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, 2021 (“2021 Form 10-K”). In addition, readers should review “Risk Factors” set forth in Item 1A of Part I of our 2021 Form 10-K and “ITEM 1A—Risk Factors” of this Form 10-Q. Tabular amounts are in U.S. Dollars in thousands, except share amounts, unless otherwise noted.

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

									Page No.
Current Outlook									42
Financial Measures									42
Comments on Non-GAAP Measures									44
Results of Operations									46
			Insurance Segment						46
			Reinsurance Segment						49
			Mortgage Segment						51
			Corporate Segment						54
Critical Accounting Policies, Estimates and Recent Accounting Pronouncements									55
Financial Condition									55
Liquidity									61
Capital Resources and Other									61

ARCH CAPITAL			41			2022 THIRD QUARTER FORM 10-Q

CURRENT OUTLOOK

As we approach the end of 2022, we are cautiously optimistic regarding the opportunities ahead of us in the fourth quarter and into 2023. Our objective remains the same, to deliver long term value for our shareholders. We are committed to agile cycle management predicated by a focus on risk-adjusted returns, and this commitment has enabled us to accelerate our growth through the deployment of meaningful capacity to our clients. We continue to execute our cycle management strategy by actively allocating capital to the sectors where rates allow for returns that are higher than our cost of capital.

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

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

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

In reinsurance, the emphasis remains on quota share treaties over excess of loss reinsurance. This strategy allows us to participate in the rate increases on primary insurance while improving the balance between risk and return. We remained disciplined in property catastrophe exposure and we will deploy more capital to the line if expected returns improve meaningfully. Excellent market conditions and the likelihood of capacity constraints will likely create an eventful January 1 renewal period, and our teams are actively planning to meet the demands of our clients.

In mortgage, we continue to be thoughtful in how we manage our portfolio and, because of our diversified model, we have the ability to take a measured view of the business as just one component of our diversified enterprise. Our mortgage business continues to deliver consistent underwriting results, once again demonstrating its sustainable earnings model. Although higher interest rates affected new loan origination volume, the persistency rate of our portfolio improved and U.S. primary mortgage insurance in force grew to nearly $295 billion. The credit quality of homebuyers remains excellent and we believe our portfolio is well positioned for a variety of economic scenarios.

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 have entered into aggregate excess of loss mortgage reinsurance agreements with various special purpose reinsurance companies domiciled in Bermuda and have issued mortgage insurance linked notes, increasing our protection for mortgage tail risk. The Bellemeade structures provided approximately $4.3 billion of aggregate reinsurance coverage at September 30, 2022.

FINANCIAL MEASURES

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

Book Value per Share

Book value per share represents total common shareholders’ equity available to Arch divided by the number of common shares outstanding. Management uses growth in book value per share as a key measure of the value generated for our common shareholders each period and believes that book value per share is the key driver of Arch Capital’s share price over time. Book value per share is impacted by, among other factors, our underwriting results, investment returns and share repurchase activity, which has an accretive or dilutive impact on book value per share depending on the purchase price. Book value per share was $29.69 at September 30, 2022, compared to $31.37 at June 30, 2022 and $32.43 at

ARCH CAPITAL			42			2022 THIRD QUARTER FORM 10-Q

September 30, 2021. The 5.4% decrease in book value per share for the 2022 third quarter reflected negative total return on investments driven by rising interest rates on fixed maturities, along with higher level of catastrophic loss activity, primarily related to Hurricane Ian.

Operating Return on Average Common Equity

Operating return on average common equity (“Operating ROAE”) represents annualized after-tax operating income available to Arch common shareholders divided by the average of beginning and ending common shareholders’ equity available to Arch during the period. After-tax operating income available to Arch common shareholders, a non-GAAP financial measure as defined in Regulation G, represents net income available to Arch common shareholders, excluding net realized gains or losses (which includes changes in the allowance for credit losses on financial assets and net impairment losses recognized in earnings) equity in net income or loss of investment funds accounted for using the equity method, net foreign exchange gains or losses, transaction costs and other, loss on redemption of preferred shares and income taxes. Management uses Operating ROAE as a key measure of the return generated to common shareholders. See “Comment on Non-GAAP Financial Measures.”

Our annualized net income return on average common equity was 0.2% for the 2022 third quarter, compared to 12.3% for the 2021 third quarter, and 6.6% for the nine months ended September 30, 2022, compared to 15.9% for the 2021 period. Our Operating ROAE was 3.8% for the 2022 third quarter, compared to 9.3% for the 2021 third quarter, and 11.6% for the nine months ended September 30, 2022, compared to 10.1% for the 2021 period. The 2022 periods reflected increased levels of catastrophic activity, while the 2021 periods reflected higher income from operating affiliates.

Total Return on Investments

Total return on investments includes investment income, equity in net income or loss of investment funds accounted for using the equity method, net realized gains and losses (excluding changes in the allowance for credit losses on non-investment related financial assets) and the change in unrealized gains and losses generated by Arch’s investment portfolio. Total return is calculated on a pre-tax basis and before investment expenses and reflects the effect of financial market conditions along with foreign currency fluctuations. In addition, total return incorporates the timing of investment returns during the periods. The following table summarizes our total return compared to the benchmark return against which we measured our portfolio during the periods. See “Comment on Non-GAAP Financial Measures.”

			Arch Portfolio						Benchmark Return
Pre-tax total return (before investment expenses):
2022 Third Quarter			(3.01)		%				(4.01)		%
2021 Third Quarter			0.01		%				(0.40)		%
Nine Months Ended September 30, 2022			(8.83)		%				(12.78)		%
Nine Months Ended September 30, 2021			1.50		%				0.87		%

Total return for the 2022 periods reflected rising interest rates on fixed maturities and weak equity markets. We continue to maintain a relative short duration on our portfolio of 2.84 years at September 30, 2022.

The benchmark return index is a customized combination of indices intended to approximate a target portfolio by asset mix and average credit quality while also matching the approximate estimated duration and currency mix of our insurance and reinsurance liabilities. Although the estimated duration and average credit quality of this index will move as the duration and rating of its constituent securities change, generally we do not adjust the composition of the benchmark return index except to incorporate changes to the mix of liability currencies and durations noted above. The benchmark return index should not be interpreted as expressing a preference for or aversion to any particular sector or sector weight. The index is intended solely to provide, unlike many master indices that change based on the size of their constituent indices, a relatively stable basket of investable indices. At September 30, 2022, the benchmark return index had an average credit quality of “Aa3” by Moody’s Investors Service (“Moody’s”), and an estimated duration of 3.15 years.

ARCH CAPITAL			43			2022 THIRD QUARTER FORM 10-Q

The benchmark return index included weightings to the following indices:

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

COMMENT ON NON-GAAP FINANCIAL MEASURES

Throughout this filing, we present our operations in the way we believe will be the most meaningful and useful to investors, analysts, rating agencies and others who use our financial information in evaluating the performance of our company. This presentation includes the use of after-tax operating income available to Arch common shareholders, which is defined as net income available to Arch common shareholders, excluding net realized gains or losses (which includes changes in the allowance for credit losses on financial assets and net impairment losses recognized in earnings), equity in net income or loss of investment funds accounted for using the equity method, net foreign exchange gains or losses, transaction costs and other, loss on redemption of preferred shares and income taxes, and the use of annualized operating return on average common equity. The presentation of after-tax operating income available to Arch common shareholders and annualized operating return on average common equity are non-GAAP financial measures as defined in Regulation G. The reconciliation of such measures to net income available to Arch common shareholders and annualized net income return on average

common equity (the most directly comparable GAAP financial measures) in accordance with Regulation G is included under “Results of Operations” below.

We believe that net realized gains or losses, equity in net income or loss of investment funds accounted for using the equity method, net foreign exchange gains or losses, transaction costs and other and loss on redemption of preferred shares in any particular period are not indicative of the performance, of or trends, in our business. Although net realized gains or losses, equity in net income or loss of investment funds accounted for using the equity method and net foreign exchange gains or losses are an integral part of our operations, the decision to realize investment gains or losses, the recognition of the change in the carrying value of investments accounted for using the fair value option in net realized gains or losses, the recognition of net impairment losses, the recognition of equity in net income or loss of investment funds accounted for using the equity method and the recognition of foreign exchange gains or losses are independent of the insurance underwriting process and result, in large part, from general economic and financial market conditions. Furthermore, certain users of our financial information believe that, for many companies, the timing of the realization of investment gains or losses is largely opportunistic. In addition, changes in the allowance for credit losses and net impairment losses recognized in earnings on our investments represent other-than-temporary declines in expected recovery values on securities without actual realization. The use of the equity method on certain of our investments 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 investments and the timing of the recognition of equity in net income or loss of investment funds accounted for using the equity method may differ from gains or losses in the future upon sale or maturity of such investments. Transaction costs and other include advisory, financing, legal, severance, incentive compensation and other transaction costs related to acquisitions. We believe that transaction costs and other, due to their non-recurring nature, are not indicative of the performance of, or trends in, our business performance. The loss on redemption of preferred shares related to the redemption of some of Arch’s preferred shares had no impact on shareholders' equity or cash flows. Due to these reasons, we exclude net realized gains or losses, equity in net income or loss of investment funds accounted for using the equity method, net foreign exchange gains or losses, transaction costs and other and loss on redemption of preferred shares from the calculation of after-tax operating income available to Arch common shareholders.

ARCH CAPITAL			44			2022 THIRD QUARTER FORM 10-Q

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

Our segment information includes the presentation of consolidated underwriting income or loss and a subtotal of underwriting income or loss before the contribution from the ‘other’ segment. The ‘other’ segment includes the results of Somers through June 30, 2021. Such measures represent the pre-tax profitability of our underwriting operations and include net premiums earned plus other underwriting income, less losses and loss adjustment expenses, acquisition expenses and other operating expenses. Other operating expenses include those operating expenses that are incremental and/or directly attributable to our individual underwriting operations. Underwriting income or loss does not incorporate items included in our corporate 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 through June 30, 2021, 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. The ‘other’ segment includes the results of Somers through June 30, 2021.

