The following is a discussion and analysis of our financial condition and
results of operations. This should be read in conjunction with our consolidated
financial statements included in Item 1 of this report and also our Management's
Discussion and Analysis of Financial Condition and Results of Operations
contained in our Annual Report on Form 10-K for the year ended December 31, 2020
("2020 Form 10-K"). In addition, readers should review "Risk Factors" set forth
in Item 1A of Part I of our 2020 Form 10-K and   "ITEM 1A-Risk Factors"   of
this Form 10-Q. Tabular amounts are in U.S. Dollars in thousands, except share
amounts, unless otherwise noted.
Arch Capital Group Ltd. ("Arch Capital" and, together with its subsidiaries,
"Arch", "we" or "us") is a publicly listed Bermuda exempted company with
approximately $16.7 billion in capital at June 30, 2021 and, through operations
in Bermuda, the United States, Europe, Canada, Australia and Hong Kong, writes
insurance, reinsurance and mortgage insurance on a worldwide basis.
CURRENT OUTLOOK


Our three primary areas of focus for 2021 are to continue our growth in the
sectors where rates allow for returns that are substantially more than our cost
of capital, to optimize our mortgage insurance book as it transitions from
forbearance to recovery on its way back to normalcy in the next few quarters,
and to actively manage our investments and capital to enhance our returns over
the long run.
From an operating perspective, the 2021 second quarter reflected the benefits of
attractive pricing in almost all of our insurance markets. As a result, we
currently expect the next several quarters to continue to show improved
underwriting margins, partially due to the compounding of rate-on-rate increases
and the rebalancing of our mix of business. Importantly, the market is showing
discipline in maintaining its momentum. We believe that this time-tested
strategy of protecting capital through soft markets and writing business
aggressively 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.
Consequently, these rate improvements have enabled us to continue to expand
writings in our property casualty segments. We are now in the sixth consecutive
quarter of rate increases with a weighted increase of approximately 10% this
quarter, comfortably in excess of loss cost trends. Premiums increased across
most lines of business and geographic areas
as pricing improvements spread and, while rate increases have tapered off from
previous highs in some lines, our insurance segment is seeing increases in lines
that had been resistant to meaningful change.
In reinsurance, strong growth was observed across most of our lines of business,
but especially in our casualty and other specialty lines where strong rates
increases and growth in new accounts helped increase the top line. Consistent
with our insurance segment, we expect the ongoing rate improvements to be
reflected in our underwriting results over the next several quarters.
For our U.S. primary mortgage operations, reported delinquencies were 3.11% at
June 30, 2021, roughly 40% lower than it was at the end of the 2020 second
quarter. Delinquencies continue to be better than our expectations at the
beginning of the COVID-19 pandemic but delinquency rates remain at elevated
levels, reflecting the impact of the recession and forbearance programs under
the CARES Act to borrowers experiencing a hardship. Forbearance allows for
mortgage payments to be suspended for up to 360 days or longer along with a
suspension of foreclosures and evictions. See "Results of Operations-Mortgage
Segment" for further details on our mortgage operations.
In the second quarter, our U.S. primary mortgage operations insurance in force
remained steady at approximately $278 billion and $422 billion for the total
mortgage segment. The refinancing boom that began last year has slowed and we
expect improving persistency through remainder of the year.
Outside of the U.S., we increased our writings in Australia as the housing
market remains strong there. We like the long-term opportunity in Australia as
demonstrated by our announcement in March to acquire Westpac's LMI business. The
agreement allows us to free up capital even as we build our Australian presence
and diversify our earning streams at attractive risk-adjusted returns.
We remain committed to providing solutions across many offerings as the
marketplace evolves, including the mortgage credit risk transfer programs
initiated by government sponsored enterprises, or "GSEs." In addition, we enter
into aggregate excess of loss mortgage reinsurance agreements with various
special purpose reinsurance companies domiciled in Bermuda and issue mortgage
insurance linked notes, increasing our protection for mortgage tail risk. The
Bellemeade structures provide approximately $4.7 billion of aggregate
reinsurance coverage at June 30, 2021.

