16,778
$ 11,207

Credit quality (FICO):
>=740 $ 10,069
60.0
$ 6,350
56.7
680-739 5,787
34.5
4,041
36.1
620-679 922
5.5
816
7.3
Total $ 16,778
100.0
$ 11,207
100.0

Loan-to-value (LTV):
95.01% and above $ 1,668
9.9
$ 1,808
16.1
90.01% to 95.00% 7,199
42.9
4,975
44.4
85.01% to 90.00% 5,329
31.8
3,149
28.1
85.01% and below 2,582
15.4
1,275
11.4
Total $ 16,778
100.0
$ 11,207
100.0

Monthly vs. single:
Monthly $ 15,692
93.5
$ 10,263
91.6
Single 1,086
6.5
944
8.4
Total $ 16,778
100.0
$ 11,207
100.0

Purchase vs. refinance:
Purchase $ 12,299
73.3
$ 10,289
91.8
Refinance 4,479
26.7
918
8.2
Total $ 16,778
100.0
$ 11,207
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 March 31,
	2021			2020
	Amount		%	Amount		%
Underwriting location:
United States	$	262,550	78.1	$	289,162	83.8
Other	73,767		21.9	55,864		16.2
Total	$	336,317	100.0	$	345,026	100.0

Three Months Ended March 31,
2020 2019
Amount % Amount %
Underwriting location:
United States $ 289,162
83.8
$ 274,473
85.0
Other 55,864
16.2
48,429
15.0
Total $ 345,026
100.0
$ 322,902
100.0

2021 First Quarter versus 2020 Period. Net premiums earned for the 2021 first quarter were 2.5% lower than in the 2020 first quarter, ~~were 6.9% higher than~~and reflected a decrease in ~~the 2019 first quarter. The increases were primarily due to growth in~~ U.S. primary mortgage insurance in force, ~~over the last twelve months combined with a higher level of~~partially offset by an increase in earnings from Australian single ~~premiums earned as a result of~~premium policy ~~terminations due to mortgage refinance activity.~~terminations.

Other Underwriting Income.

Other underwriting income, which is primarily related to ~~older~~ GSE credit risk-sharing transactions ~~receiving derivative accounting treatment,~~ was $6.9 million for the 2021 first quarter, compared to $4.6 million for the 2020 first ~~quarter, compared to $3.9 million for the 2019 first~~ quarter.



~~ARCH CAPITAL~~	47	~~2020 FIRST QUARTER FORM 10-Q~~

~~Table of Contents~~

Losses and Loss Adjustment Expenses.

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


	Three Months Ended					Three Months Ended
	March 31,					March 31,
	2020		2019			2021		2020
Current year	21.4	%	14.8	%	Current year	22.1	%	21.4	%
Prior period reserve development	(1.8	)%	(11.3	)%	Prior period reserve development	(3.2)	%	(1.8)	%
Loss ratio	19.6	%	3.5	%	Loss ratio	18.9	%	19.6	%

Current Year Loss Ratio.

2021 First Quarter versus 2020 Period. The mortgage segment’s current year loss ratio was ~~6.6~~0.7 points higher in the ~~2020~~2021 first quarter than in the ~~2019~~2020 first quarter. The 2021 first quarter loss ratio ~~for the 2020 first quarter~~ reflected ~~12.0 points of losses which resulted from~~continued elevated new delinquency rates, primarily due to financial stress ~~due~~related to the COVID-19 ~~global~~ pandemic. ~~These~~

For both the 2021 and 2020 periods, incurred losses ~~are largely a result of loss reserving selections being set at~~were due, in part, to financial stress from the ~~higher end~~COVID-19 pandemic. Segregating estimated losses due to COVID-19 from the overall mortgage segment estimated losses would require knowledge of the ~~range~~number of ~~indications across~~delinquencies specifically attributable to COVID-19. As this analysis cannot be performed accurately, the mortgage segment as of March 31, 2020. Pursuant to GAAP, incurred losses are based only on reported delinquencies as of March 31, 2020 for the mortgage segment’s U.S. primary insurance operations. The Company is not ~~aware of any reported delinquencies being directly the result of recent events as of the end of the first quarter.~~reporting COVID-19 provisions separately from its overall loss provisions.

Prior Period Reserve Development.

The mortgage segment’s net favorable development was $10.9 million, or 3.2 points, for the 2021 first quarter, compared to $6.1 million, or 1.8 points, for the 2020 first ~~quarter, compared to $36.6 million, or 11.3 points, for the 2019 first~~ quarter. See note 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 First Quarter versus 2020 Period. The underwriting expense ratio for the mortgage segment was 23.5% in the 2021 first quarter, compared to 24.5% in the 2020 first quarter, ~~compared~~with the decrease reflecting lower acquisition expenses on U.S. primary mortgage insurance and to ~~22.1% in the 2019 first quarter. The higher ratio in the 2020 first quarter reflected higher incentive compensation costs.~~a lesser extent international 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


ARCH CAPITAL			46			2021 FIRST QUARTER FORM 10-Q

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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, income or loss from operating affiliates and income taxes. 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.

Net Investment Income.

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


	Three Months Ended
	March 31,
	2021		2020
Fixed maturities	$	79,017	$	101,763

Equity securities	5,650		5,630
Short-term investments	644		3,385

Other (1)	15,559		20,479
Gross investment income	100,870		131,257
Investment expenses (2)	(22,141)		(18,229)
Net investment income	$	78,729	$	113,028

Three Months Ended
March 31,
2020 2019
Fixed maturities $ 101,763
$ 110,651
Equity securities 5,630
2,246
Short-term investments 3,385
4,298
Other (1) 20,479
22,944
Gross investment income 131,257
140,139
Investment expenses (2) (18,229 ) (18,890 )
Net investment income $ 113,028
$ 121,249
(1) Amounts include dividends and other distributions on investment funds, term loan investments, funds held balances, cash balances and other items.


~~(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 0.35% of average invested assets for the 2020 first quarter, compared to 0.38% for the 2019 first quarter.~~

(2) Investment expenses were approximately 0.35% of average invested assets for the 2021 first quarter, consistent with 0.35% for the 2020 first quarter.

The lower level of net investment income for the ~~2020~~2021 first quarter primarily related to lower yields available in the financial market. The pre-tax investment income yield, calculated based on amortized cost and on an annualized basis, was 1.31% for the 2021 first quarter, compared to 2.20% for the 2020 ~~first quarter, compare to 2.67% for the 2019~~ first quarter.

Corporate Expenses.