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

company (together with Somers Group Holdings Ltd., “Somers”). Pursuant to GAAP, Somers was considered a variable interest entity and we concluded that we were the primary beneficiary of Somers. As such, we consolidated the results of Somers in our consolidated financial statements through June 30, 2021. In the 2020 fourth quarter, Arch Capital, Somers, and Greysbridge Ltd., a wholly-owned subsidiary of Arch Capital, entered into an Agreement and Plan of Merger (as amended, the “Merger Agreement”). Arch Capital assigned its rights under the Merger Agreement to Greysbridge Holdings Ltd. (“Greysbridge”). The merger contemplated by the Merger Agreement and the related Greysbridge equity financing closed on July 1, 2021. In connection therewith and effective July 1, 2021, Somers became wholly owned by Greysbridge, and Greysbridge became owned 40% by Arch and 30% by certain funds managed by Kelso and 30% by certain funds managed by Warburg. Based on the governing documents of Greysbridge, we concluded that, while we retain significant influence over Greysbridge, Greysbridge does not constitute a variable interest entity. Accordingly, effective July 1, 2021, we no longer consolidate the results of Somers in our consolidated financial statements and footnotes. See note 11, “Variable Interest Entities and Noncontrolling Interests” and note 4, “Segment Information,” to our consolidated financial statements for additional information on Somers.

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.

ARCH CAPITAL			45			2022 THIRD QUARTER FORM 10-Q

RESULTS OF OPERATIONS

The following table summarizes our consolidated financial data, including a reconciliation of net income or loss available to Arch common shareholders to after-tax operating income or loss available to Arch common shareholders.

			Three Months Ended												Nine Months Ended
			September 30,												September 30,
			2022						2021						2022						2021
Net income available to Arch common shareholders			$	6,917					$	388,751					$	586,693					$	1,480,324
Net realized (gains) losses			183,674						25,040						742,667						(247,949)
Equity in net (income) loss of investment funds accounted for using the equity method			18,861						(105,398)						(75,505)						(299,270)
Net foreign exchange (gains) losses			(90,537)						(36,078)						(182,189)						(39,522)
Transaction costs and other			76						1,036						734						889
Loss on redemption of preferred shares			—						15,101						—						15,101
Income tax expense (benefit) (1)			(13,019)						6,236						(37,933)						32,100
After-tax operating income available to Arch common shareholders			$	105,972					$	294,688					$	1,034,467					$	941,673
Beginning common shareholders’ equity			$	11,587,566					$	12,706,072					$	12,715,896					$	12,325,886
Ending common shareholders’ equity			$	10,965,110					$	12,557,526					$	10,965,110					$	12,557,526
Average common shareholders’ equity			$	11,276,338					$	12,631,799					$	11,840,503					$	12,441,706
Annualized net income return on average common equity %			0.2						12.3						6.6						15.9
Annualized operating return on average common equity %			3.8						9.3						11.6						10.1

(1) Income tax expense on net realized gains or losses, equity in net income or loss of investment funds accounted for using the equity method, net foreign exchange gains or losses and transaction costs and other reflects the relative mix reported by jurisdiction and the varying tax rates in each jurisdiction.

Segment Information

We classify our businesses into three underwriting segments — insurance, reinsurance and mortgage — and two other operating segments — corporate and ‘other.’ Our insurance, reinsurance and mortgage segments each have managers who are responsible for the overall profitability of their respective segments and who are directly accountable to our chief operating decision makers, the Chief Executive Officer of Arch Capital, the Chief Financial Officer and Treasurer of Arch Capital and the President and Chief Underwriting Officer of Arch Capital. The chief operating decision makers do not assess performance, measure return on equity or make resource allocation decisions on a line of business basis. Management measures segment performance for our three underwriting segments based on underwriting income or loss. We do not manage our assets by underwriting segment, with the exception of goodwill and intangible assets, and, accordingly, investment income is not allocated to each underwriting segment.

We determined our reportable segments using the management approach described in accounting guidance regarding disclosures about segments of an enterprise and related information. The accounting policies of the segments are the same as those used for the preparation of our consolidated financial statements. Intersegment business is allocated to the segment accountable for the underwriting results.

Insurance Segment

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

			Three Months Ended September 30,
			2022						2021						% Change
Gross premiums written			$	1,862,026					$	1,596,619					16.6
Premiums ceded			(493,267)						(442,806)
Net premiums written			1,368,759						1,153,813						18.6
Change in unearned premiums			(181,851)						(215,143)
Net premiums earned			1,186,908						938,670						26.4
Losses and loss adjustment expenses			(822,663)						(668,630)
Acquisition expenses			(232,469)						(152,467)
Other operating expenses			(165,499)						(138,931)
Underwriting income (loss)			$	(33,723)					$	(21,358)					(57.9)
Underwriting Ratios															% Point Change
Loss ratio			69.3		%				71.2		%				(1.9)
Acquisition expense ratio			19.6		%				16.2		%				3.4
Other operating expense ratio			13.9		%				14.8		%				(0.9)
Combined ratio			102.8		%				102.2		%				0.6

ARCH CAPITAL			46			2022 THIRD QUARTER FORM 10-Q

			Nine Months Ended September 30,
			2022						2021						% Change
Gross premiums written			$	5,286,798					$	4,381,372					20.7
Premiums ceded			(1,482,886)						(1,269,165)
Net premiums written			3,803,912						3,112,207						22.2
Change in unearned premiums			(488,164)						(488,636)
Net premiums earned			3,315,748						2,623,571						26.4
Losses and loss adjustment expenses			(2,053,161)						(1,750,257)
Acquisition expenses			(641,807)						(417,541)
Other operating expenses			(493,412)						(409,386)
Underwriting income (loss)			$	127,368					$	46,387					174.6
Underwriting Ratios															% Point Change
Loss ratio			61.9		%				66.7		%				(4.8)
Acquisition expense ratio			19.4		%				15.9		%				3.5
Other operating expense ratio			14.9		%				15.6		%				(0.7)
Combined ratio			96.2		%				98.2		%				(2.0)

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

Construction and national accounts: primary and excess casualty coverages to middle and large accounts in the construction industry and a wide range of products for middle and large national accounts, specializing in loss sensitive primary casualty insurance programs (including large deductible, self-insured retention and retrospectively rated programs).

Excess and surplus casualty: primary and excess casualty insurance coverages, including middle market energy business, and contract binding, which primarily provides casualty coverage through a network of appointed agents to small and medium risks.

Lenders products: collateral protection, debt cancellation and service contract reimbursement products to banks, credit unions, automotive dealerships and original equipment manufacturers and other specialty programs that pertain to automotive lending and leasing.

Professional lines: directors’ and officers’ liability, errors and omissions liability, employment practices liability, fiduciary liability, crime, professional indemnity and other financial related coverages for corporate, private equity, venture capital, real estate investment trust, limited partnership, financial institution and not-for-profit clients of all sizes, cyber insurance, and medical professional and general liability insurance coverages for the healthcare industry. The business is predominately written on a claims-made basis.

Programs: primarily package policies, underwriting workers’ compensation and umbrella liability business in support of desirable package programs, targeting program managers with unique expertise and niche products offering general

liability, commercial automobile, inland marine and property business with minimal catastrophe exposure.

Property, energy, marine and aviation: primary and excess general property insurance coverages, including catastrophe-exposed property coverage, for commercial clients. Coverages for marine include hull, war, specie and liability. Aviation and standalone terrorism are also offered.

Travel, accident and health: specialty travel and accident and related insurance products for individual, group travelers, travel agents and suppliers, as well as accident and health, which provides accident, disability and medical plan insurance coverages for employer groups, medical plan members, students and other participant groups.

Other: includes alternative market risks (including captive insurance programs), excess workers’ compensation and employer’s liability insurance coverages for qualified self-insured groups, associations and trusts, and contract and commercial surety coverages, including contract bonds (payment and performance bonds) primarily for medium and large contractors and commercial surety bonds for Fortune 1,000 companies and smaller transaction business programs.

Premiums Written.

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

			Three Months Ended September 30,
			2022												2021
			Amount						%						Amount						%
Professional lines			$	412,173					30.1						$	310,185					26.9
Property, energy, marine and aviation			241,357						17.6						205,021						17.8
Programs			189,263						13.8						196,048						17.0
Excess and surplus casualty			110,917						8.1						98,320						8.5
Travel, accident and health			107,434						7.8						62,837						5.4
Construction and national accounts			98,381						7.2						102,294						8.9
Lenders products			41,889						3.1						38,905						3.4
Other			167,345						12.2						140,203						12.2
Total			$	1,368,759					100.0						$	1,153,813					100.0

2022 Third Quarter versus 2021 Period. Gross premiums written by the insurance segment in the 2022 third quarter were 16.6% higher than in the 2021 third quarter, while net premiums written were 18.6% higher. The higher level of net premiums written reflected increases in most lines of business, due in part to rate increases, new business opportunities and growth in existing accounts.

ARCH CAPITAL			47			2022 THIRD QUARTER FORM 10-Q

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

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

Net Premiums Earned.