ARCH CAPITAL 43 2021 SECOND QUARTER FORM 10-Q

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FINANCIAL MEASURES


Management uses the following three key financial indicators in evaluating our
performance and measuring the overall growth in value generated for Arch
Capital's common shareholders:
Book Value per Share
Book value per share represents total common shareholders' equity available to
Arch divided by the number of common shares outstanding. Management uses growth
in book value per share as a key measure of the value generated for our common
shareholders each period and believes that book value per share is the key
driver of Arch Capital's share price over time. Book value per share is impacted
by, among other factors, our underwriting results, investment returns and share
repurchase activity, which has an accretive or dilutive impact on book value per
share depending on the purchase price.
Book value per share was $32.02 at June 30, 2021, compared to $30.54 at March
31, 2021 and $27.62 at June 30, 2020. The 4.8% increase in book value per share
for the 2021 second quarter and 15.9% increase in book value per share over the
trailing twelve months reflected strong underwriting results and investment
returns.
Operating Return on Average Common Equity
Operating return on average common equity ("Operating ROAE") represents
annualized after-tax operating income available to Arch common shareholders
divided by the average of beginning and ending common shareholders' equity
available to Arch during the period. After-tax operating income available to
Arch common shareholders, a non-GAAP financial measure as defined in Regulation
G, represents net income available to Arch common shareholders, excluding net
realized gains or losses (which includes changes in the allowance for credit
losses on financial assets and net impairment losses recognized in earnings)
equity in net income or loss of investment funds accounted for using the equity
method, net foreign exchange gains or losses, transaction costs and other and
income taxes. Management uses Operating ROAE as a key measure of the return
generated to common shareholders. See "Comment on Non-GAAP Financial Measures."
Our Operating ROAE was 13.0% for the 2021 second quarter, compared to 0.6% for
the 2020 second quarter, and 10.3% for the six months ended June 30, 2021,
compared to 3.8% for the 2020 period. The higher 2021 period results, reflected
strong underwriting returns and a one-time gain of $74.5 million realized during
the 2021 first quarter from our acquisition of 29.5% stake in Coface, while the
2020 period
reflected the impact of COVID-19 on the underwriting results.
Total Return on Investments
Total return on investments includes investment income, equity in net income or
loss of investment funds accounted for using the equity method, net realized
gains and losses (excluding changes in the allowance for credit losses on
non-investment related financial assets) and the change in unrealized gains and
losses generated by Arch's investment portfolio. Total return is calculated on a
pre-tax basis and before investment expenses, excludes amounts reflected in the
'other' segment, and reflects the effect of financial market conditions along
with foreign currency fluctuations. In addition, total return incorporates the
timing of investment returns during the periods. The following table summarizes
our total return compared to the benchmark return against which we measured our
portfolio during the periods. See "Comment on Non-GAAP Financial Measures."
                                      Arch         Benchmark
                                    Portfolio       Return

Pre-tax total return (before investment expenses): 2021 Second Quarter

                    1.58  %        1.80  %
2020 Second Quarter                    3.72  %        6.06  %

Six Months Ended June 30, 2021 1.39 % 1.28 % Six Months Ended June 30, 2020 2.82 % 1.23 %





Total return for the 2021 second quarter reflected movements in interest rates
and credit spreads on our fixed income portfolio. We continue to maintain a
short duration on our portfolio of 2.31 years at June 30, 2021.
The benchmark return index is a customized combination of indices intended to
approximate a target portfolio by asset mix and average credit quality while
also matching the approximate estimated duration and currency mix of our
insurance and reinsurance liabilities. Although the estimated duration and
average credit quality of this index will move as the duration and rating of its
constituent securities change, generally we do not adjust the composition of the
benchmark return index except to incorporate changes to the mix of liability
currencies and durations noted above. The benchmark return index should not be
interpreted as expressing a preference for or aversion to any particular sector
or sector weight. The index is intended solely to provide, unlike many master
indices that change based on the size of their constituent indices, a relatively
stable basket of investable indices. At June 30, 2021, the benchmark return
index had an average credit quality of "Aa2" by Moody's Investors Service
("Moody's"), and an estimated duration of 3.13 years.
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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 and income taxes, and the use of
annualized operating return on average common equity. The presentation of
after-tax operating income available to Arch common shareholders and annualized
operating return on average common equity are non-GAAP financial measures as
defined in Regulation G. The reconciliation of such measures to net income
available to Arch common shareholders and annualized return on average common
equity (the most directly comparable
GAAP financial measures) in accordance with Regulation G is included under
"Results of Operations" below.
We believe that net realized gains or losses, equity in net income or loss of
investment funds accounted for using the equity method, net foreign exchange
gains or losses and transaction costs and other in any particular period are not
indicative of the performance of, or trends in, our business. Although net
realized gains or losses, equity in net income or loss of investment funds
accounted for using the equity method and net foreign exchange gains or losses
are an integral part of our operations, the decision to realize investment gains
or losses, the recognition of the change in the carrying value of investments
accounted for using the fair value option in net realized gains or losses, the
recognition of net impairment losses, the recognition of equity in net income or
loss of investment funds accounted for using the equity method and the
recognition of foreign exchange gains or losses are independent of the insurance
underwriting process and result, in large part, from general economic and
financial market conditions. Furthermore, certain users of our financial
information believe that, for many companies, the timing of the realization of
investment gains or losses is largely opportunistic. In addition, changes in the
allowance for credit losses and net impairment losses recognized in earnings on
the Company's investments represent other-than-temporary declines in expected
recovery values on securities without actual realization. The use of the equity
method on certain of our investments in certain funds that invest in fixed
maturity securities is driven by the ownership structure of such funds (either
limited partnerships or limited liability companies). In applying the equity
method, these investments are initially recorded at cost and are subsequently
adjusted based on our proportionate share of the net income or loss of the funds
(which include changes in the market value of the underlying securities in the
funds). This method of accounting is different from the way we account for our
other fixed maturity securities and the timing of the recognition of equity in
net income or loss of investment funds accounted for using the equity method may
differ from gains or losses in the future upon sale or maturity of such
investments. Transaction costs and other include advisory, financing, legal,
severance, incentive compensation and other transaction costs related to
acquisitions. We believe that transaction costs and other, due to their
non-recurring nature, are not indicative of the performance of, or trends in,
our business performance. Due to these reasons, we exclude net realized gains or
losses, equity in net income or loss of investment funds accounted for using the
equity method, net foreign exchange gains or losses and transaction costs and
other from the calculation of after-tax operating income available to Arch
common shareholders.
We believe that showing net income available to Arch common shareholders
exclusive of the items referred to above reflects the underlying fundamentals of
our business
ARCH CAPITAL     45     2021 SECOND QUARTER FORM 10-Q