Corporate expenses were $23.5 million for the 2021 first quarter, compared to $18.2 million for the 2020 ~~first quarter, compared to $16.8 million for the 2019~~ first quarter. The increase in corporate expenses was primarily ~~reflected~~due to higher ~~professional fees and other~~incentive compensation costs.

Transaction Costs and Other.

Transaction costs and other were $1.2 million for the 2021 first quarter, compared to $2.6 million for the 2020 first ~~quarter, compared to $1.2 million for the 2019 first~~ quarter. Amounts in the 2021 and 2020 ~~period~~periods are primarily related to ~~recent acquisition activity.~~acquisitions activity for the respective period.

Amortization of Intangible Assets.

Amortization of intangible assets for the ~~2020~~2021 first quarter was ~~$16.6~~$14.4 million, compared to ~~$20.4~~$16.6 million for the ~~2019~~2020 first quarter. ~~Such expenses~~Amounts in 2021 and 2020 primarily related to ~~the UGC acquisition and other acquisitions in late 2018 to 2019.~~

amortization of finite-lived intangible assets. See the consolidated financial statements contained in our ~~2019~~2020 Form 10-K for disclosures on our amortization pattern.

Interest Expense.

Interest expense was $34.2 million for the 2021 first quarter, compared to the $25.2 million for the 2020 first ~~quarter, compared to the $23.5 million for the 2019 first~~ quarter. The ~~increase~~higher level of interest expense mainly resulted from the issuance of $1.0 billion of 3.635% senior notes in ~~the 2020 period reflected an increase in funds held liabilities.~~June 2020.



~~ARCH CAPITAL~~	48	~~2020 FIRST QUARTER FORM 10-Q~~

~~Table of Contents~~

Net Realized Gains or Losses.

We recorded net realized gains of $101.3 million for the 2021 first quarter, compared to net realized losses of $72.1 million for the 2020 ~~first quarter, compared to net realized gains of $111.1 million for the 2019~~ first quarter. Currently, our portfolio is 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 and re-measurement of contingent consideration liability amounts.~~earnings. See note 7, “Investment Information—Net Realized Gains (Losses),” to our consolidated financial statements for additional information. See note 7, “Investment Information—Allowance for Credit Losses,” to our consolidated financial statements for additional information.

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

We recorded ~~a loss~~$71.7 million of ~~$4.2 million for~~ equity in net income ~~or loss~~ related to investment funds accounted for using the equity method in the ~~2020~~2021 first quarter, compared to ~~$46.9~~a loss of $4.2 million ~~of income~~ for the ~~2019~~2020 first quarter. 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 ~~$1.68~~$2.3 billion at March 31, ~~2020,~~2021, compared to ~~$1.66~~$2.0 billion at December 31, ~~2019.~~2020. See note 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 ~~2020~~2021 first quarter were ~~$63.3~~$21.5 million, compared to net foreign exchange gains for the ~~2019~~2020 first quarter of ~~$5.2~~$63.3 million. Amounts in both periods


ARCH CAPITAL			47			2021 FIRST QUARTER FORM 10-Q

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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 ~~13.6%~~8.2% for the ~~2020~~2021 first quarter, compared to ~~9.4%~~13.6% for the ~~2019~~2020 first quarter. Such amounts exclude the results of the ‘other’ segment. ~~The effective tax~~

~~rates for the 2020 first quarter included a discrete income tax benefit of $2.4 million related to share based compensation.~~ 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) from operating affiliates.

We recorded $75.5 million of net income from our operating affiliates in the 2021 first quarter, compared to $8.5 million for the 2020 first quarter. Results for the 2021 first quarter reflected a one-time gain of $74.5 million realized from the Company’s acquisition of 29.5% of the common equity in Coface, a global trade credit insurer. 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.

Other Segment

The ‘other’ segment includes the results of Watford. Pursuant to generally accepted accounting principles, Watford is considered a variable interest entity and we concluded that we are the primary beneficiary of Watford. As such, we consolidate the results of Watford in our consolidated financial statements, although we only own approximately ~~13%~~10% of Watford’s common equity. See note ~~12,~~11, “Variable Interest Entities and Noncontrolling Interests,” and note 4, “Segment Information,” to our consolidated financial statements for additional information on Watford.

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 ~~2019~~2020 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



~~ARCH CAPITAL~~	49	~~2020 FIRST QUARTER FORM 10-Q~~

~~Table of Contents~~

~~FINANCIAL CONDITION~~

Investable Assets

At March 31, ~~2020,~~2021, total investable assets held by Arch were ~~$22.38~~$26.3 billion, excluding the ~~$2.50~~$2.7 billion included in the ‘other’ segment (i.e., attributable to Watford).

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
March 31, 2021
Fixed maturities (2)	$	18,627,372		70.7
Short-term investments (2)	1,409,960			5.4
Cash	705,787			2.7
Equity securities (2)	1,507,029			5.7
Other investments (2)	1,527,999			5.8
Other investable assets (3)	500,000			1.9
Investments accounted for using the equity method	2,256,327			8.6

Securities transactions entered into but not settled at the balance sheet date	(195,875)			(0.7)
Total investable assets held by Arch	$	26,338,599		100.0

Average effective duration (in years)	2.71
Average S&P/Moody’s credit ratings (4)	AA-/Aa3
Embedded book yield (5)	1.59		%

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.

(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.

Investable assets (1):
Estimated
Fair Value

% of
Total
March 31, 2020
Fixed maturities (2) $ 16,683,385
74.6
Short-term investments (2) 997,079
4.5
Cash 785,704
3.5
Equity securities (2) 1,148,639
5.1
Other investments (2) 1,153,737
5.2
Investments accounted for using the equity method 1,676,055
7.5
Securities transactions entered into but not settled at the balance sheet date (68,747 ) (0.3 )
Total investable assets held by Arch $ 22,375,852
100.0

Average effective duration (in years) 3.19

Average S&P/Moody’s credit ratings (3) AA/Aa2

Embedded book yield (4) 2.34 %

December 31, 2019
Fixed maturities (2) $ 16,894,021
75.8
Short-term investments (2) 1,004,257
4.5
Cash 623,793
2.8
Equity securities (2) 827,842
3.7
Other investments (2) 1,336,920
6.0
Investments accounted for using the equity method 1,660,396
7.5
Securities transactions entered into but not settled at the balance sheet date (61,553 ) (0.3 )
Total investable assets held by Arch $ 22,285,676
100.0

Average effective duration (in years) 3.40

Average S&P/Moody’s credit ratings (3) AA/Aa2

Embedded book yield (4) 2.55 %


~~(1)~~ARCH CAPITAL			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. 48			2021 FIRST QUARTER FORM 10-Q


~~(2)~~	~~Includes investments carried at fair value under the fair value option.~~