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

			Three Months Ended September 30,
			2022												2021
			Amount						%						Amount						%
Professional lines			$	341,833					28.8						$	249,007					26.5
Property, energy, marine and aviation			202,483						17.1						178,167						19.0
Programs			150,453						12.7						137,299						14.6
Excess and surplus casualty			100,175						8.4						84,048						9.0
Travel, accident and health			133,445						11.2						56,102						6.0
Construction and national accounts			109,905						9.3						104,261						11.1
Lenders products			33,253						2.8						33,030						3.5
Other			115,361						9.7						96,756						10.3
Total			$	1,186,908					100.0						$	938,670					100.0

			Nine Months Ended September 30,
			2022												2021
			Amount						%						Amount						%
Professional lines			$	945,761					28.5						$	662,776					25.3
Property, energy, marine and aviation			557,481						16.8						488,326						18.6
Programs			438,943						13.2						369,113						14.1
Excess and surplus casualty			289,305						8.7						232,314						8.9
Travel, accident and health			368,260						11.1						168,378						6.4
Construction and national accounts			306,204						9.2						317,597						12.1
Lenders products			91,435						2.8						119,507						4.6
Other			318,359						9.6						265,560						10.1
Total			$	3,315,748					100.0						$	2,623,571					100.0

Net premiums written are primarily earned on a pro rata basis over the terms of the policies for all products, usually 12 months. Net premiums earned reflect changes in net premiums written over the previous five quarters. Net premiums earned for both 2022 periods were 26.4% higher than in the 2021 periods.

Losses and Loss Adjustment Expenses.

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

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

Current Year Loss Ratio.

2022 Third Quarter versus 2021 Period. The insurance segment’s current year loss ratio in the 2022 third quarter was 1.9 points lower than in the 2021 third quarter. The 2022 third quarter loss ratio reflected 13.4 points of current year catastrophic activity, primarily related to Hurricane Ian, compared to 12.2 points of catastrophic activity for the 2021 third quarter, primarily related to Hurricane Ida.

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

ARCH CAPITAL			48			2022 THIRD QUARTER FORM 10-Q

Prior Period Reserve Development.

The insurance segment’s net favorable development was $5.4 million, or 0.5 points, for the 2022 third quarter, compared to $5.1 million, or 0.5 points, for the 2021 third quarter, and $19.4 million, or 0.6 points, for the nine months ended September 30, 2022, compared to $13.1 million, or 0.5 points, for the 2021 period. See note 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.

2022 Third Quarter versus 2021 Period. The insurance segment’s underwriting expense ratio was 33.5% in the 2022 third quarter, compared to 31.0% in the 2021 third quarter. The increase in the 2022 third quarter was primarily due to growth in lines with higher acquisition costs, such as travel, higher contingent commission accruals on profitable business and a slightly lower ceded premium ratio. Partially offsetting this increase in the acquisition expense ratio was a reduction in the operating expense ratio where the growth in net earned premium outpaced the growth in operating expense.

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

Reinsurance Segment

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

			Three Months Ended September 30,
			2022						2021						% Change
Gross premiums written			$	1,639,061					$	1,251,760					30.9
Premiums ceded			(560,225)						(630,371)
Net premiums written			1,078,836						621,389						73.6
Change in unearned premiums			(77,062)						57,313
Net premiums earned			1,001,774						678,702						47.6
Other underwriting income (loss)			452						3,293
Losses and loss adjustment expenses			(927,911)						(545,846)
Acquisition expenses			(208,425)						(129,450)
Other operating expenses			(62,777)						(45,647)
Underwriting income (loss)			$	(196,887)					$	(38,948)					(405.5)
Underwriting Ratios															% Point Change
Loss ratio			92.6		%				80.4		%				12.2
Acquisition expense ratio			20.8		%				19.1		%				1.7
Other operating expense ratio			6.3		%				6.7		%				(0.4)
Combined ratio			119.7		%				106.2		%				13.5

			Nine Months Ended September 30,
			2022						2021						% Change
Gross premiums written			$	5,151,401					$	4,080,840					26.2
Premiums ceded			(1,770,807)						(1,535,607)
Net premiums written			3,380,594						2,545,233						32.8
Change in unearned premiums			(646,421)						(484,607)
Net premiums earned			2,734,173						2,060,626						32.7
Other underwriting income			5,814						3,148
Losses and loss adjustment expenses			(1,920,189)						(1,494,539)
Acquisition expenses			(569,915)						(381,060)
Other operating expenses			(198,606)						(150,856)
Underwriting income (loss)			$	51,277					$	37,319					37.4
Underwriting Ratios															% Point Change
Loss ratio			70.2		%				72.5		%				(2.3)
Acquisition expense ratio			20.8		%				18.5		%				2.3
Other operating expense ratio			7.3		%				7.3		%				—
Combined ratio			98.3		%				98.3		%				—

The reinsurance segment consists of our reinsurance underwriting units which offer specialty product lines on a worldwide basis. Reinsurance agreements are typically offered on a proportional and/or excess of loss basis and provide coverage to ceding company clients for specific underlying written policies. Product lines include:

Casualty: provides coverage on third party liability exposures including, among others, executive assurance, professional liability, excess and umbrella liability, excess motor and healthcare business, and workers’ compensation. Business is assumed primarily on a treaty basis, with some facultative coverages also offered.

Marine and aviation: provides coverage for energy, hull, cargo, specie, liability and transit, and aviation business, including airline and general aviation risks. Business written may also include space business, which includes coverages for satellite assembly, launch and operation for commercial space programs.

Other specialty: provides coverage for proportional motor reinsurance, whole account multi-line treaties, cyber, trade credit and surety, accident and health, workers’ compensation catastrophe, agriculture and political risk, among others.

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

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

ARCH CAPITAL			49			2022 THIRD QUARTER FORM 10-Q

explosion, collapse, riot, vandalism, wind, tornado, flood and earthquake. Business is assumed on either a treaty basis or facultative basis.

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

Premiums Written.

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

			Three Months Ended September 30,
			2022												2021
			Amount						%						Amount						%
Other specialty			$	381,004					35.3						$	167,006					26.9
Property excluding property catastrophe			341,809						31.7						237,025						38.1
Casualty			230,308						21.3						187,066						30.1
Property catastrophe			77,606						7.2						(7,125)						(1.1)
Marine and aviation			28,633						2.7						19,159						3.1
Other			19,476						1.8						18,258						2.9
Total			$	1,078,836					100.0						$	621,389					100.0

2022 Third Quarter versus 2021 Period. Gross premiums written by the reinsurance segment in the 2022 third quarter were 30.9% higher than in the 2021 third quarter, while net premiums written were 73.6% higher. Net premiums written for the reinsurance segment in the 2021 third quarter were affected by a one time $161.2 million adjustment, resulting from retrocessions to Somers Re Ltd. (formerly known as Watford Re Ltd.) following its ownership change on July 1, 2021. Absent this item, net premiums written by the reinsurance segment were 37.9% higher than in the 2021 third quarter. The growth in net premiums written reflected increases in all lines of business, primarily related to rate increases, new business opportunities and growth in existing accounts.

			Nine Months Ended September 30,
			2022												2021
			Amount						%						Amount						%
Other specialty			$	1,179,548					34.9						$	747,662					29.4
Property excluding property catastrophe			936,270						27.7						778,959						30.6
Casualty			709,487						21.0						631,212						24.8
Property catastrophe			361,028						10.7						197,724						7.8
Marine and aviation			115,579						3.4						131,045						5.1
Other			78,682						2.3						58,631						2.3
Total			$	3,380,594					100.0						$	2,545,233					100.0

Nine Months Ended September 30, 2022 versus 2021 period. Gross premiums written by the reinsurance segment for the nine months ended September 30, 2022 were 26.2% higher than in the 2021 period, while net premiums written were 32.8% higher than in the 2021 period. The increase in net premiums written reflected growth in most lines of business,

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

Net Premiums Earned.

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

			Three Months Ended September 30,
			2022												2021
			Amount						%						Amount						%
Other specialty			$	330,142					33.0						$	195,649					28.8
Property excluding property catastrophe			282,488						28.2						210,280						31.0
Casualty			221,636						22.1						159,697						23.5
Property catastrophe			117,820						11.8						61,107						9.0
Marine and aviation			25,182						2.5						29,818						4.4
Other			24,506						2.4						22,151						3.3
Total			$	1,001,774					100.0						$	678,702					100.0

			Nine Months Ended September 30,
			2022												2021
			Amount						%						Amount						%
Other specialty			$	846,081					30.9						$	571,364					27.7
Property excluding property catastrophe			781,562						28.6						600,842						29.2
Casualty			634,208						23.2						492,574						23.9
Property catastrophe			289,575						10.6						225,285						10.9
Marine and aviation			109,142						4.0						112,699						5.5
Other			73,605						2.7						57,862						2.8
Total			$	2,734,173					100.0						$	2,060,626					100.0

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

Other Underwriting Income (Loss).

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

Losses and Loss Adjustment Expenses.

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

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

ARCH CAPITAL			50			2022 THIRD QUARTER FORM 10-Q

Current Year Loss Ratio.

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

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

Prior Period Reserve Development.

The reinsurance segment’s net favorable development was $49.2 million, or 4.9 points, for the 2022 third quarter, compared to $72.3 million, or 10.7 points, for the 2021 third quarter, and $128.1 million, or 4.7 points, for the nine months ended September 30, 2022, compared to $119.6 million, or 5.8 points, for the 2021 period. See note 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.

2022 Third Quarter versus 2021 Period. The underwriting expense ratio for the reinsurance segment was 27.1% in the 2022 third quarter, compared to 25.8% in the 2021 third quarter, with the increase primarily resulting from higher level of pro rata business, which generally has higher ceding commissions than excess of loss business. Such increase in the acquisition expense ratio was partially offset by a lower operating expense ratio due to a higher level of earned premium.

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

Mortgage Segment

Our mortgage operations include U.S. and international mortgage insurance and reinsurance operations as well as participation in GSE credit risk-sharing transactions.