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since we evaluate the performance of and manage our business to produce an
underwriting profit. In addition to presenting net income available to Arch
common shareholders, we believe that this presentation enables investors and
other users of our financial information to analyze our performance in a manner
similar to how management analyzes performance. We also believe that this
measure follows industry practice and, therefore, allows the users of financial
information to compare our performance with our industry peer group. We believe
that the equity analysts and certain rating agencies which follow us and the
insurance industry as a whole generally exclude these items from their analyses
for the same reasons.
Our segment information includes the presentation of consolidated underwriting
income or loss and a subtotal of underwriting income or loss before the
contribution from the 'other' segment. Such measures represent the pre-tax
profitability of our underwriting operations and include net premiums earned
plus other underwriting income, less losses and loss adjustment expenses,
acquisition expenses and other operating expenses. Other operating expenses
include those operating expenses that are incremental and/or directly
attributable to our individual underwriting operations. Underwriting income or
loss does not incorporate items included in our corporate (non-underwriting)
segment. While these measures are presented in   note 4, "Segment
Information,"   of the notes accompanying our consolidated financial statements,
they are considered non-GAAP financial measures when presented elsewhere on a
consolidated basis. The reconciliations of underwriting income or loss to income
before income taxes (the most directly comparable GAAP financial measure) on a
consolidated basis and a subtotal before the contribution from the 'other'
segment, in accordance with Regulation G, is shown in   note 4, "Segment
Information"   to our consolidated financial statements.

We measure segment performance for our three underwriting segments based on underwriting income or loss. We do not manage our assets by underwriting segment, with the exception of goodwill and intangibles and, accordingly, investment income and other non-underwriting related items are not allocated to each underwriting segment. For the 'other' segment, performance is measured based on net income or loss.



Along with consolidated underwriting income, we provide a subtotal of
underwriting income or loss before the contribution from the 'other' segment.
Through June 30, 2021, the 'other' segment included the results of Watford
Holdings Ltd. Watford Holdings Ltd. is the parent of Watford Re Ltd., a
multi-line Bermuda reinsurance company (together with Watford Holdings Ltd.,
"Watford"). Pursuant to GAAP, Watford was considered a variable interest entity
and we
concluded that we are the primary beneficiary of Watford. As such, we
consolidated the results of Watford in our consolidated financial statements
through June 30, 2021, although we only owned approximately 10% of Watford's
common equity. Watford's own management and board of directors are responsible
for its results and profitability. In addition, we do not guarantee or provide
credit support for Watford. Since Watford is an independent company, the assets
of Watford can be used only to settle obligations of Watford and Watford is
solely responsible for its own liabilities and commitments. Our financial
exposure to Watford is limited to our investment in Watford's senior notes,
common and preferred shares and counterparty credit risk (mitigated by
collateral) arising from the reinsurance transactions. We believe that
presenting certain information excluding the 'other' segment enables investors
and other users of our financial information to analyze our performance in a
manner similar to how our management analyzes performance. See   note 11,
"Variable Interest Entities and Noncontrolling Interests,"     note 4, "Segment
Information,"   and   Note 16, "Subsequent Event,"   to our consolidated
financial statements for additional information on Watford.

Our presentation of segment information includes the use of a current year loss
ratio which excludes favorable or adverse development in prior year loss
reserves. This ratio is a non-GAAP financial measure as defined in Regulation G.
The reconciliation of such measure to the loss ratio (the most directly
comparable GAAP financial measure) in accordance with Regulation G is shown on
the individual segment pages. Management utilizes the current year loss ratio in
its analysis of the underwriting performance of each of our underwriting
segments.
Total return on investments includes investment income, equity in net income or
loss of investment funds accounted for using the equity method, net realized
gains and losses (excluding changes in the allowance for credit losses on
non-investment related financial assets) and the change in unrealized gains and
losses generated by Arch's investment portfolio. Total return is calculated on a
pre-tax basis and before investment expenses, excludes amounts reflected in the
'other' segment, and reflects the effect of financial market conditions along
with foreign currency fluctuations. In addition, total return incorporates the
timing of investment returns during the periods. There is no directly comparable
GAAP financial measure for total return. Management uses total return on
investments as a key measure of the return generated to Arch common
shareholders, and compares the return generated by our investment portfolio
against benchmark returns during the periods.
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RESULTS OF OPERATIONS