~~(3)~~	~~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”).~~


~~(4)~~	~~Before investment expenses.~~

Table of Contents

At March 31, ~~2020,~~2021, approximately ~~$16.03~~$18.1 billion, or ~~71.6%~~68.8%, of total investable assets held by Arch were internally managed, compared to ~~$15.80~~$19.2 billion, or ~~70.9%~~71.4%, at December 31, ~~2019.~~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
March 31, 2021
Corporate bonds	$	8,233,771	44.2
Residential mortgage backed securities	558,584		3.0
Municipal bonds	455,550		2.4
Commercial mortgage backed securities	256,598		1.4
U.S. government and government agencies	4,876,796		26.2
Non-U.S. government securities	2,287,921		12.3
Asset backed securities	1,958,152		10.5
Total	$	18,627,372	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

Estimated
Fair Value

% of
Total
March 31, 2020

Corporate bonds $ 6,678,007
40.0
Mortgage backed securities 449,024
2.7
Municipal bonds 860,593
5.2
Commercial mortgage backed securities 781,417
4.7
U.S. government and government agencies 4,309,804
25.8
Non-U.S. government securities 1,964,810
11.8
Asset backed securities 1,639,730
9.8
Total $ 16,683,385
100.0

December 31, 2019

Corporate bonds $ 6,561,354
38.8
Mortgage backed securities 541,800
3.2
Municipal bonds 880,119
5.2
Commercial mortgage backed securities 734,244
4.3
U.S. government and government agencies 4,632,947
27.4
Non-U.S. government securities 1,995,813
11.8
Asset backed securities 1,547,744
9.2
Total $ 16,894,021
100.0

The following table provides the credit quality distribution of our 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
March 31, 2021
U.S. government and gov’t agencies (1)	$	5,432,191	29.2
AAA	3,145,642		16.9
AA	2,069,764		11.1
A	3,878,113		20.8
BBB	2,829,202		15.2
BB	622,448		3.3
B	331,144		1.8
Lower than B	57,659		0.3
Not rated	261,209		1.4
Total	$	18,627,372	100.0

December 31, 2020
U.S. government and gov’t agencies (1)	$	5,963,758	31.8
AAA	3,117,046		16.6
AA	2,063,738		11.0
A	3,760,280		20.0
BBB	2,699,201		14.4
BB	574,189		3.1
B	268,095		1.4
Lower than B	54,795		0.3
Not rated	270,194		1.4
Total	$	18,771,296	100.0

Estimated Fair Value
% of
Total
March 31, 2020
U.S. government and gov’t agencies (1) $ 4,804,048
28.8
AAA 3,486,700
20.9
AA 1,994,127
12.0
A 3,937,053
23.6
BBB 1,565,912
9.4
BB 366,759
2.2
B 205,181
1.2
Lower than B 51,712
0.3
Not rated 271,893
1.6
Total $ 16,683,385
100.0

December 31, 2019
U.S. government and gov’t agencies (1) $ 5,215,489
30.9
AAA 3,392,341
20.1
AA 2,115,828
12.5
A 3,849,458
22.8
BBB 1,495,467
8.9
BB 355,803
2.1
B 216,663
1.3
Lower than B 56,865
0.3
Not rated 196,107
1.2
Total $ 16,894,021
100.0
(1)Includes U.S. government-sponsored agency residential mortgage-backed securities and agency commercial mortgage-backed securities.


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



~~ARCH CAPITAL~~	50	~~2020 FIRST QUARTER FORM 10-Q~~

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


Severity of gross unrealized losses:	Estimated Fair Value		Gross Unrealized Losses		% of Total Gross Unrealized Losses
March 31, 2021
0-10%	$	9,047,946	$	(139,904)	93.0
10-20%	58,325		(7,860)		5.2
20-30%	8,556		(2,095)		1.4
Greater than 30%	193		(570)		0.4
Total	$	9,115,020	$	(150,429)	100.0

December 31, 2020
0-10%	$	3,583,981	$	(55,542)	79.4
10-20%	95,495		(12,183)		17.4
20-30%	1,061		(406)		0.6
Greater than 30%	1,249		(1,785)		2.6
Total	$	3,681,786	$	(69,916)	100.0

Severity of gross unrealized losses: Estimated Fair Value
Gross
Unrealized
Losses

% of
Total Gross
Unrealized
Losses
March 31, 2020
0-10% $ 4,816,094
$ (157,556 ) 52.3
10-20% 682,411
(106,756 ) 35.4
20-30% 60,705
(19,804 ) 6.6
Greater than 30% 20,411
(17,142 ) 5.7
Total $ 5,579,621
$ (301,258 ) 100.0

December 31, 2019
0-10% $ 4,136,798
$ (49,072 ) 95.3
10-20% 12,405
(1,796 ) 3.5
20-30% 830
(273 ) 0.5
Greater than 30% 315
(363 ) 0.7
Total $ 4,150,348
$ (51,504 ) 100.0


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The following table summarizes our top ten exposures to fixed income corporate issuers by fair value at March 31, ~~2020,~~2021, excluding guaranteed amounts and covered bonds:

Estimated Fair Value
Credit
Rating (1)
Bank of America Corporation $ 267,690
A-/A2
Wells Fargo & Company 266,260
A-/A2
JPMorgan Chase & Co. 231,644
A-/A2
Apple Inc. 188,372
AA+/Aa1
Morgan Stanley 139,910
BBB+/A3
Citigroup Inc. 126,042
A-/A2
The Walt Disney Company 125,294
A/A2
BP p.l.c. 110,570
A-/A1
The Goldman Sachs Group, Inc. 108,376
BBB+/A3
Oracle Corporation 108,266
A+/A3
Total $ 1,672,424


~~(1)~~	~~Average credit ratings as assigned by S&P and Moody’s, respectively.~~Estimated Fair Value		Credit Rating (1)
JPMorgan Chase & Co.	$	389,799	A-/A2
Bank of America Corporation	312,603		A-/A2
Wells Fargo & Company	237,410		BBB+/A2
Citigroup Inc.	231,573		BBB+/A3
Morgan Stanley	214,190		BBB+/A1
The Goldman Sachs Group, Inc.	174,407		BBB+/A2
Nestlé S.A.	158,152		AA-/Aa3
Apple Inc.	131,135		AA+/Aa1
Chevron Corporation	110,767		AA-/Aa2
AT&T Inc.	103,918		BBB/Baa2
Total	$	2,063,954

(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
Mar 31, 2020
RMBS $ 413,311
$ 6,014
$ 29,699
$ 449,024
CMBS 80,933
654,819
45,665
781,417
ABS —
1,585,648
54,082
1,639,730
Total $ 494,244
$ 2,246,481
$ 129,446
$ 2,870,171

Dec 31, 2019
RMBS $ 503,929
$ 7,770
$ 30,101
$ 541,800
CMBS 78,612
629,424
26,208
734,244
ABS —
1,483,449
64,295
1,547,744
Total $ 582,541
$ 2,120,643
$ 120,604
$ 2,823,788

At March 31, 2020, our structured securities included $37.7 million par value in sub-prime securities with a fair value of $28.9 million and average credit quality ratings from S&P/Moody’s of “CCC-/Caa3,” compared to $38.3 million par value with a fair value of $30.6 million and average credit quality ratings of “CCC-/Caa3” at December 31, 2019.