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

			Three Months Ended September 30,
			2022						2021						% Change
Gross premiums written			$	362,409					$	360,934					0.4
Premiums ceded			(86,230)						(60,207)
Net premiums written			276,179						300,727						(8.2)
Change in unearned premiums			5,889						11,238
Net premiums earned			282,068						311,965						(9.6)
Other underwriting income			2,625						3,981
Losses and loss adjustment expenses			67,878						(11,543)
Acquisition expenses			(6,693)						(24,098)
Other operating expenses			(46,471)						(46,254)
Underwriting income			$	299,407					$	234,051					27.9
Underwriting Ratios															% Point Change
Loss ratio			(24.1)		%				3.7		%				(27.8)
Acquisition expense ratio			2.4		%				7.7		%				(5.3)
Other operating expense ratio			16.5		%				14.8		%				1.7
Combined ratio			(5.2)		%				26.2		%				(31.4)

			Nine Months Ended September 30,
			2022						2021						% Change
Gross premiums written			$	1,099,144					$	1,143,691					(3.9)
Premiums ceded			(241,097)						(171,923)
Net premiums written			858,047						971,768						(11.7)
Change in unearned premiums			9,190						10,735
Net premiums earned			867,237						982,503						(11.7)
Other underwriting income			6,130						15,026
Losses and loss adjustment expenses			187,163						(85,112)
Acquisition expenses			(27,343)						(84,297)
Other operating expenses			(150,064)						(143,697)
Underwriting income			$	883,123					$	684,423					29.0
Underwriting Ratios															% Point Change
Loss ratio			(21.6)		%				8.7		%				(30.3)
Acquisition expense ratio			3.2		%				8.6		%				(5.4)
Other operating expense ratio			17.3		%				14.6		%				2.7
Combined ratio			(1.1)		%				31.9		%				(33.0)

ARCH CAPITAL			51			2022 THIRD QUARTER FORM 10-Q

Premiums Written.

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

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

2022 Third Quarter versus 2021 Period. Gross premiums written by the mortgage segment in the 2022 third quarter were 0.4% higher than in the 2021 third quarter, while net premiums written were 8.2% lower. Net premiums written for the 2022 third quarter reflected a higher level of premiums ceded than in the 2021 third quarter.

			Nine Months Ended September 30,
			2022												2021
			Amount						%						Amount						%
Underwriting location:
United States			$	590,606					68.8						$	703,489					72.4
Other			267,441						31.2						268,279						27.6
Total			$	858,047					100.0						$	971,768					100.0

Nine Months Ended September 30, 2022 versus 2021 Period. Gross premiums written by the mortgage segment for the nine months ended September 30, 2022 were 3.9% lower than in the 2021 period. The reduction in gross premiums written primarily reflected a lower U.S. primary mortgage insurance single premium volume and a decrease in monthly premiums. Net premiums written for the nine months ended September 30, 2022 were 11.7% lower than in the 2021 period and reflected a higher level of premiums ceded than in the 2021 period.

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

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

(U.S. Dollars in millions)			Three Months Ended September 30,
2022												2021
			Amount						%						Amount						%
Total new insurance written (NIW) (1)			$	17,425											$	27,841
Credit quality (FICO):
>=740			$	11,615					66.7						$	17,514					62.9
680-739			5,322						30.5						9,012						32.4
620-679			485						2.8						1,315						4.7
<620			3						—						—						—
Total			$	17,425					100.0						$	27,841					100.0
Loan-to-value (LTV):
95.01% and above			$	973					5.6						$	1,554					5.6
90.01% to 95.00%			9,916						56.9						14,240						51.1
85.01% to 90.00%			4,839						27.8						8,394						30.1
85.00% and below			1,697						9.7						3,653						13.1
Total			$	17,425					100.0						$	27,841					100.0
Monthly vs. single:
Monthly			$	16,911					97.1						$	26,515					95.2
Single			514						2.9						1,326						4.8
Total			$	17,425					100.0						$	27,841					100.0
Purchase vs. refinance:
Purchase			$	17,159					98.5						$	25,711					92.3
Refinance			266						1.5						2,130						7.7
Total			$	17,425					100.0						$	27,841					100.0

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

ARCH CAPITAL			52			2022 THIRD QUARTER FORM 10-Q

(U.S. Dollars in millions)			Nine Months Ended September 30,
2022												2021
			Amount						%						Amount						%
Total new insurance written (NIW) (1)			$	60,939											$	83,232
Credit quality (FICO):
>=740			$	40,888					67.1						$	54,572					65.6
680-739			18,376						30.2						25,543						30.7
620-679			1,667						2.7						3,117						3.7
<620			8						—						—						—
Total			$	60,939					100.0						$	83,232					100.0
Loan-to-value (LTV):
95.01% and above			$	3,264					5.4						$	4,646					5.6
90.01% to 95.00%			33,984						55.8						40,464						48.6
85.01% to 90.00%			17,163						28.2						25,381						30.5
85.01% and below			6,528						10.7						12,741						15.3
Total			$	60,939					100.0						$	83,232					100.0
Monthly vs. single:
Monthly			$	58,984					96.8						$	78,229					94.0
Single			1,955						3.2						5,003						6.0
Total			$	60,939					100.0						$	83,232					100.0
Purchase vs. refinance:
Purchase			$	59,375					97.4						$	71,226					85.6
Refinance			1,564						2.6						12,006						14.4
Total			$	60,939					100.0						$	83,232					100.0

Net Premiums Earned.

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

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

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

			Nine Months Ended September 30,
			2022												2021
			Amount						%						Amount						%
Underwriting location:
United States			$	615,599					71.0						$	747,830					76.1
Other			251,638						29.0						234,673						23.9
Total			$	867,237					100.0						$	982,503					100.0

Nine Months Ended September 30, 2022 versus 2021 Period. For the nine months ended September 30, 2022, net premiums earned were 11.7% lower than in the 2021 period, and reflected a lower level of earnings from single premium policy terminations and a decline in monthly premiums.

Other Underwriting Income (Loss).

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

Losses and Loss Adjustment Expenses.

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

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

Current Year Loss Ratio.

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

Nine Months Ended September 30, 2022 versus 2021 Period. The mortgage segment’s current year loss ratio was 0.5 points lower for the nine months ended September 30, 2022 than for the 2021 period. The lower current year loss ratio for the 2022 period reflected lower delinquencies.

Prior Period Reserve Development.

The mortgage segment’s net favorable development was $126.2 million, or 44.7 points, for the 2022 third quarter, compared to $45.1 million, or 14.5 points, for the 2021 third quarter, and $346.4 million, or 39.9 points, for the nine months ended September 30, 2022, compared to $99.1 million, or 10.1 points, for the 2021 period. 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.

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

ARCH CAPITAL			53			2022 THIRD QUARTER FORM 10-Q

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

Corporate Segment

The corporate segment results include net investment income, net realized gains or losses (which includes changes in the allowance for credit losses on financial assets and net impairment losses recognized in earnings), equity in net income or loss of investments accounted for using the equity method, other income (loss), corporate expenses, transaction costs and other, amortization of intangible assets, interest expense, net foreign exchange gains or losses, income taxes, income from operating affiliates and items related to our non-cumulative preferred shares. Such amounts exclude the results of the ‘other’ segment.

Net Investment Income.

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

			Three Months Ended												Nine Months Ended
			September 30,												September 30,
			2022						2021						2022						2021
Fixed maturities			$	123,568					$	75,964					$	310,963					$	232,690
Equity securities			4,261						9,867						16,620						23,799
Short-term investments			9,304						1,858						15,999						3,474
Other (1)			8,644						19,114						28,704						55,699
Gross investment income			145,777						106,803						372,286						315,662
Investment expenses (2)			(17,137)						(18,608)						(56,818)						(59,308)
Net investment income			$	128,640					$	88,195					$	315,468					256,354

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

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

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

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

Corporate Expenses.

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

Other Income (Losses)

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

Transaction Costs and Other.

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

Amortization of Intangible Assets.

Amortization of intangible assets for the 2022 third quarter was $26.1 million, compared to $20.1 million for the 2021 third quarter, and $80.5 million for the nine months ended September 30, 2022, compared to $48.9 million for the 2021 period. Amounts in 2022 and 2021 period primarily attributed to amortization of finite-lived intangible assets. The increase in amortization of intangible assets expense was a result of acquisitions closed during the 2021 period.

Interest Expense.

Interest expense was $33.1 million for the 2022 third quarter, compared to the $33.2 million for the 2021 third quarter, and $98.6 million for the nine months ended September 30, 2022, consistent with $98.8 million for the 2021 period. Interest expense primarily reflects amounts related to our outstanding senior notes.

Net Realized Gains or Losses.

We recorded net realized losses of $183.7 million for the 2022 third quarter, of which approximately 40% represented unrealized changes in the fair value of equity securities and assets accounted for using the fair value option, compared to net realized losses of $25.0 million for the 2021 third quarter, and net realized losses of $742.7 million for the nine months ended September 30, 2022, compared to net realized gains of $239.7 million for the 2021 period. Currently, our portfolio is

ARCH CAPITAL			54			2022 THIRD QUARTER FORM 10-Q

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

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

Equity in Net Income or Losses of Investment Funds Accounted for Using the Equity Method.

We recorded a loss of $18.9 million related to investment funds accounted for using the equity method in the 2022 third quarter, compared to an income of $105.4 million for the 2021 third quarter, and $75.5 million for the nine months ended September 30, 2022, compared to $299.3 million for the 2021 period. Such investments are generally recorded on a one to three month lag based on the availability of reports from the investment funds. Investment funds accounted for using the equity method totaled $3.6 billion at September 30, 2022, compared to $3.1 billion at December 31, 2021. 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 2022 third quarter were $90.5 million, compared to net foreign exchange gains for the 2021 third quarter of $36.1 million. Net foreign exchange gains for the nine months ended September 30, 2022 were $182.1 million, compared to net foreign exchange gains for the 2021 period of $39.7 million. Amounts in both periods were primarily unrealized and resulted from the effects of revaluing our net insurance liabilities required to be settled in foreign currencies at each balance sheet date.