The following table summarizes our consolidated financial data, including a
reconciliation of net income or loss available to Arch common shareholders to
after-tax operating income or loss available to Arch common shareholders. Each
line item reflects the impact of our percentage ownership of Watford's common
equity during such period.
                                         Three Months Ended                           Six Months Ended
                                              June 30,                                    June 30,
                                     2021                  2020                  2021                  2020
Net income available to Arch
common shareholders             $    663,820          $    288,418          $  1,091,573          $    422,132
Net realized (gains) losses         (167,438)             (406,645)             (272,989)             (297,281)

Equity in net (income) loss of
investment funds accounted for
using the equity method             (122,186)               65,119              (193,872)               69,328
Net foreign exchange (gains)
losses                                17,888                42,032                (3,444)              (22,459)
Transaction costs and other           (1,421)                  977                  (147)                3,572

Income tax expense (1)                16,553                26,713                25,864                31,078
After-tax operating income
available to Arch common
shareholders                    $    407,216          $     16,614

$ 646,985 $ 206,370



Beginning common shareholders'
equity                          $ 12,316,472          $ 10,587,244          $ 12,325,886          $ 10,717,371
Ending common shareholders'
equity                          $ 12,706,072          $ 11,211,825          $ 12,706,072          $ 11,211,825
Average common shareholders'
equity                          $ 12,511,272          $ 10,899,535

$ 12,515,979 $ 10,964,598



Annualized return on average
common equity %                         21.2                  10.6                  17.4                   7.7
Annualized operating return on
average
common equity %                         13.0                   0.6                  10.3                   3.8


(1) Income tax expense on net realized gains or losses, equity in net income or
loss of investment funds accounted for using the equity method, net foreign
exchange gains or losses and transaction costs and other reflects the relative
mix reported by jurisdiction and the varying tax rates in each jurisdiction.
Segment Information
We classify our businesses into three underwriting segments - insurance,
reinsurance and mortgage - and two other operating segments - corporate
(non-underwriting) and 'other.' Our insurance, reinsurance and mortgage segments
each have managers who are responsible for the overall profitability of their
respective segments and who are directly accountable to our chief operating
decision makers, the 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 June 30,
                                                                                 %
                                            2021                2020           Change
Gross premiums written                $    1,368,867       $ 1,030,362         32.9
Premiums ceded                              (405,312)         (358,101)
Net premiums written                         963,555           672,261         43.3
Change in unearned premiums                  (98,128)           15,648
Net premiums earned                          865,427           687,909         25.8

Losses and loss adjustment expenses         (545,880)         (518,203)
Acquisition expenses                        (136,852)         (107,671)
Other operating expenses                    (133,342)         (118,757)
Underwriting income (loss)            $       49,353       $   (56,722)       187.0

                                                                              % Point
Underwriting Ratios                                                            Change
Loss ratio                                      63.1  %           75.3  %     (12.2)
Acquisition expense ratio                       15.8  %           15.7  %       0.1
Other operating expense ratio                   15.4  %           17.3  %      (1.9)
Combined ratio                                  94.3  %          108.3  %     (14.0)



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                                                 Six Months Ended June 30,
                                           2021               2020          % Change
Gross premiums written                $  2,784,753       $ 2,238,007         24.4
Premiums ceded                            (826,359)         (736,998)
Net premiums written                     1,958,394         1,501,009         30.5
Change in unearned premiums               (273,493)          (97,181)
Net premiums earned                      1,684,901         1,403,828         20.0

Losses and loss adjustment expenses     (1,081,627)       (1,025,311)
Acquisition expenses                      (265,074)         (215,008)
Other operating expenses                  (270,455)         (248,406)
Underwriting income (loss)            $     67,745       $   (84,897)       179.8

                                                                             % Point
Underwriting Ratios                                                          Change
Loss ratio                                    64.2  %           73.0  %      (8.8)
Acquisition expense ratio                     15.7  %           15.3  %       0.4
Other operating expense ratio                 16.1  %           17.7  %      (1.6)
Combined ratio                                96.0  %          106.0  %     (10.0)


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 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 June 30,
                                                         2021                                            2020
                                             Amount                    %                    Amount                    %
Property, energy, marine and aviation  $       207,762                   21.6          $      159,801                   23.8
Professional lines                             254,961                   26.5                 157,899                   23.5
Programs                                       149,373                   15.5                 104,930                   15.6
Construction and national accounts              77,579                    8.1                  57,144                    8.5
Excess and surplus casualty                     74,346                    7.7                  64,703                    9.6
Travel, accident and health                     71,071                    7.4                  27,997                    4.2
Lenders products                                40,386                    4.2                  23,690                    3.5
Other                                           88,077                    9.1                  76,097                   11.3
Total                                  $       963,555                  100.0          $      672,261                  100.0