	Agencies		Investment Grade		Below Investment Grade		Total
Mar 31, 2021
RMBS	$	525,144	$	1,627	$	31,813	$	558,584
CMBS	30,251		201,132		25,215		256,598
ABS	—		1,765,074		193,078		1,958,152
Total	$	555,395	$	1,967,833	$	250,106	$	2,773,334

Dec 31, 2020
RMBS	$	584,499	$	4,102	$	28,018	$	616,619
CMBS	24,396		342,491		24,103		390,990
ABS	—		1,403,137		163,051		1,566,188
Total	$	608,895	$	1,749,730	$	215,172	$	2,573,797

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


	March 31, 2021		December 31, 2020
Equities (1)	$	782,747	$	676,437
Exchange traded funds
Fixed income (2)	235,606		341,139
Equity and other (3)	488,676		418,528
Total	$	1,507,029	$	1,436,104

(1)Primarily in consumer non-cyclical, consumer cyclical, technology, communications and financial stocks at March 31, 2021.

(2)Primarily in corporate, MBS and municipal strategies at March 31, 2021.

(3)Primarily in utilities, large cap stocks and foreign equities at March 31, 2021.

March 31,
2020 December 31,
2019
Equities (1) $ 311,081
$ 375,067
Exchange traded funds
Fixed income (2) 474,870
7,237
Equity and other (3) 362,688
445,538
Total $ 1,148,639
$ 827,842


~~(1)~~	~~Primarily in consumer non-cyclical, consumer cyclical, technology, communications and financial stocks at March 31, 2020.~~


~~(2)~~	~~Primarily in MBS, corporate and municipal strategies at March 31, 2020.~~


~~(3)~~	~~Primarily in large cap stocks and foreign equities at March 31, 2020.~~



~~ARCH CAPITAL~~	51	~~2020 FIRST QUARTER FORM 10-Q~~

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The following table summarizes our other investments ~~which are included in investments accounted for using the fair value option, by strategy:~~and other investable assets:


	March 31, 2020		December 31, 2019			March 31, 2021		December 31, 2020
Lending	$	544,308	$	602,841	Lending	$	606,207	$	572,636
Term loan investments	228,586		264,083		Term loan investments	397,566		380,193
Energy	63,057		97,402		Energy	78,500		65,813
Credit related funds	111,874		123,020		Credit related funds	79,355		90,780
Investment grade fixed income	137,370		151,594		Investment grade fixed income	142,630		138,646
Infrastructure	33,644		61,786		Infrastructure	152,352		165,516
Private equity	20,602		18,915		Private equity	52,064		48,750
Real estate	14,296		17,279		Real estate	19,325		18,013
Total	$	1,153,737	$	1,336,920
Total fair value option					Total fair value option	$	1,527,999	$	1,480,347

Other investable assets					Other investable assets	$	500,000	$	500,000

Total other investments					Total other investments	$	2,027,999	$	1,980,347

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 9, “Derivative Instruments,” to our consolidated financial statements for additional disclosures related to derivatives.


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Investable Assets in the ‘Other’ Segment

Investable assets in the ‘other’ segment are managed by Watford. The board of directors of Watford establishes its investment policies and guidelines. A significant amount of Watford’s investments are accounted for using the fair value option with changes in the carrying value of such investments recorded in net realized gains or losses.

The following table summarizes investable assets in the ‘other’ segment:


	March 31, 2020			December 31, 2019				March 31, 2021		December 31, 2020
Investments accounted for using the fair value option:							Investments accounted for using the fair value option:
Other investments	$	937,680		$	1,092,396		Other investments	$	790,186	$	851,538
Fixed maturities	392,453			416,592			Fixed maturities	539,688		455,163
Short-term investments	343,861			329,303			Short-term investments	483,601		418,690
Equity securities	58,092			59,799			Equity securities	67,295		64,994
Total	1,732,086			1,898,090			Total	1,880,770		1,790,385
Fixed maturities available for sale, at fair value	677,869			706,875			Fixed maturities available for sale, at fair value	586,431		613,503
Equity securities, at fair value	63,169			65,337			Equity securities, at fair value	62,314		52,410
Cash	96,580			102,437			Cash	236,164		211,451
Securities sold but not yet purchased	(30,076		)	(66,257		)	Securities sold but not yet purchased	(34,097)		(21,679)
Securities transactions entered into but not settled at the balance sheet date	(37,039		)	(1,893		)	Securities transactions entered into but not settled at the balance sheet date	8,846		11,542
Total investable assets included in ‘other’ segment	$	2,502,589		$	2,704,589		Total investable assets included in ‘other’ segment	$	2,740,428	$	2,657,612

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
	March 31,
	2021		2020
Premiums written:
Direct	$	1,892,245	$	1,688,798
Assumed	1,504,961		1,144,032
Ceded	(888,749)		(695,584)
Net	$	2,508,457	$	2,137,246

Premiums earned:
Direct	$	1,712,925	$	1,545,825
Assumed	947,614		761,074
Ceded	(712,117)		(562,455)
Net	$	1,948,422	$	1,744,444

Losses and LAE:
Direct	$	985,933	$	985,083
Assumed	667,311		545,869
Ceded	(450,144)		(415,533)
Net	$	1,203,100	$	1,115,419

Three Months Ended
March 31,
2020 2019
Premiums written:
Direct $ 1,688,798
$ 1,363,506
Assumed 1,144,032
714,373
Ceded (695,584 ) (552,620 )
Net $ 2,137,246
$ 1,525,259

Premiums earned:
Direct $ 1,545,825
$ 1,266,063
Assumed 761,074
533,279
Ceded (562,455 ) (430,476 )
Net $ 1,744,444
$ 1,368,866

Losses and LAE:
Direct $ 985,083
$ 616,062
Assumed 545,869
338,400
Ceded (415,533 ) (235,930 )
Net $ 1,115,419
$ 718,532

See note 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 various aggregate excess of loss mortgage reinsurance agreements with various special purpose reinsurance companies domiciled in Bermuda (the