Income Tax Expense.

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

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

Income or Losses from Operating Affiliates.

Income from operating affiliates for 2022 third quarter was $8.5 million, compared to $124.1 million for the 2021 third quarter, and $37.7 million for the nine months ended September 30, 2022, compared to $224.1 million for the 2021 period. Results for the 2021 period reflected a one-time gain of $95.7 million and $74.5 million realized from our investments in Somers and Coface SA, respectively. See note 7, “Investment Information—Investments in Operating Affiliates,” to our consolidated financial statements for additional information.

CRITICAL ACCOUNTING POLICIES,

ESTIMATES AND RECENT ACCOUNTING PRONOUNCEMENTS

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

FINANCIAL CONDITION

Investable Assets Held by Arch

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

			September 30, 2022,						December 31, 2021
Average effective duration (in years)			2.84						2.70
Average S&P/Moody’s credit ratings (1)			AA/Aa2						AA-/Aa3

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

ARCH CAPITAL			55			2022 THIRD QUARTER FORM 10-Q

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
September 30, 2022
U.S. government and gov’t agencies (1)			$	5,746,853					30.8
AAA			3,344,746						17.9
AA			2,030,730						10.9
A			3,382,545						18.1
BBB			3,001,304						16.1
BB			532,162						2.9
B			357,543						1.9
Lower than B			12,417						0.1
Not rated			242,730						1.3
Total			$	18,651,030					100.0
December 31, 2021
U.S. government and gov’t agencies (1)			$	5,063,191					27.5
AAA			3,783,386						20.5
AA			2,459,413						13.4
A			2,943,594						16.0
BBB			2,936,398						15.9
BB			501,588						2.7
B			371,747						2.0
Lower than B			43,756						0.2
Not rated			311,734						1.7
Total			$	18,414,807					100.0

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

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
September 30, 2022
0-10%			$	10,662,904					$	(551,217)					29.6
10-20%			5,851,810						(952,285)						51.2
20-30%			1,070,957						(326,093)						17.5
Greater than 30%			63,903						(31,059)						1.7
Total			$	17,649,574					$	(1,860,654)					100.0
December 31, 2021
0-10%			$	12,231,146					$	(166,867)					97.6
10-20%			16,884						(2,412)						1.4
20-30%			2,593						(759)						0.4
Greater than 30%			684						(916)						0.5
Total			$	12,251,307					$	(170,954)					100.0

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

			Estimated Fair Value						Credit Rating (1)
Bank of America Corporation			$	430,809					A-/A2
JPMorgan Chase & Co.			297,868						A-/A1
Morgan Stanley			268,742						A-/A1
Citigroup Inc.			260,312						BBB+/A3
The Goldman Sachs Group, Inc.			243,516						BBB+/A2
Wells Fargo & Company			237,947						BBB+/A1
Blackstone Inc.			165,585						BBB/Baa3
Blue Owl Capital Inc.			157,904						BBB-/Baa3
UBS Group AG			125,810						A/Aa3
Dai-ichi Life Holdings, Inc.			106,357						AA-/A1
Total			$	2,294,850

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

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

			Agencies						Investment Grade						Below Investment Grade						Total
September 30, 2022
RMBS			$	602,423					$	143,188					$	17,760					$	763,371
CMBS			18,022						957,327						88,889						1,064,238
ABS			—						1,410,672						180,970						1,591,642
Total			$	620,445					$	2,511,187					$	287,619					$	3,419,251
December 31, 2021
RMBS			$	268,229					$	129,296					$	10,952					$	408,477
CMBS			22,198						926,302						97,984						1,046,484
ABS			—						2,543,907						152,551						2,696,458
Total			$	290,427					$	3,599,505					$	261,487					$	4,151,419

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

			September 30, 2022						December 31, 2021
Equities (1)			$	527,658					$	883,722
Exchange traded funds
Fixed income (2)			269,276						455,467
Equity and other (3)			26,840						491,474
Total			$	823,774					$	1,830,663

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

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

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

For details on our other investments and other investable assets, see note 7, “Investment Information—Other Investments” to our consolidated financial statements.

ARCH CAPITAL			56			2022 THIRD QUARTER FORM 10-Q

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.

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. See note 8, “Fair Value,” to our consolidated financial statements for a summary of our financial assets and liabilities measured at fair value, segregated by level in the fair value hierarchy.

Reinsurance

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

			Three Months Ended												Nine Months Ended
			September 30,												September 30,
			2022						2021						2022						2021
Premiums written:
Direct			$	2,247,480					$	1,993,098					$	6,503,383					$	5,795,236
Assumed			1,613,203						1,214,317						5,027,802						4,095,676
Ceded			(1,136,909)						(1,131,486)						(3,488,632)						(2,907,002)
Net			$	2,723,774					$	2,075,929					$	8,042,553					$	6,983,910
Premiums earned:
Direct			$	2,067,084					$	1,754,462					$	5,925,934					$	5,263,286
Assumed			1,525,027						1,129,434						4,037,580						3,169,016
Ceded			(1,121,361)						(954,559)						(3,046,356)						(2,433,634)
Net			$	2,470,750					$	1,929,337					$	6,917,158					$	5,998,668
Losses and LAE:
Direct			$	1,228,281					$	1,101,793					$	3,016,634					$	3,134,305
Assumed			1,370,308						961,285						2,661,854						2,182,852
Ceded			(915,893)						(837,059)						(1,892,301)						(1,728,207)
Net			$	1,682,696					$	1,226,019					$	3,786,187					$	3,588,950

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

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

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

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

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

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

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

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

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

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

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

ARCH CAPITAL			57			2022 THIRD QUARTER FORM 10-Q

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

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

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

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

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

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

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

Reserve for Losses and Loss Adjustment Expenses

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

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

			September 30, 2022						December 31, 2021
Insurance segment:
Case reserves			$	2,214,924					$	2,102,891
IBNR reserves			4,797,323						4,269,904
Total net reserves			7,012,247						6,372,795
Reinsurance segment:
Case reserves			1,720,426						1,733,571
Additional case reserves			583,197						426,531
IBNR reserves			3,100,704						2,656,527
Total net reserves			5,404,327						4,816,629
Mortgage segment:
Case reserves			542,975						741,897
IBNR reserves			222,194						226,604
Total net reserves			765,169						968,501
Total:
Case reserves			4,478,325						4,578,359
Additional case reserves			583,197						426,531
IBNR reserves			8,120,221						7,153,035
Total net reserves			$	13,181,743					$	12,157,925

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

			September 30, 2022						December 31, 2021
Insurance segment:
Professional lines			$	1,888,083					$	1,673,615
Construction and national accounts			1,559,888						1,490,206
Programs			846,580						793,187
Excess and surplus casualty			739,676						657,307
Property, energy, marine and aviation			713,021						599,093
Travel, accident and health			132,337						96,051
Lenders products			40,960						58,351
Other			1,091,702						1,004,985
Total net reserves			$	7,012,247					$	6,372,795

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

			September 30, 2022						December 31, 2021
Reinsurance segment:
Casualty			$	2,223,204					$	2,123,360
Other specialty			1,215,362						1,113,766
Property excluding property catastrophe			971,430						711,859
Property catastrophe			586,249						486,911
Marine and aviation			270,574						246,861
Other			137,508						133,872
Total net reserves			$	5,404,327					$	4,816,629

ARCH CAPITAL			58			2022 THIRD QUARTER FORM 10-Q

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

			September 30, 2022						December 31, 2021
U.S. primary mortgage insurance (1)			$	545,577					$	710,708
U.S. credit risk transfer (CRT) and other			108,667						112,549
International mortgage insurance/ reinsurance			110,925						145,244
Total net reserves			$	765,169					$	968,501

(1) At September 30, 2022, 34.9% of total net reserves represents policy years 2012 and prior and the remainder from later policy years. At December 31, 2021, 27.9% of total net reserves represent policy years 2012 and prior and the remainder from later policy years.

Mortgage Operations Supplemental Information

The mortgage segment’s insurance in force (“IIF”) and risk in force (“RIF”) were as follows at September 30, 2022 and December 31, 2021:

(U.S. Dollars in millions)			September 30, 2022												December 31, 2021
Amount						%						Amount						%
Insurance In Force (IIF) (1):
U.S. primary mortgage insurance			$	294,857					58.8						$	280,945					61.0
U.S. credit risk transfer (CRT) and other (2)			143,897						28.7						110,018						23.9
International mortgage insurance/reinsurance (3)			63,068						12.6						69,655						15.1
Total			$	501,822					100.0						$	460,618					100.0
Risk In Force (RIF) (4):
U.S. primary mortgage insurance			$	75,343					85.1						$	70,619					84.3
U.S. credit risk transfer (CRT) and other (2)			6,473						7.3						5,120						6.1
International mortgage insurance/reinsurance (3)			6,727						7.6						7,983						9.5
Total			$	88,543					100.0						$	83,722					100.0

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

(2)Includes all CRT transactions, which are predominantly with GSEs, and other U.S. reinsurance transactions.

(3)International mortgage insurance and reinsurance with risk primarily located in Australia and to lesser extent Europe and Asia.

(4)The aggregate dollar amount of each insured mortgage loan’s current principal balance multiplied by the insurance coverage percentage specified in the policy for insurance policies issued and after contract limits and/or loss ratio caps for risk-sharing or reinsurance.