2021 Second Quarter versus 2020 Period. Gross premiums written by the insurance
segment in the 2021 second quarter were 32.9% higher than in the 2020 second
quarter, while net premiums written were 43.3% higher. The higher level of net
premiums written reflected increases across most lines of business, due in part
to rate increases, new business opportunities and growth in existing accounts.
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                                                        Six Months Ended June 30,
                                                    2021                          2020
                                             Amount            %           Amount           %
Property, energy, marine and aviation   $      378,260        19.3      $   287,386        19.1
Professional Lines                             493,207        25.2          327,017        21.8
Programs                                       307,774        15.7          217,462        14.5
Construction and national accounts             212,371        10.8          173,143        11.5
Excess and surplus casualty                    159,939         8.2          130,122         8.7
Travel, accident and health                    163,377         8.3          154,043        10.3
Lenders products                                75,246         3.8           56,982         3.8
Other                                          168,220         8.6          154,854        10.3
Total                                   $    1,958,394       100.0      $ 1,501,009       100.0


Six Months Ended June 30, 2021 versus 2020 period. Gross premiums written by the
insurance segment for the six months ended June 30, 2021 were 24.4% higher than
in the 2020 period, while net premiums written were 30.5% higher than in the
2020 period. The increase in net premiums written reflected growth across most
lines of business, due in part to rate increases, new business opportunities 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 June 30,
                                                         2021                                            2020
                                             Amount                    %                    Amount                    %
Property, energy, marine and aviation  $       167,716                   19.4          $      120,781                   17.6
Professional lines                             214,098                   24.7                 154,812                   22.5
Programs                                       118,974                   13.7                 108,464                   15.8
Construction and national accounts              95,849                   11.1                  91,605                   13.3
Excess and surplus casualty                     72,899                    8.4                  60,966                    8.9
Travel, accident and health                     62,610                    7.2                  52,117                    7.6
Lenders products                                46,396                    5.4                  23,111                    3.4
Other                                           86,885                   10.0                  76,053                   11.1
Total                                  $       865,427                  100.0          $      687,909                  100.0


                                                        Six Months Ended June 30,
                                                    2021                          2020
                                             Amount            %           Amount           %
Property, energy, marine and aviation   $      324,975        19.3      $   231,964        16.5
Professional Lines                             413,769        24.6          306,512        21.8
Programs                                       231,814        13.8          217,342        15.5
Construction and national accounts             198,520        11.8          191,305        13.6
Excess and surplus casualty                    148,266         8.8          126,063         9.0
Travel, accident and health                    112,276         6.7          129,492         9.2
Lenders products                                86,477         5.1           48,454         3.5
Other                                          168,804        10.0          152,696        10.9
Total                                   $    1,684,901       100.0      $ 1,403,828       100.0


Net premiums written are primarily earned on a pro rata basis over the terms of
the policies for all products, usually 12 months. Net premiums earned reflect
changes in net premiums written over the previous five quarters. Net premiums
earned in the 2021 second quarter were 25.8% higher than in the 2020 second
quarter. Net premiums earned for the six months ended June 30, 2021 were 20.0%
higher than in the 2020 period.
Losses and Loss Adjustment Expenses.
The table below shows the components of the insurance segment's loss ratio:
                                         Three Months Ended                 Six Months Ended
                                              June 30,                          June 30,
                                          2021              2020            2021             2020
Current year                                   63.6  %     75.7  %              64.7  %     73.3  %
Prior period reserve development               (0.5) %     (0.4) %              (0.5) %     (0.3) %
Loss ratio                                     63.1  %     75.3  %              64.2  %     73.0  %


Current Year Loss Ratio.
2021 Second Quarter versus 2020 Period. The insurance segment's current year
loss ratio in the 2021 second quarter was 12.1 points lower than in the 2020
second quarter. The 2021 second quarter loss ratio reflected 3.2 points of
current year catastrophic activity, primarily from winter storms Uri and Viola,
compared to 12.5 points of catastrophic activity for the 2020 second quarter,
which included exposure to the COVID-19 global pandemic. The insurance segment's
current year loss ratio for the six months ended June 30, 2021 was 8.6 points
lower than in the 2020 period and reflected 4.1 points of current year
catastrophic activity, compared to 9.6 points in the 2020 period. The balance of
the change in the 2021 loss ratios resulted, in part, from changes in mix of
business and the level of large attritional losses.
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Prior Period Reserve Development.
The insurance segment's net favorable development was $4.0 million, or 0.5
points, for the 2021 second quarter, compared to $2.5 million, or 0.4 points,
for the 2020 second quarter, and $8.1 million, or 0.5 points for the six months
ended June 30, 2021, compared to $3.6 million, or 0.3 points, for the 2020
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.
2021 Second Quarter versus 2020 Period. The insurance segment's underwriting
expense ratio was 31.2% in the 2021 second quarter, compared to 33.0% in the
2020 second quarter, with the decrease primarily due to growth in net premiums
earned.
Six Months Ended June 30, 2021 versus 2020 Period. The insurance segment's
underwriting expense ratio was 31.8% six months ended June 30, 2021, compared to
33.0% for the 2020 period, with the decrease primarily due to growth in net
premiums earned.
Reinsurance Segment
The following tables set forth our reinsurance segment's underwriting results:
                                                 Three Months Ended June 30,
                                                                                 %
                                             2021                2020          Change
Gross premiums written                $     1,358,020        $ 807,065         68.3
Premiums ceded                               (433,288)        (241,971)
Net premiums written                          924,732          565,094         63.6
Change in unearned premiums                  (187,708)         (84,897)
Net premiums earned                           737,024          480,197         53.5
Other underwriting income (loss)                1,053             (651)
Losses and loss adjustment expenses          (463,823)        (383,433)
Acquisition expenses                         (133,585)         (90,522)
Other operating expenses                      (44,695)         (38,716)
Underwriting income (loss)            $        95,974        $ (33,125)       389.7