~~ARCH CAPITAL~~	52	~~2020 FIRST QUARTER FORM 10-Q~~

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~~“Bellemeade~~ “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.~~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 March 31, ~~2020:~~2021:


			March 31, 2021
	Initial Coverage at Issuance		Current Coverage		Remaining Retention, Net
Bellemeade 2017-1 Ltd. (1)	$	368,114	$	145,573	$	124,281
Bellemeade 2018-1 Ltd. (2)	374,460		250,095		121,963
Bellemeade 2018-2 Ltd. (3)	653,278		66,747		303,766
Bellemeade 2018-3 Ltd. (4)	506,110		302,563		125,226
Bellemeade 2019-1 Ltd. (5)	341,790		219,256		104,221
Bellemeade 2019-2 Ltd. (6)	621,022		398,316		158,732
Bellemeade 2019-3 Ltd. (7)	700,920		528,084		178,241
Bellemeade 2019-4 Ltd. (8)	577,267		468,737		114,325
Bellemeade 2020-1 Ltd. (9)	528,540		141,262		750,797
Bellemeade 2020-2 Ltd. (10)	449,167		380,888		235,372
Bellemeade 2020-3 Ltd. (11)	451,816		451,816		167,556
Bellemeade 2020-4 Ltd. (12)	337,013		337,013		142,435
Bellemeade 2021-1 Ltd. (13)	643,577		643,577		169,634
Total	$	6,553,074	$	4,333,927	$	2,696,549

(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 August 2018, covering in-force policies issued between April 1, 2013 and December 31, 2015.

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

(5) 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.

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

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

Initial Coverage at Issuance Coverage at Mar. 31, 2020 First Layer Retention
Bellemeade 2017-1 Ltd. (1) $ 368,114
$ 190,324
$ 165,652
Bellemeade 2018-1 Ltd. (2) 374,460
299,909
168,510
Bellemeade 2018-2 Ltd. (3) 653,278
380,986
352,258
Bellemeade 2018-3 Ltd. (4) 506,110
383,268
179,331
Bellemeade 2019-1 Ltd. (5) 341,790
228,940
208,046
Bellemeade 2019-2 Ltd. (6) 621,022
462,057
221,794
Bellemeade 2019-3 Ltd. (7) 700,920
603,465
232,093
Bellemeade 2019-4 Ltd. (8) 577,267
563,160
162,357
Total $ 4,142,961
$ 3,112,109
$ 1,690,041


~~(1)~~ARCH CAPITAL			~~Issued in October 2017, covering in-force policies issued between January 1, 2017 and June 30, 2017.~~ 51			2021 FIRST QUARTER FORM 10-Q


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


~~(3)~~	~~Issued in August 2018, covering in-force policies issued between April 1, 2013 and December 31, 2015.~~


~~(4)~~	~~Issued in October 2018, covering in-force policies issued between January 1, 2018 and June 30, 2018.~~


~~(5)~~	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.


~~(6)~~	~~Issued in April 2019, covering in-force policies issued between July 1, 2018 and December 31, 2018.~~


~~(7)~~	~~Issued in July 2019, covering in-force policies issued in 2016.~~


~~(8)~~	~~Issued in October 2019, covering in-force policies issued between January 1, 2019 and June 30, 2019.~~

Table of Contents

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

(9) Issued in June 2020, covering in-force policies issued between July 1, 2019 and December 31, 2019. $450 million was directly funded by Bellemeade 2020-1 Ltd. with an additional $79 million of capacity provided directly to Arch MI U.S. by a separate panel of reinsurers.

(10) 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.

(11) 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.

(12) 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.

(13) 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.

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, which is exacerbated by the fact that we have relatively limited historical experience upon which to base such estimates.~~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 March 31, ~~2020~~2021 and December 31, ~~2019,~~2020, our Loss Reserves, net of unpaid losses and loss adjustment expenses recoverable, by type and by operating segment were as follows:


	March 31, 2021		December 31, 2020
Insurance segment:
Case reserves	$	1,998,483	$	2,051,640
IBNR reserves	4,036,207		3,889,823
Total net reserves	6,034,690		5,941,463
Reinsurance segment:
Case reserves	1,503,315		1,560,523
Additional case reserves	368,458		280,472
IBNR reserves	2,351,015		2,253,953
Total net reserves	4,222,788		4,094,948
Mortgage segment:
Case reserves	688,005		631,921
IBNR reserves	277,739		271,702
Total net reserves	965,744		903,623
Other segment:
Case reserves	588,036		566,587
Additional case reserves	39,312		32,321
IBNR reserves	676,732		660,132
Total net reserves	1,304,080		1,259,040
Total:
Case reserves	4,777,839		4,810,671
Additional case reserves	407,770		312,793
IBNR reserves	7,341,693		7,075,610
Total net reserves	$	12,527,302	$	12,199,074

March 31,
2020 December 31,
2019
Insurance segment:

Case reserves $ 1,626,058
$ 1,601,627
IBNR reserves 3,541,959
3,403,051
Total net reserves 5,168,017
5,004,678
Reinsurance segment:
Case reserves 1,403,792
1,273,523
Additional case reserves 159,972
166,251
IBNR reserves 1,935,726
1,835,993
Total net reserves 3,499,490
3,275,767
Mortgage segment:
Case reserves 247,766
266,030
IBNR reserves 208,236
157,712
Total net reserves (1) 456,002
423,742
Other segment:
Case reserves 501,107
478,036
Additional case reserves 5,598
29,059
IBNR reserves 609,252
597,910
Total net reserves 1,115,957
1,105,005
Total:

Case reserves 3,778,723
3,619,216
Additional case reserves 165,570
195,310
IBNR reserves 6,295,173
5,994,666
Total net reserves $ 10,239,466
$ 9,809,192

~~(1)~~

At March 31, 2020, total net reserves include $287.0 million from U.S. primary mortgage insurance business, of which 56.1% represents policy years 2010 and prior and the remainder from later policy years. At December 31, 2019, total net reserves include $278.7 million from U.S. primary mortgage insurance business, of which 58.2% represents policy years 2010 and prior and the remainder from later policy years.

At March 31, ~~2020~~2021 and December 31, ~~2019,~~2020, the insurance segment’s Loss Reserves by major line of business, net of unpaid losses and loss adjustment expenses recoverable, were as follows:


	March 31, 2021		December 31, 2020
Insurance segment:
Professional lines (1)	$	1,457,723	$	1,482,820
Construction and national accounts	1,433,994		1,395,067
Excess and surplus casualty (2)	833,272		816,495
Programs	733,193		699,354
Property, energy, marine and aviation	506,565		517,692
Travel, accident and health	86,135		98,910
Lenders products	56,964		48,946
Other (3)	926,844		882,179
Total net reserves	$	6,034,690	$	5,941,463

(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.