The IIF and RIF for our U.S. primary mortgage insurance business by policy year were as follows at September 30, 2022:

(U.S. Dollars in millions)			IIF												RIF												Delinquency
Amount						%						Amount						%						Rate (1)
Policy year:
2012 and prior			$	10,362					3.5						$	2,509					3.3						8.22		%
2013			3,196						1.1						855						1.1						2.12		%
2014			3,903						1.3						1,071						1.4						2.61		%
2015			6,607						2.2						1,780						2.4						2.11		%
2016			11,021						3.7						2,953						3.9						2.47		%
2017			10,017						3.4						2,654						3.5						3.27		%
2018			10,744						3.6						2,742						3.6						3.95		%
2019			19,961						6.8						5,038						6.7						2.24		%
2020			68,974						23.4						17,294						23.0						0.87		%
2021			91,486						31.0						23,152						30.7						0.66		%
2022			58,586						19.9						15,295						20.3						0.17		%
Total			$	294,857					100.0						$	75,343					100.0						1.73		%

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

The IIF and RIF for our U.S. primary mortgage insurance business by policy year were as follows at December 31, 2021:

(U.S. Dollars in millions)			IIF												RIF												Delinquency
Amount						%						Amount						%						Rate (1)
Policy year:
2012 and prior			$	13,030					4.6						$	2,960					4.2						8.48		%
2013			4,206						1.5						1,148						1.6						2.63		%
2014			4,822						1.7						1,328						1.9						3.14		%
2015			8,703						3.1						2,340						3.3						2.67		%
2016			14,344						5.1						3,841						5.4						3.29		%
2017			13,128						4.7						3,436						4.9						4.09		%
2018			14,046						5.0						3,562						5.0						5.28		%
2019			25,841						9.2						6,467						9.2						3.13		%
2020			82,502						29.4						20,341						28.8						0.97		%
2021			100,323						35.7						25,196						35.7						0.29		%
Total			$	280,945					100.0						$	70,619					100.0						2.36		%

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

ARCH CAPITAL			59			2022 THIRD QUARTER FORM 10-Q

The following tables provide supplemental disclosures on risk in force for our U.S. primary mortgage insurance business at September 30, 2022 and December 31, 2021:

(U.S. Dollars in millions)			September 30, 2022												December 31, 2021
Amount						%						Amount						%
Credit quality (FICO):
>=740			$	46,538					61.8						$	42,451					60.1
680-739			24,671						32.7						23,646						33.5
620-679			3,850						5.1						4,196						5.9
<620			284						0.4						326						0.5
Total			$	75,343					100.0						$	70,619					100.0
Weighted average FICO score			748												746
Loan-to-value (LTV):
95.01% and above			$	7,334					9.7						$	7,538					10.7
90.01% to 95.00%			43,049						57.1						38,829						55.0
85.01% to 90.00%			20,876						27.7						20,006						28.3
85.00% and below			4,084						5.4						4,246						6.0
Total			$	75,343					100.0						$	70,619					100.0
Weighted average LTV			92.9		%										92.8		%
Total RIF, net of external reinsurance			$	56,890											$	54,574

(U.S. Dollars in millions)			September 30, 2022												December 31, 2021
Amount						%						Amount						%
Total RIF by State:
California			$	6,219					8.3						$	5,559					7.9
Texas			6,080						8.1						5,594						7.9
Florida			3,275						4.3						3,303						4.7
Georgia			3,150						4.2						2,902						4.1
North Carolina			3,139						4.2						2,921						4.1
Illinois			3,087						4.1						2,933						4.2
Minnesota			2,996						4.0						2,916						4.1
Massachusetts			2,771						3.7						2,537						3.6
Virginia			2,647						3.5						2,446						3.5
Michigan			2,587						3.4						2,492						3.5
Other			39,392						52.3						37,016						52.4
Total			$	75,343					100.0						$	70,619					100.0

The following table provides supplemental disclosures for our U.S. primary mortgage insurance business related to insured loans and loss metrics:

(U.S. Dollars in thousands, except policy, loan and claim count)			Nine Months Ended
September 30,
2022						2021
Roll-forward of insured loans in default:
Beginning delinquent number of loans			27,645						52,234
New notices			26,328						26,483
Cures			(33,225)						(46,334)
Paid claims			(534)						(613)
Ending delinquent number of loans (1)			20,214						31,770
Ending number of policies in force (1)			1,168,735						1,188,768
Delinquency rate (1)			1.73		%				2.67		%
Losses:
Number of claims paid			534						613
Total paid claims			$	16,865					$	22,848
Average per claim			$	31.6					$	37.3
Severity (2)			74.3		%				80.2		%
Average case reserve per default (in thousands) (1)			$	27.7					$	23.5

(1)Includes first lien primary and pool policies.

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

The risk to capital ratio, which represents total current (non-delinquent) risk in force, net of reinsurance, divided by total statutory capital, for Arch MI U.S. was approximately 7.6 to 1 at September 30, 2022, compared to 8 to 1 at December 31, 2021.

Shareholders’ Equity and Book Value per Share

The following table presents the calculation of book value per share:

(U.S. dollars in thousands, except share data)			September 30, 2022						December 31, 2021
Total shareholders’ equity available to Arch			$	11,795,110					$	13,545,896
Less preferred shareholders’ equity			830,000						830,000
Common shareholders’ equity available to Arch			$	10,965,110					$	12,715,896
Common shares and common share equivalents outstanding, net of treasury shares (1)			369,321,990						378,923,894
Book value per share			$	29.69					$	33.56

(1)Excludes the effects of 15,628,546 and 17,083,160 stock options and 560,945 and 729,636 restricted stock units outstanding at September 30, 2022 and December 31, 2021, respectively.

ARCH CAPITAL			60			2022 THIRD QUARTER FORM 10-Q

LIQUIDITY

Liquidity is a measure of our ability to access sufficient cash flows to meet the short-term and long-term cash requirements of our business operations.

Arch Capital is a holding company whose assets primarily consist of the shares in its subsidiaries. Generally, Arch Capital depends on its available cash resources, liquid investments and dividends or other distributions from its subsidiaries to make payments, including the payment of debt service obligations and operating expenses it may incur and any dividends or liquidation amounts with respect to our preferred and common shares.

For the nine months ended September 30, 2022, Arch Capital received dividends of $735.3 million from Arch Reinsurance Ltd. (“Arch Re Bermuda”), our Bermuda based reinsurer and insurer which can pay approximately $3.1 billion to Arch Capital during the remainder of 2022 without providing an affidavit to the Bermuda Monetary Authority.

We expect that our liquidity needs, including our anticipated (re)insurance obligations and operating and capital expenditure needs, for at least the next twelve months and thereafter for the forseable future, will be met by funds generated from underwriting activities and investment income, as well as by our balance of cash, short-term investments, proceeds on the sale or maturity of our investments, and our credit facilities. On April 7, 2022 Arch Capital and certain of its subsidiaries amended the existing credit agreement. For details on our credit agreement, see note 10, “Commitments and Contingencies” to our consolidated financial statements.

Cash Flows

The following table summarizes our cash flows from operating, investing and financing activities.

			Nine Months Ended
			September 30,
			2022						2021
Total cash provided by (used for):
Operating activities			$	2,833,717					$	2,580,697
Investing activities			(2,106,721)						(1,184,436)
Financing activities			(703,877)						(895,943)
Effects of exchange rate changes on foreign currency cash			(79,566)						(30,501)
Increase (decrease) in cash and restricted cash			$	(56,447)					$	469,817

• Cash provided by operating activities for the nine months ended September 30, 2022 primarily reflected a higher level premium volume than in the 2021 period.

• Cash used for investing activities for the nine months ended September 30, 2022 was higher than in the 2021 period. Activity for the 2022 period reflected a lower level of proceeds from sales and redemptions of fixed

income securities. Activity for the 2021 period reflected cash used to invest in Coface and Somers.

• Cash used for financing activities for the nine months ended September 30, 2022 reflected $585.8 million of repurchases under our share repurchase program. Activity for the 2021 period, reflected $872.2 million of repurchases under our share repurchase program.

CAPITAL RESOURCES

The following table provides an analysis of our capital structure:

(U.S. dollars in thousands, except share data)			September 30, 2022						December 31, 2021
Senior notes			$	2,725,153					$	2,724,394
Shareholders’ equity available to Arch:
Series F non-cumulative preferred shares			330,000						330,000
Series G non-cumulative preferred shares			500,000						500,000
Common shareholders’ equity			10,965,110						12,715,896
Total			$	11,795,110					$	13,545,896
Total capital available to Arch			$	14,520,263					$	16,270,290
Debt to total capital (%)			18.8						16.7
Preferred to total capital (%)			5.7						5.1
Debt and preferred to total capital (%)			24.5						21.8

Arch MI U.S. is required to maintain compliance with the GSEs requirements, known as the Private Mortgage Insurer Eligibility Requirements or “PMIERs.” The financial requirements require an eligible mortgage insurer’s available assets, which generally include only the most liquid assets of an insurer, to meet or exceed “minimum required assets” as of each quarter end. Minimum required assets are calculated from PMIERs tables with several risk dimensions (including origination year, original loan-to-value and original credit score of performing loans, and the delinquency status of non-performing loans) and are subject to a minimum amount. Arch MI U.S. satisfied the PMIERs’ financial requirements as of September 30, 2022 with an estimated PMIER sufficiency ratio of 237%, compared to 197% at December 31, 2021.

Arch Capital, through its subsidiaries, provides financial support to certain of its insurance subsidiaries and affiliates, through certain reinsurance arrangements beneficial to the ratings of such subsidiaries. Historically, our insurance, reinsurance and mortgage insurance subsidiaries have entered into separate reinsurance arrangements with Arch Re Bermuda covering individual lines of business.

