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•	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;

•	the integration of any businesses 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;

•	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;

•	severity and/or frequency of losses;

•	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;

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

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

•	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;

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•	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 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.

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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.

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The Company classifies its businesses into three underwriting segments — insurance, reinsurance and mortgage — and two 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 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 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.

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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.’

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	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.’

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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.

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At March 31, 2020, total investable assets of $24.88 billion included $22.38 billion held by the Company and $2.50 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, 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.”

(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.

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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, 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.”

At March 31, 2020, on a lot level basis, approximately 5,420 security lots out of a total of approximately 9,960 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 million. At December 31, 2019, on a lot level basis, approximately 2,230 security lots out of a total of approximately 9,590 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.

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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, 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.

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, 2020, the fair value of the cash collateral received on securities lending was $26.2 million and the fair value of security collateral received was $156.1 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.

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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, 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

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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:

		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)	Includes asset backed securities, mortgage backed securities and commercial mortgage backed securities.

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The following table presents the Company’s financial assets and liabilities measured at fair value by level at March 31, 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	$	6,552,825			$	—			$	6,550,845			$	1,980
Mortgage backed securities	466,045				—				465,821				224
Municipal bonds	862,415				—				862,415				—
Commercial mortgage backed securities	780,358				—				780,358				—
U.S. government and government agencies	4,574,630				4,480,074				94,556				—
Non-U.S. government securities	2,035,459				—				2,035,459				—
Asset backed securities	1,747,281				—				1,743,659				3,622
Total	17,019,013				4,480,074				12,533,113				5,826
Short-term investments	944,531				884,527				60,004				—
Equity securities, at fair value	1,181,903				1,122,694				3,577				55,632
Derivative instruments (4)	92,052				—				92,052				—
Fair value option:
Corporate bonds	493,639				—				492,674				965
Non-U.S. government bonds	79,209				—				79,209				—
Mortgage backed securities	13,293				—				13,293				—
Municipal bonds	251				—				251				—
Commercial mortgage backed securities	1,059				—				1,059				—
Asset backed securities	146,646				—				146,646				—
U.S. government and government agencies	597				484				113				—
Short-term investments	396,409				321,401				75,008				—
Equity securities	87,997				27,825				157				60,015
Other investments	1,177,508				24,930				1,097,958				54,620
Other investments measured at net asset value (2)	913,909
Total	3,310,517				374,640				1,906,368				115,600
Total assets measured at fair value	$	22,548,016			$	6,861,935			$	14,595,114			$	177,058
Liabilities measured at fair value:
Contingent consideration liabilities	$	(7,967	)		$	—			$	—			$	(7,967	)
Securities sold but not yet purchased (3)	(30,076		)		—				(30,076		)		—
Derivative instruments (4)	(116,572		)		—				(116,572		)		—
Total liabilities measured at fair value	$	(154,615	)		$	—			$	(146,648	)		$	(7,967	)

(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.

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The following table presents the Company’s financial assets and liabilities measured at fair value by level at December 31, 2019:

					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)	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.

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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, 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).

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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

	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

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

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(1)

Represents repurchases by Arch Capital of shares, from time to time, from employees in order to facilitate the payment of withholding taxes on restricted shares granted and the exercise of stock appreciation rights. We purchased these shares at their fair value, as determined by reference to the closing price of our common shares on the day the restricted shares vested or the stock appreciation rights were exercised.

(2)

Remaining amount available at March 31, 2020 under Arch Capital’s share repurchase authorization, under which repurchases may be effected from time to time in open market or privately negotiated transactions. On November 8, 2019, the board of directors of ACGL increased the aggregate purchase amount authorized under the share repurchase program to $1.0 billion. Repurchases under this authorization may be effected from time to time in open market or privately negotiated transactions through December 31, 2021.

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