March 31,
2020 December 31,
2019
Insurance segment:
Professional lines (1) $ 1,347,333
$ 1,322,969
Construction and national accounts 1,282,120
1,248,750
Excess and surplus casualty (2) 601,344
564,254
Programs 587,511
571,926
Property, energy, marine and aviation 400,605
371,822
Travel, accident and health 118,754
109,613
Lenders products 27,387
28,233
Other (3) 802,963
787,111
Total net reserves $ 5,168,017
$ 5,004,678


~~(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	5352	~~2020~~2021 FIRST QUARTER FORM 10-Q

Table of Contents

At March 31, ~~2020~~2021 and December 31, ~~2019,~~2020, the reinsurance segment’s Loss Reserves by major line of business, net of unpaid losses and loss adjustment expenses recoverable, were as follows:


	March 31, 2021		December 31, 2020
Reinsurance segment:
Casualty (1)	$	1,937,311	$	1,995,849
Other specialty (2)	942,302		917,178
Property excluding property catastrophe	628,305		594,033
Marine and aviation	201,813		204,205
Property catastrophe	396,878		268,858
Other (3)	116,179		114,825
Total net reserves	$	4,222,788	$	4,094,948

(1)Includes executive assurance, professional liability, workers’ compensation, excess motor, healthcare and other.

(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 March 31, 2021 and December 31, 2020, the mortgage segment’s Loss Reserves by major line of business, net of unpaid losses and loss adjustment expenses recoverable, were as follows:


	March 31, 2021		December 31, 2020
U.S. primary mortgage insurance (1)	$	700,169	$	649,748
Other	265,575		253,875
Total net reserves	$	965,744	$	903,623

(1) At March 31, 2021, 29.1% represents policy years 2011 and prior and the remainder from later policy years. At December 31, 2020 , 28.3% of total net reserves represent policy years 2011 and prior and the remainder from later policy years.

March 31,
2020 December 31,
2019
Reinsurance segment:
Casualty (1) $ 1,845,832
$ 1,796,073
Other specialty (2) 748,824
649,309
Property excluding property catastrophe 504,005
471,775
Marine and aviation 176,987
160,930
Property catastrophe 131,343
113,565
Other (3) 92,499
84,115
Total net reserves $ 3,499,490
$ 3,275,767


~~(1)~~	~~Includes executive assurance, professional liability, workers’ compensation, excess motor, healthcare and other.~~


~~(2)~~	~~Includes non-excess motor, surety, accident and health, workers’ compensation catastrophe, agriculture, trade credit and other.~~


~~(3)~~	~~Includes life, casualty clash and other.~~

Mortgage Operations Supplemental Information

The mortgage segment’s insurance in force (“IIF”) and risk in force (“RIF”) were as follows at March 31, ~~2020~~2021 and December 31, ~~2019:~~2020:


(U.S. Dollars in millions)	March 31, 2021			December 31, 2020
	Amount		%	Amount		%
Insurance In Force (IIF) (1):
U.S. primary mortgage insurance	$	276,179	64.7	$	280,579	66.2
Mortgage reinsurance	31,699		7.4	31,220		7.4
Other (2)	119,138		27.9	111,740		26.4
Total	$	427,016	100.0	$	423,539	100.0

Risk In Force (RIF) (3):
U.S. primary mortgage insurance	$	69,234	89.9	$	70,522	90.5
Mortgage reinsurance	2,214		2.9	2,226		2.9
Other (2)	5,573		7.2	5,146		6.6
Total	$	77,021	100.0	$	77,894	100.0

(U.S. Dollars in millions) March 31, 2020 December 31, 2019
Amount % Amount %
Insurance In Force (IIF) (1):
U.S. primary mortgage insurance $ 284,203
68.9
$ 287,150
68.7
Mortgage reinsurance 24,335
5.9
26,768
6.4
Other (2) 103,731
25.2
104,346
24.9
Total $ 412,269
100.0
$ 418,264
100.0

Risk In Force (RIF) (3):
U.S. primary mortgage insurance $ 72,566
92.0
$ 73,388
91.9
Mortgage reinsurance 1,961
2.5
2,129
2.7
Other (2) 4,387
5.6
4,380
5.5
Total $ 78,914
100.0
$ 79,897
100.0


~~(1)~~	~~Represents the aggregate dollar amount of each insured mortgage loan’s current principal balance.~~


~~(2)~~	~~Includes GSE credit risk-sharing transactions and international insurance business.~~


~~(3)~~	Represents 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 credit risk-sharing or reinsurance transactions.

(1)Represents the aggregate dollar amount of each insured mortgage loan’s current principal balance.

(2)Includes GSE credit risk-sharing transactions and international insurance business.

(3)Represents 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 credit risk-sharing or reinsurance transactions.

The ~~insurance in force~~IIF and ~~risk in force~~RIF for our U.S. primary mortgage insurance business by policy year were as follows at March 31, ~~2020:~~2021:


(U.S. Dollars in millions)	IIF			RIF			Delinquency
	Amount		%	Amount		%	Rate (1)
Policy year:
2011 and prior	$	13,569	4.9	$	3,086	4.5	11.16	%
2012	2,769		1.0	734		1.1	3.17	%
2013	6,522		2.4	1,817		2.6	3.17	%
2014	7,250		2.6	1,993		2.9	3.96	%
2015	12,971		4.7	3,495		5.0	3.64	%
2016	21,354		7.7	5,718		8.3	4.66	%
2017	20,826		7.5	5,413		7.8	5.46	%
2018	22,856		8.3	5,794		8.4	6.98	%
2019	40,743		14.8	10,157		14.7	4.72	%
2020	100,435		36.4	24,460		35.3	0.91	%
2021	26,884		9.7	6,567		9.5	0.03	%
Total	$	276,179	100.0	$	69,234	100.0	3.86	%

(1)Represents the ending percentage of loans in default.