                                                                              % Point
Underwriting Ratios                                                            Change
Loss ratio                                       62.9   %         79.8  %     (16.9)
Acquisition expense ratio                        18.1   %         18.9  %      (0.8)
Other operating expense ratio                     6.1   %          8.1  %      (2.0)
Combined ratio                                   87.1   %        106.8  %     (19.7)


                                                 Six Months Ended June 30,
                                           2021               2020          % Change
Gross premiums written                $  2,829,080       $ 1,929,584         46.6
Premiums ceded                            (905,236)         (567,310)
Net premiums written                     1,923,844         1,362,274         41.2
Change in unearned premiums               (541,920)         (338,617)
Net premiums earned                      1,381,924         1,023,657         35.0
Other underwriting income                     (145)            1,469
Losses and loss adjustment expenses       (948,693)         (813,502)
Acquisition expenses                      (251,610)         (170,128)
Other operating expenses                  (105,209)          (84,013)
Underwriting income (loss)            $     76,267       $   (42,517)       279.4

                                                                             % Point
Underwriting Ratios                                                          Change
Loss ratio                                    68.7  %           79.5  %     (10.8)
Acquisition expense ratio                     18.2  %           16.6  %       1.6
Other operating expense ratio                  7.6  %            8.2  %      (0.6)
Combined ratio                                94.5  %          104.3  %      (9.8)


The reinsurance segment consists of our reinsurance underwriting units which
offer specialty product lines on a worldwide basis. Product lines include:
•Casualty: provides coverage to ceding company clients on third party liability
and workers' compensation exposures from ceding company clients, primarily on a
treaty basis. Exposures include, among others, executive assurance, professional
liability, workers' compensation, excess and umbrella liability, excess motor
and healthcare business.
•Marine and aviation: provides coverage for energy, hull, cargo, specie,
liability and transit, and aviation business, including airline and general
aviation risks. Business written may also include space business, which includes
coverages for satellite assembly, launch and operation for commercial space
programs.
•Other specialty: provides coverage to ceding company clients for proportional
motor and other lines, including surety, accident and health, workers'
compensation catastrophe, agriculture, trade credit and political risk.
•Property catastrophe: provides protection for most catastrophic losses that are
covered in the underlying policies written by reinsureds, including hurricane,
earthquake, flood, tornado, hail and fire, and coverage for other perils on a
case-by-case basis. Property catastrophe reinsurance provides coverage on an
excess of loss basis when aggregate losses and loss adjustment expense from a
single occurrence or aggregation of losses from a covered peril exceed the
retention specified in the contract.
•Property excluding property catastrophe: provides coverage for both personal
lines and commercial property exposures and principally covers buildings,
structures, equipment and contents. The primary perils in this business
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include fire, explosion, collapse, riot, vandalism, wind, tornado, flood and
earthquake. Business is assumed on both a proportional and excess of loss treaty
basis and on a facultative basis. In addition, facultative business is written
which focuses on commercial property risks on an excess of loss basis.
•Other: includes life reinsurance business on both a proportional and
non-proportional basis, casualty clash business and, in limited instances,
non-traditional business which is intended to provide insurers with risk
management solutions that complement traditional reinsurance.
Premiums Written.
The following tables set forth our reinsurance segment's net premiums written by
major line of business:
                                                                    Three Months Ended June 30,
                                                        2021                                            2020
                                            Amount                    %                    Amount                    %
Property excluding property
catastrophe                           $       249,101                   26.9          $      163,639                   29.0
Property catastrophe                           87,642                    9.5                 117,676                   20.8
Other specialty                               296,325                   32.0                 117,375                   20.8
Casualty                                      225,890                   24.4                 105,049                   18.6
Marine and aviation                            50,248                    5.4                  32,372                    5.7
Other                                          15,526                    1.7                  28,983                    5.1
Total                                 $       924,732                  100.0          $      565,094                  100.0