ARCH CAPITAL			61			2022 THIRD QUARTER FORM 10-Q

GUARANTOR INFORMATION

The below table provides a description of our senior notes payable at September 30, 2022:

						Interest						Principal						Carrying
Issuer/Due						(Fixed)						Amount						Amount
Arch Capital:
May 1, 2034						7.350		%				$	300,000					$	297,585
June 30, 2050						3.635		%				1,000,000						988,891
Arch-U.S.:
Nov. 1, 2043 (1)						5.144		%				500,000						495,156
Arch Finance:
Dec. 15, 2026 (1)						4.011		%				500,000						497,962
Dec. 15, 2046 (1)						5.031		%				450,000						445,559
Total												$	2,750,000					$	2,725,153

(1)Fully and unconditionally guaranteed by Arch Capital.

Our senior notes were issued by Arch Capital, Arch Capital Group (U.S.) Inc. (“Arch-U.S.”) and Arch Capital Finance LLC (“Arch Finance”). Arch-U.S. is a wholly-owned subsidiary of Arch Capital and Arch Finance is a wholly-owned finance subsidiary of Arch-U.S. Our 2034 senior notes and 2050 senior notes issued by Arch Capital are unsecured and unsubordinated obligations of Arch Capital and ranked equally with all of its existing and future unsecured and unsubordinated indebtedness. The 2043 senior notes issued by Arch-U.S. are unsecured and unsubordinated obligations of Arch-U.S. and Arch Capital and rank equally and ratably with the other unsecured and unsubordinated indebtedness of Arch-U.S. and Arch Capital. The 2026 senior notes and 2046 senior notes issued by Arch Finance are unsecured and unsubordinated obligations of Arch Finance and Arch Capital and rank equally and ratably with the other unsecured and unsubordinated indebtedness of Arch Finance and Arch Capital.

Arch-U.S. and Arch Finance depend on their available cash resources, liquid investments and dividends or other distributions from their subsidiaries or affiliates to make payments, including the payment of debt service obligations and operating expenses they may incur.

The following tables present condensed financial information for Arch Capital (parent guarantor) and Arch-U.S. (subsidiary issuer):

			September 30, 2022
			Arch Capital						Arch-U.S.
Assets
Total investments			$	47,722					$	169,143
Cash			12,798						7,463
Investment in operating affiliates			5,448						—
Due from subsidiaries and affiliates			1,485						15
Other assets			7,437						29,346
Total assets			$	74,890					$	205,967
Liabilities
Senior notes			1,286,476						495,156
Due to subsidiaries and affiliates			1,838						507,103
Other liabilities			36,038						41,580
Total liabilities			$	1,324,352					$	1,043,839
Non-cumulative preferred shares			$	830,000					—

									December 31, 2021
															Arch Capital						Arch-U.S.
Assets
Total investments															$	2,038					$	137,124
Cash															16,317						18,392
Investment in operating affiliates															6,877						—
Due from subsidiaries and affiliates															—						26,000
Other assets															9,615						37,040
Total assets															$	34,847					$	218,556
Liabilities
Senior notes															1,286,208						495,063
Due to subsidiaries and affiliates															—						521,839
Other liabilities															24,767						47,410
Total liabilities															$	1,310,975					$	1,064,312
Non-cumulative preferred shares															$	830,000					—

									September 30, 2022
Nine Months Ended									Arch Capital						Arch-U.S.
Revenues
Net investment income															$	1,349					$	600
Net realized gains (losses)															23						(338)
Equity in net income (loss) of investments accounted for using the equity method															—						6,913
Total revenues															1,372						7,175
Expenses
Corporate expenses															70,048						10,882
Interest expense															44,068						35,328
Total expenses															114,116						46,210
Income (loss) before income taxes and income (loss) from operating affiliates															(112,744)						(39,035)
Income tax (expense) benefit															—						7,918
Income (loss) from operating affiliates															(758)						—
Net income available to Arch															(113,502)						(31,117)
Preferred dividends															(30,552)						—
Net income (loss) available to Arch common shareholders															$	(144,054)					$	(31,117)

ARCH CAPITAL			62			2022 THIRD QUARTER FORM 10-Q

															December 31, 2021
Year Ended																					Arch Capital						Arch-U.S.
Revenues
Net investment income																											1,524						11,596
Net realized gains (losses)																											—						72,437
Equity in net income (loss) of investments accounted for using the equity method																											—						18,149
Total revenues																											1,524						102,182
Expenses
Corporate expenses																											71,818						5,875
Interest expense																											58,741						47,292
Net foreign exchange (gains) losses																											7						—
Total expenses																											130,566						53,167
Income (loss) before income taxes and income (loss) from operating affiliates																											(129,042)						49,015
Income tax (expense) benefit																											—						(12,513)
Income (loss) from operating affiliates																											(590)						—
Net income available to Arch																											(129,632)						36,502
Preferred dividends																											(48,343)						—
Loss on redemption of preferred shares																											(15,101)						—
Net income (loss) available to Arch common shareholders																											$	(193,076)					$	36,502

SHARE REPURCHASE PROGRAM

The board of directors of Arch Capital has authorized the investment in Arch Capital’s common shares through a share repurchase program. For the nine months ended September 30, 2022, Arch Capital repurchased 12.9 million shares under the share repurchase program with an aggregate purchase price of $585.8 million. Since the inception of the share repurchase program through September 30, 2022, Arch Capital has repurchased 433.6 million common shares for an aggregate purchase price of $5.9 billion. At September 30, 2022, approximately $596.4 million of share repurchases were available under the program. The timing and amount of the repurchase transactions under this program will depend on a variety of factors, including market conditions and corporate and regulatory considerations. We will continue to monitor our share price and, depending upon results of operations, market conditions and the development of the economy, as well as other factors, we will consider share repurchases on an opportunistic basis.

CATASTROPHIC EVENTS AND SEVERE ECONOMIC EVENTS

We have large aggregate exposures to natural and man-made catastrophic events, pandemic events like COVID-19 and severe economic events. Natural catastrophes can be caused by various events, including hurricanes, floods, windstorms, earthquakes, hailstorms, tornadoes, explosions, severe winter weather, fires, droughts and other natural disasters. Man-made catastrophic events may include acts of war, acts of terrorism and political instability. Catastrophes can also cause

losses in non-property business such as mortgage insurance, workers’ compensation or general liability. In addition to the nature of property business, we believe that economic and geographic trends affecting insured property, including inflation, property value appreciation and geographic concentration, tend to generally increase the size of losses from catastrophic events over time.

Our models employ both proprietary and vendor-based systems and include cross-line correlations for property, marine, offshore energy, aviation, workers compensation and personal accident. We seek to limit the probable maximum pre-tax loss to a specific level for severe catastrophic events. Currently, we seek to limit our 1-in-250 year return period net probable maximum loss from a severe catastrophic event in any geographic zone to approximately 25% of tangible shareholders’ equity available to Arch (total shareholders’ equity available to Arch less goodwill and intangible assets). We reserve the right to change this threshold at any time.

Based on in-force exposure estimated as of October 1, 2022, our modeled peak zone catastrophe exposure was a windstorm affecting the Florida Tri-County, with a net probable maximum pre-tax loss of $851 million, followed by windstorms affecting the Gulf of Mexico and the Northeastern U.S. regions with net probable maximum pre-tax losses of $748 and $747 million, respectively. Our exposures to other perils, such as U.S. earthquake and international events, were less than the exposures arising from U.S. windstorms and hurricanes. As of October 1, 2022, our modeled peak zone earthquake exposure (San Francisco earthquake) represented approximately 69% of our peak zone catastrophe exposure, and our modeled peak zone international exposure (UK windstorm) was substantially less than both our peak zone windstorm and earthquake exposures.

We also have significant exposure to losses due to mortgage defaults resulting from severe economic events in the future. For our U.S. mortgage insurance business, we have developed a proprietary risk model (“Realistic Disaster Scenario” or “RDS”) that simulates the maximum loss resulting from a severe economic downturn impacting the housing market. The RDS models the collective impact of adverse conditions for key economic indicators, the most significant of which is a decline in home prices. The RDS model projects paths of future home prices, unemployment rates, income levels and interest rates and assumes correlation across states and geographic regions. The resulting future performance of our in-force portfolio is then estimated under the economic stress scenario, reflecting loan and borrower information.

Currently, we seek to limit our modeled RDS loss from a severe economic event to approximately 25% of tangible shareholders’ equity available to Arch. We reserve the right to change this threshold at any time. Based on in-force

ARCH CAPITAL			63			2022 THIRD QUARTER FORM 10-Q

exposure estimated as of October 1, 2022, our modeled RDS loss was approximately 10% of tangible shareholders’ equity available to Arch.

Net probable maximum loss estimates are net of expected reinsurance recoveries, before income tax and before excess reinsurance reinstatement premiums. RDS loss estimates are net of expected reinsurance recoveries and before income tax. Catastrophe loss estimates are reflective of the zone indicated and not the entire portfolio. Since hurricanes and windstorms can affect more than one zone and make multiple landfalls, our catastrophe loss estimates include clash estimates from other zones. Our catastrophe loss estimates and RDS loss estimates do not represent our maximum exposures and it is highly likely that our actual incurred losses would vary materially from the modeled estimates. There can be no assurances that we will not suffer pre-tax losses greater than 25% of our tangible shareholders’ equity from one or more catastrophic events or severe economic events due to several factors. These factors include the inherent uncertainties in estimating the frequency and severity of such events and the margin of error in making such determinations resulting from potential inaccuracies and inadequacies in the data provided by clients and brokers, the modeling techniques and the application of such techniques or as a result of a decision to change the percentage of shareholders' equity exposed to a single catastrophic event or severe economic event. In addition, actual losses may increase if our reinsurers fail to meet their obligations to us or the reinsurance protections purchased by us are exhausted or are otherwise unavailable. See “Risk Factors—Risks Relating to Our Industry” and “Management’s Discussion and Analysis of Financial Condition and Results of Operations—Catastrophic Events and Severe Economic Events” in our 2021 Form 10-K.