	Three Months Ended
	March 31, 2019
	Insurance			Reinsurance			Mortgage			Sub-Total			Other			Total

Gross premiums written (1)	$	941,954		$	682,855		$	356,050		$	1,980,453		$	186,689		$	2,077,879
Premiums ceded	(320,622		)	(231,567		)	(48,798		)	(600,581		)	(41,302		)	(552,620		)
Net premiums written	621,332			451,288			307,252			1,379,872			145,387			1,525,259
Change in unearned premiums	(67,827		)	(104,923		)	15,650			(157,100		)	707			(156,393		)
Net premiums earned	553,505			346,365			322,902			1,222,772			146,094			1,368,866
Other underwriting income (loss)	—			4,377			3,856			8,233			592			8,825
Losses and loss adjustment expenses	(356,723		)	(239,810		)	(11,149		)	(607,682		)	(110,850		)	(718,532		)
Acquisition expenses	(82,824		)	(54,326		)	(31,672		)	(168,822		)	(29,026		)	(197,848		)
Other operating expenses	(113,396		)	(35,704		)	(39,875		)	(188,975		)	(12,188		)	(201,163		)
Underwriting income (loss)	$	562		$	20,902		$	244,062		265,526			(5,378		)	260,148

Net investment income										121,249			35,700			156,949
Net realized gains (losses)										111,124			29,132			140,256
Equity in net income (loss) of investment funds accounted for using the equity method										46,867			—			46,867
Other income (loss)										1,083			—			1,083
Corporate expenses (2)										(16,772		)	—			(16,772		)
Transaction costs and other (2)										(1,190		)	—			(1,190		)
Amortization of intangible assets										(20,417		)	—			(20,417		)
Interest expense										(23,482		)	(5,583		)	(29,065		)
Net foreign exchange gains (losses)										5,175			(1,650		)	3,525
Income before income taxes										489,163			52,221			541,384
Income tax expense										(45,886		)	—			(45,886		)
Net income										443,277			52,221			495,498
Amounts attributable to redeemable noncontrolling interests										—			(4,588		)	(4,588		)
Amounts attributable to nonredeemable noncontrolling interests										—			(42,382		)	(42,382		)
Net income available to Arch										443,277			5,251			448,528
Preferred dividends										(10,403		)	—			(10,403		)
Net income available to Arch common shareholders										$	432,874		$	5,251		$	438,125

Underwriting Ratios
Loss ratio	64.4		%	69.2		%	3.5		%	49.7		%	75.9		%	52.5		%
Acquisition expense ratio	15.0		%	15.7		%	9.8		%	13.8		%	19.9		%	14.5		%
Other operating expense ratio	20.5		%	10.3		%	12.3		%	15.5		%	8.3		%	14.7		%
Combined ratio	99.9		%	95.2		%	25.6		%	79.0		%	104.1		%	81.7		%

Goodwill and intangible assets	$	156,735		$	—		$	494,830		$	651,565		$	7,650		$	659,215



	March 31, 2020				December 31, 2019
Maturity	Estimated Fair Value		Amortized Cost		Estimated Fair Value		Amortized Cost
Due in one year or less	$	445,134	$	445,701	$	428,659	$	423,617
Due after one year through five years	9,622,046		9,558,975		10,126,403		9,996,206
Due after five years through 10 years	3,435,903		3,358,574		3,317,535		3,219,567
Due after 10 years	522,246		496,249		411,269		388,280
	14,025,329		13,859,499		14,283,866		14,027,670
Mortgage backed securities	466,045		456,455		562,309		553,571
Commercial mortgage backed securities	780,358		787,417		733,108		720,487
Asset backed securities	1,747,281		1,828,933		1,683,753		1,664,460
Total (1)	$	17,019,013	$	16,932,304	$	17,263,036	$	16,966,188



Years Ending December 31,
2020 (remainder)	$	23,994
2021	31,279
2022	28,198
2023	23,692
2024	17,473
2025 and thereafter	40,124
Total undiscounted lease liability	$	164,760
Less: present value adjustment	(18,804		)
Operating lease liability	$	145,956



	Initial Coverage at Issuance		Coverage at Mar. 31, 2020		First Layer Retention
Bellemeade 2017-1 Ltd. (1)	$	368,114	$	190,324	$	165,652
Bellemeade 2018-1 Ltd. (2)	374,460		299,909		168,510
Bellemeade 2018-2 Ltd. (3)	653,278		380,986		352,258
Bellemeade 2018-3 Ltd. (4)	506,110		383,268		179,331
Bellemeade 2019-1 Ltd. (5)	341,790		228,940		208,046
Bellemeade 2019-2 Ltd. (6)	621,022		462,057		221,794
Bellemeade 2019-3 Ltd. (7)	700,920		603,465		232,093
Bellemeade 2019-4 Ltd. (8)	577,267		563,160		162,357
Total	$	4,142,961	$	3,112,109	$	1,690,041


~~(1)~~ARCH CAPITAL			~~Represents the ending percentage of loans in default.~~ 53			2021 FIRST QUARTER FORM 10-Q


~~(1)~~	(1)Represents the ending percentage ~~of loans in default.~~


(U.S. Dollars in thousands, except policy, loan and claim count)	Three Months Ended
	March 31,
	2021			2020
Roll-forward of insured loans in default:
Beginning delinquent number of loans	52,234			20,163
New notices	10,990			9,419
Cures	(16,131)			(10,541)
Paid claims	(179)			(627)

Ending delinquent number of loans (1)	46,914			18,414

Ending number of policies in force (1)	1,214,245			1,293,799

Delinquency rate (1)	3.86		%	1.42		%

Losses:
Number of claims paid	179			627
Total paid claims	$	6,882		$	26,038
Average per claim	$	38.4		$	41.5
Severity (2)	82.0		%	92.8		%
Average case reserve per default (in thousands)	$	15.2		$	14.4


~~(2)~~	~~Represents total paid claims divided by RIF of loans for which claims were paid.~~


(U.S. dollars in thousands, except share data)	March 31, 2021		December 31, 2020
Total shareholders’ equity available to Arch	$	13,096,472	$	13,105,886
Less preferred shareholders’ equity	780,000		780,000
Common shareholders’ equity available to Arch	$	12,316,472	$	12,325,886
Common shares and common share equivalents outstanding, net of treasury shares (1)	403,313,377		406,720,642
Book value per share	$	30.54	$	30.31


~~(1)~~	~~Excludes the effects of 18,257,290 and 18,853,018 stock options and 1,438,347 and 1,586,779 restricted stock units outstanding at March 31, 2020 and December 31, 2019, respectively.~~


(U.S. dollars in thousands, except share data)					(U.S. dollars in thousands, except share data)	Mar 31, 2021		Dec 31, 2020

(U.S. dollars in thousands, except share data)	Mar 31, 2020		Dec 31, 2019

Senior notes	$	1,734,384	$	1,734,209	Senior notes	$	2,723,660	$	2,723,423

Shareholders’ equity available to Arch:					Shareholders’ equity available to Arch:
Series E non-cumulative preferred shares	$	450,000	$	450,000	Series E non-cumulative preferred shares	$	450,000	$	450,000
Series F non-cumulative preferred shares	330,000		330,000		Series F non-cumulative preferred shares	330,000		330,000
Common shareholders’ equity	10,587,244		10,717,371		Common shareholders’ equity	12,316,472		12,325,886
Total	$	11,367,244	$	11,497,371	Total	$	13,096,472	$	13,105,886