2021 Second Quarter versus 2020 Period. Gross premiums written by the
reinsurance segment in the 2021 second quarter were 68.3% higher than in the
2020 second quarter, while net premiums written were 63.6% higher. The growth in
net premiums written was observed in most lines of business, primarily related
to new business opportunities in other specialty, casualty and property
excluding property catastrophe lines and the benefit of rate increases.
                                                          Six Months Ended June 30,
                                                      2021                          2020
                                               Amount            %           Amount           %

Property excluding property catastrophe $ 541,934 28.2 $


  322,563        23.7
Property catastrophe                             204,849        10.6          206,768        15.2
Other Specialty                                  580,656        30.2          402,327        29.5
Casualty                                         444,146        23.1          295,929        21.7
Marine and aviation                              111,886         5.8           82,157         6.0
Other                                             40,373         2.1           52,530         3.9
Total                                     $    1,923,844       100.0      $ 1,362,274       100.0


Six Months Ended June 30, 2021 versus 2020 period. Gross premiums written by the
reinsurance segment for the six months ended June 30, 2021 were 46.6% higher
than in the 2020 period, while net premiums written were 41.2% higher than in
the 2020 period. The increase in net premiums written reflected growth in
property excluding property catastrophe,
other specialty and casualty primarily due to new business and rate increases.
Net Premiums Earned.
The following tables set forth our reinsurance segment's net premiums earned by
major line of business:
                                                                    Three Months Ended June 30,
                                                        2021                                            2020
                                            Amount                    %                    Amount                    %
Property excluding property
catastrophe                           $       202,780                   27.5          $      124,019                   25.8
Property catastrophe                           76,167                   10.3                  55,226                   11.5
Other specialty                               211,817                   28.7                 123,006                   25.6
Casualty                                      183,846                   24.9                 132,756                   27.6
Marine and aviation                            42,773                    5.8                  24,960                    5.2
Other                                          19,641                    2.7                  20,230                    4.2
Total                                 $       737,024                  100.0          $      480,197                  100.0


                                                          Six Months Ended June 30,
                                                      2021                          2020
                                               Amount            %           Amount           %

Property excluding property catastrophe $ 390,562 28.3 $


  236,671        23.1
Property catastrophe                             164,178        11.9          108,226        10.6
Other Specialty                                  375,715        27.2          326,391        31.9
Casualty                                         332,877        24.1          267,827        26.2
Marine and aviation                               82,881         6.0           49,818         4.9
Other                                             35,711         2.6           34,724         3.4
Total                                     $    1,381,924       100.0      $ 1,023,657       100.0


Net premiums written, irrespective of the class of business, are generally
earned on a pro rata basis over the terms of the underlying policies or
reinsurance contracts. Net premiums earned by the reinsurance segment in the
2021 second quarter were 53.5% higher than in the 2020 second quarter, and
reflect changes in net premiums written over the previous five quarters.
Other Underwriting Income (Loss).
Other underwriting income for the 2021 second quarter was $1.1 million, compared
to a loss of $0.7 million for the 2020 second quarter, and a loss of $0.1
million for the six months ended June 30, 2021, compared to an income of $1.5
million for the 2020 period.

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Losses and Loss Adjustment Expenses.
The table below shows the components of the reinsurance segment's loss ratio:
                                         Three Months Ended                 Six Months Ended
                                              June 30,                          June 30,
                                          2021              2020            2021             2020
Current year                                   65.7  %     88.2  %              72.1  %     84.6  %
Prior period reserve development               (2.8) %     (8.4) %              (3.4) %     (5.1) %
Loss ratio                                     62.9  %     79.8  %              68.7  %     79.5  %