MARKET SENSITIVE INSTRUMENTS AND RISK MANAGEMENT

In accordance with the SEC’s Financial Reporting Release No. 48, we performed a sensitivity analysis to determine the effects that market risk exposures could have on the future earnings, fair values or cash flows of our financial instruments as of September 30, 2022. Market risk represents the risk of changes in the fair value of a financial instrument and is comprised of several components, including liquidity, basis and price risks.

An analysis of material changes in market risk exposures at September 30, 2022 that affect the quantitative and qualitative disclosures presented in our 2021 Form 10-K (see section captioned “Management’s Discussion and Analysis of Financial Condition and Results of Operations—Market Sensitive Instruments and Risk Management”) were as follows:

Investment Market Risk

Fixed Income Securities. We invest in interest rate sensitive securities, primarily debt securities. We consider the effect of interest rate movements on the fair value of our fixed maturities, short-term investments and certain of our other investments, equity securities and investment funds accounted for using the equity method which invest in fixed income securities (collectively, “Fixed Income Securities”) and the corresponding change in unrealized appreciation. As interest rates rise, the fair value of our Fixed Income Securities falls, and the converse is also true. Based on historical observations, there is a low probability that all interest rate yield curves would shift in the same direction at the same time. Furthermore, at times interest rate movements in certain credit sectors exhibit a much lower correlation to changes in U.S. Treasury yields. Accordingly, the actual effect of interest rate movements may differ materially from the amounts set forth in the following tables.

The following table summarizes the effect that an immediate, parallel shift in the interest rate yield curve would have had on our Fixed Income Securities:

(U.S. dollars in billions)			Interest Rate Shift in Basis Points
-100						-50						—						+50						+100
September 30, 2022
Total fair value			$	25.75					$	25.40					$	25.05					$	24.70					$	24.37
Change from base			2.8		%				1.4		%										(1.4)		%				(2.7)		%
Change in unrealized value			$	0.70					$	0.35											$	(0.35)					$	(0.68)
December 31, 2021
Total fair value			$	25.79					$	25.44					$	25.21					$	24.75					$	24.43
Change from base			2.3		%				0.9		%										(1.8)		%				(3.1)		%
Change in unrealized value			$	0.58					$	0.23											$	(0.45)					$	(0.78)

In addition, we consider the effect of credit spread movements on the market value of our Fixed Income Securities and the corresponding change in unrealized value. As credit spreads widen, the fair value of our Fixed Income Securities falls, and the converse is also true. In periods where the spreads on our Fixed Income Securities are much higher than their historical average due to short-term market dislocations, a parallel shift in credit spread levels would result in a much more pronounced change in unrealized value.

ARCH CAPITAL			64			2022 THIRD QUARTER FORM 10-Q

The following table summarizes the effect that an immediate, parallel shift in credit spreads in a static interest rate environment would have had on our Fixed Income Securities:

(U.S. dollars in billions)			Credit Spread Shift in Percentage Points
-100						-50						—						+50						+100
September 30, 2022
Total fair value			$	26.03					$	25.54					$	25.05					$	24.56					$	24.07
Change from base			3.9		%				2.0		%										(2.0)		%				(3.9)		%
Change in unrealized value			$	0.98					$	0.49											$	(0.49)					$	(0.98)
December 31, 2021
Total fair value			$	26.17					$	25.69					$	25.21					$	24.72					$	24.24
Change from base			3.8		%				1.9		%										(1.9)		%				(3.8)		%
Change in unrealized value			$	0.97					$	0.48											$	(0.48)					$	(0.97)

Another method that attempts to measure portfolio risk is Value-at-Risk (“VaR”). VaR measures the worst expected loss under normal market conditions over a specific time interval at a given confidence level. The 1-year 95th percentile parametric VaR reported herein estimates that 95% of the time, the portfolio loss in a one-year horizon would be less than or equal to the calculated number, stated as a percentage of the measured portfolio’s initial value. The VaR is a variance-covariance based estimate, based on linear sensitivities of a portfolio to a broad set of systematic market risk factors and idiosyncratic risk factors mapped to the portfolio exposures. The relationships between the risk factors are estimated using historical data, and the most recent data points are generally given more weight. As of September 30, 2022, our portfolio’s VaR was estimated to be 7.9% compared to an estimated 4.8% at December 31, 2021. In periods where the volatility of the risk factors mapped to our portfolio’s exposures is higher due to market conditions, the resulting VaR is higher than in other periods.

Equity Securities. At September 30, 2022 and December 31, 2021, the fair value of our investments in equity securities and certain investments accounted for using the equity method with underlying equity strategies totaled $0.8 billion and $1.4 billion, respectively. These investments are exposed to price risk, which is the potential loss arising from decreases in fair value. An immediate hypothetical 10% decline in the value of each position would reduce the fair value of such investments by approximately $81.9 million and $137.5 million at September 30, 2022 and December 31, 2021, respectively, and would have decreased book value per share by approximately $0.22 and $0.36, respectively. An immediate hypothetical 10% increase in the value of each position would increase the fair value of such investments by approximately $81.9 million and $137.5 million at September 30, 2022 and December 31, 2021, respectively, and would have increased book value per share by approximately $0.22 and $0.36, respectively.

Investment-Related Derivatives. At September 30, 2022, the notional value of all derivative instruments (excluding foreign currency forward contracts which are included in the foreign currency exchange risk analysis below) was $5.9 billion, compared to $6.4 billion at December 31, 2021. If the underlying exposure of each investment-related derivative held at September 30, 2022 depreciated by 100 basis points, it would have resulted in a reduction in net income of approximately $58.6 million, and a decrease in book value per share of approximately $0.16 per share, compared to $63.8 million and $0.17 per share, respectively, on investment-related derivatives held at December 31, 2021. If the underlying exposure of each investment-related derivative held at September 30, 2022 appreciated by 100 basis points, it would have resulted in an increase in net income of approximately $58.6 million, and an increase in book value per share of approximately $0.16 per share, compared to $63.8 million and $0.17 per share, respectively, on investment-related derivatives held at December 31, 2021. See note 9, “Derivative Instruments,” to our consolidated financial statements for additional disclosures concerning derivatives.

For further discussion on investment activity, please refer to “Financial Condition—Investable Assets.”

ARCH CAPITAL			65			2022 THIRD QUARTER FORM 10-Q

Foreign Currency Exchange Risk

Foreign currency rate risk is the potential change in value, income and cash flow arising from adverse changes in foreign currency exchange rates. Through our subsidiaries and branches located in various foreign countries, we conduct our insurance and reinsurance operations in a variety of local currencies other than the U.S. Dollar. We generally hold investments in foreign currencies which are intended to mitigate our exposure to foreign currency fluctuations in our net insurance liabilities. We may also utilize foreign currency forward contracts and currency options as part of our investment strategy. See note 9, “Derivative Instruments,” to our consolidated financial statements for additional information.

The following table provides a summary of our net foreign currency exchange exposures, as well as foreign currency derivatives in place to manage these exposures:

(U.S. dollars in thousands, except per share data)			September 30, 2022						December 31, 2021
Net assets (liabilities), denominated in foreign currencies, excluding shareholders’ equity and derivatives			$	(366,136)					$	(825,371)
Shareholders’ equity denominated in foreign currencies (1)			978,889						1,095,706
Net foreign currency forward contracts outstanding (2)			8,369						15,151
Net exposures denominated in foreign currencies			$	621,122					$	285,486
Pre-tax impact of a hypothetical 10% appreciation of the U.S. Dollar against foreign currencies:
Shareholders’ equity			$	(62,112)					$	(28,549)
Book value per share			$	(0.17)					$	(0.08)
Pre-tax impact of a hypothetical 10% decline of the U.S. Dollar against foreign currencies:
Shareholders’ equity			$	62,112					$	28,549
Book value per share			$	0.17					$	0.08

(1) Represents capital contributions held in the foreign currencies of our operating units.

(2) Represents the net notional value of outstanding foreign currency forward contracts.

Although we generally attempt to match the currency of our projected liabilities with investments in the same currencies, from time to time we may elect to over or underweight one or more currencies, which could increase our exposure to foreign currency fluctuations and increase the volatility of our shareholders’ equity. Historical observations indicate a low probability that all foreign currency exchange rates would shift against the U.S. Dollar in the same direction and at the same time and, accordingly, the actual effect of foreign currency rate movements may differ materially from the

amounts set forth above. For further discussion on foreign exchange activity, please refer to “Results of Operations.”

Effects of Inflation

General economic inflation has increased in recent quarters and may continue to remain at elevated levels for an extended period of time. The potential also exists, after a catastrophe loss or pandemic events like COVID-19, for the development of inflationary pressures in a local economy. This may have a material effect on the adequacy of our reserves for losses and loss adjustment expenses, especially in longer-tailed lines of business, and on the market value of our investment portfolio through rising interest rates. The anticipated effects of inflation are considered in our pricing models, reserving processes and exposure management, across all lines of business and types of loss including natural catastrophe events. The actual effects of inflation on our results cannot be accurately known until claims are ultimately settled and will vary by the specific type of inflation affecting each line of business.

OTHER FINANCIAL INFORMATION

The consolidated financial statements as of September 30, 2022 have been reviewed by PricewaterhouseCoopers LLP, the registrant's independent public accountants, whose report is included as an exhibit to this filing. The report of PricewaterhouseCoopers LLP states that they did not audit and they do not express an opinion on that unaudited financial information. Accordingly, the degree of reliance on their report on such information should be restricted in light of the limited nature of the review procedures applied. PricewaterhouseCoopers LLP is not subject to the liability provisions of Section 11 of the Securities Act of 1933 for their report on the unaudited financial information because that report is not a "report" or a "part" of the registration statement prepared or certified by PricewaterhouseCoopers LLP within the meaning of Sections 7 and 11 of the Securities Act of 1933.