Total capital available to Arch	$	13,101,628	$	13,231,580	Total capital available to Arch	$	15,820,132	$	15,829,309


Debt to total capital (%)	13.2		13.1		Debt to total capital (%)	17.2		17.2
Preferred to total capital (%)	6.0		5.9		Preferred to total capital (%)	4.9		4.9
Debt and preferred to total capital (%)	19.2		19.0		Debt and preferred to total capital (%)	22.1		22.1


	Interest		Principal		Carrying
Issuer/Due	(Fixed)		Amount		Amount
Arch Capital:
May 1, 2034	7.350	%	$	300,000	$	297,396
June 30, 2050	3.635	%	1,000,000		988,554
Arch-U.S.:
Nov. 1, 2043 (1)	5.144	%	500,000		494,973
Arch Finance:
Dec. 15, 2026 (1)	4.011	%	500,000		497,314
Dec. 15, 2046 (1)	5.031	%	450,000		445,423
Total			$	2,750,000	$	2,723,660


~~(1)~~	~~Fully and unconditionally guaranteed by Arch Capital.~~


	Three Months Ended			Year Ended
	March 31, 2021			December 31, 2020
		Arch Capital		Arch-U.S.		Arch Capital		Arch-U.S.

Revenues

Net investment income		$	432	$	2,608	$	53	$	18,084
Net realized gains (losses)		—		55,108		(2,110)		26,096


Equity in net income (loss) of investments accounted for using the equity method		—		(336)		—		2,507

Total revenues		432		57,380		(2,057)		46,687

Expenses



Corporate expenses		23,315		1,586		65,566		7,227

Interest expense		14,683		11,801		40,445		47,566
Net foreign exchange (gains) losses		1		—		3		—
Total expenses		37,999		13,387		106,014		54,793

Income (loss) before income taxes and income (loss) from operating affiliates		(37,567)		43,993		(108,071)		(8,106)
Income tax (expense) benefit		—		(8,896)		—		2,689

Income (loss) from operating affiliates		(171)		—		(437)		—


Net income available to Arch		(37,738)		35,097		(108,508)		(5,417)
Preferred dividends		(10,403)		—		(41,612)		—

Net income available to Arch common shareholders		$	(48,141)	$	35,097	$	(150,120)	$	(5,417)


(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
Mar 31, 2020
Mar 31, 2021															Mar 31, 2021
Total fair value	$	21.05		$	20.73		$	20.44	$	20.07		$	19.75		Total fair value	$	24.99		$	24.68		$	24.36	$	24.04		$	23.73
Change from base	3.0		%	1.4		%			(1.8		)%	(3.4		)%	Change from base	2.6		%	1.3		%			(1.3)		%	(2.6)		%
Change in unrealized value	$	0.61		$	0.29				$	(0.37	)	$	(0.70	)	Change in unrealized value	$	0.63		$	0.32				$	(0.32)		$	(0.63)

Dec 31, 2019
Dec 31, 2020															Dec 31, 2020
Total fair value	$	21.54		$	21.19		$	20.83	$	20.48		$	20.13		Total fair value	$	25.82		$	25.44		$	25.07	$	24.69		$	24.31
Change from base	3.4		%	1.7		%			(1.7		)%	(3.4		)%	Change from base	3.0		%	1.5		%			(1.5)		%	(3.0)		%
Change in unrealized value	$	0.71		$	0.35				$	(0.35	)	$	(0.71	)	Change in unrealized value	$	0.75		$	0.38				$	(0.38)		$	(0.75)


(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
Mar 31, 2020
Mar 31, 2021															Mar 31, 2021
Total fair value	$	21.42		$	20.93		$	20.44	$	19.95		$	19.46		Total fair value	$	24.87		$	24.61		$	24.36	$	24.12		$	23.85
Change from base	4.8		%	2.4		%			(2.4		)%	(4.8		)%	Change from base	2.1		%	1.0		%			(1.0)		%	(2.1)		%
Change in unrealized value	$	0.98		$	0.49				$	(0.49	)	$	(0.98	)	Change in unrealized value	$	0.51		$	0.24				$	(0.24)		$	(0.51)

Dec 31, 2019
Dec 31, 2020															Dec 31, 2020
Total fair value	$	21.19		$	21.02		$	20.83	$	20.65		$	20.48		Total fair value	$	25.54		$	25.32		$	25.07	$	24.82		$	24.59
Change from base	1.7		%	0.9		%			(0.9		)%	(1.7		)%	Change from base	1.9		%	1.0		%			(1.0)		%	(1.9)		%
Change in unrealized value	$	0.35		$	0.19				$	(0.19	)	$	(0.35	)	Change in unrealized value	$	0.48		$	0.25				$	(0.25)		$	(0.48)


(U.S. dollars in thousands, except per share data)	March 31, 2021		December 31, 2020
Net assets (liabilities), denominated in foreign currencies, excluding shareholders’ equity and derivatives	$	(30,221)	$	(309,968)
Shareholders’ equity denominated in foreign currencies (1)	704,173		695,355
Net foreign currency forward contracts outstanding (2)	477,734		1,108,161
Net exposures denominated in foreign currencies	$	1,151,686	$	1,493,548

Pre-tax impact of a hypothetical 10% appreciation of the U.S. Dollar against foreign currencies:
Shareholders’ equity	$	(115,169)	$	(149,355)
Book value per share	$	(0.29)	$	(0.37)

Pre-tax impact of a hypothetical 10% decline of the U.S. Dollar against foreign currencies:
Shareholders’ equity	$	115,169	$	149,355
Book value per share	$	0.29	$	0.37


~~(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.~~



	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)
1/1/2020 - 1/31/2020	34,418	$	43.87	—	$	1,000,000
2/1/2020 - 2/29/2020	135,852	42.35		—	$	1,000,000
3/1/2020 - 3/31/2020	2,608,668	29.05		2,599,388	$	924,514
Total	2,778,938	$	29.88	2,599,388



						ARCH CAPITAL GROUP LTD.
						(REGISTRANT)

						/s/ Marc Grandisson
Date: May ~~8, 2020~~6, 2021						Marc Grandisson
						~~President and~~ Chief Executive Officer (Principal Executive Officer)

						/s/ François Morin
Date: May ~~8, 2020~~6, 2021						François Morin
						Executive Vice President, Chief Financial Officer ~~and Treasurer~~ (Principal Financial and Accounting Officer) and Treasurer