Current Year Loss Ratio.
2021 Second Quarter versus 2020 Period. The reinsurance segment's current year
loss ratio in the 2021 second quarter was 22.5 points lower than in the 2020
second quarter. The 2021 second quarter loss ratio reflected 2.6 points of
current year catastrophic activity, including winter storms Uri and Viola as
well as other minor global events. The 2020 second quarter included 26.3 points
of catastrophic activity, which included exposure to the COVID-19 pandemic.
Six Months Ended June 30, 2021 versus 2020 period.The reinsurance segment's
current year loss ratio for the six months ended June 30, 2021 was 12.5 points
lower than in the 2020 period and reflected 12.9 points of current year
catastrophic activity, compared to 19.1 points in the 2020 period. The 2020
period loss ratio included exposure to the COVID-19 pandemic.
Prior Period Reserve Development.
The reinsurance segment's net favorable development was $20.5 million, or 2.8
points, for the 2021 second quarter, compared to $40.2 million, or 8.4 points,
for the 2020 second quarter, and $47.3 million, or 3.4 points, for the six
months ended June 30, 2021, compared to $51.8 million, or 5.1 points, for the
2020 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.
2021 Second Quarter versus 2020 Period. The underwriting expense ratio for the
reinsurance segment was 24.2% in the 2021 second quarter, compared to 27.0% in
the 2020 second quarter. Approximately 2.1 points of the difference is due to a
lower level of acquisition expenses related to favorable prior year loss reserve
development this quarter than in the 2020 second quarter. The remainder of the
decrease in the underwriting expense ratio was primarily related to growth in
net premiums earned.
Six Months Ended June 30, 2021 versus 2020 period. The underwriting expense
ratio for the reinsurance segment was 25.8% for the six months ended June 30,
2021, compared to 24.8% for the 2020 period. The comparison of the underwriting
expense ratios also reflected changes in the mix and type of business and a
higher level of net premiums earned for the 2021 period.
Mortgage Segment
Our mortgage operations include U.S. and international mortgage insurance and
reinsurance operations as well as participation in GSE credit risk-sharing
transactions. Our mortgage group includes direct mortgage insurance in the U.S.
primarily through Arch Mortgage Insurance Company, United Guaranty Residential
Insurance Company and Arch Mortgage Guaranty Company (together, "Arch MI U.S.");
mortgage reinsurance by Arch Reinsurance Ltd. ("Arch Re Bermuda") to mortgage
insurers on both a proportional and non-proportional basis globally; direct
mortgage insurance in Europe through Arch Insurance (EU) Designated Activity
Company ("Arch Insurance EU"); in Hong Kong through Arch MI Asia Limited ("Arch
MI Asia"); in Australia through Arch LMI Pty Ltd ("Arch LMI") and participation
in various GSE credit risk-sharing products primarily through Arch Re Bermuda.
The following tables set forth our mortgage segment's underwriting results.
                                                    Three Months Ended June 30,
                                            2021                      2020         % Change
Gross premiums written                $     391,511               $ 369,144          6.1
Premiums ceded                              (55,665)                (44,044)
Net premiums written                        335,846                 325,100          3.3
Change in unearned premiums                  (1,625)                 40,613
Net premiums earned                         334,221                 365,713         (8.6)
Other underwriting income                     4,148                   6,450
Losses and loss adjustment expenses          (9,880)               (224,100)
Acquisition expenses                        (30,117)                (34,052)
Other operating expenses                    (48,312)                (37,574)
Underwriting income                   $     250,060               $  76,437        227.1

                                                                                    % Point
Underwriting Ratios                                                                 Change
Loss ratio                                      3.0   %                61.3  %     (58.3)
Acquisition expense ratio                       9.0   %                 9.3  %      (0.3)
Other operating expense ratio                  14.5   %                10.3  %       4.2
Combined ratio                                 26.5   %                80.9  %     (54.4)


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                                                   Six Months Ended June 30,
                                            2021                   2020         % Change
Gross premiums written                $    782,757             $ 738,089          6.1
Premiums ceded                            (111,716)              (88,371)
Net premiums written                       671,041               649,718          3.3
Change in unearned premiums                   (503)               61,021
Net premiums earned                        670,538               710,739         (5.7)
Other underwriting income                   11,045                11,049
Losses and loss adjustment expenses        (73,569)             (291,666)
Acquisition expenses                       (60,199)              (72,588)
Other operating expenses                   (97,443)              (83,470)
Underwriting income                   $    450,372             $ 274,064         64.3

                                                                                 % Point
Underwriting Ratios                                                              Change
Loss ratio                                    11.0   %              41.0  %     (30.0)
Acquisition expense ratio                      9.0   %              10.2  %      (1.2)
Other operating expense ratio                 14.5   %              11.7  %       2.8
Combined ratio                                34.5   %              62.9  %     (28.4)


Premiums Written.
The following tables set forth our mortgage segment's net premiums written by
underwriting location (i.e., where the business is underwritten):
                                           Three Months Ended June 30,
                                         2021                              2020
                                  Amount                 %          Amount          %
Underwriting location:
United States            $      234,645                 69.9      $ 261,124        80.3
Other                           101,201                 30.1         63,976        19.7
Total                    $      335,846                100.0      $ 325,100       100.0


2021 Second Quarter versus 2020 Period. Gross premiums written by the mortgage
segment in the 2021 second quarter were 6.1% higher than in the 2020 second
quarter, while net premiums written were 3.3% higher, primarily reflecting
growth in Australian single premium mortgage insurance and the benefit of
premiums received related to the exercise of early redemption options by GSEs
for certain seasoned callable credit risk transfer contracts. This growth was
partially offset by a lower level of U.S. primary mortgage insurance in force on
monthly premium policies, which resulted from the continued high level of
refinancing activity.
                                           Six Months Ended June 30,
                                        2021                             2020
                                 Amount                %          Amount          %

Underwriting location:
United States            $      482,174               71.9      $ 525,232        80.8
Other                           188,867               28.1        124,486        19.2
Total                    $      671,041              100.0      $ 649,718       100.0


Six Months Ended June 30, 2021 versus 2020 period. Gross premiums written by the
mortgage segment for the six months ended June 30, 2021 were 6.1% higher than in
the 2020 period, while net premiums written for the six months
ended June 30, 2021 were 3.3% higher than in the 2020 period, primarily
reflecting growth in Australian single premium mortgage insurance and the
benefit of premiums received related to the exercise of early redemption options
by GSEs for certain seasoned callable credit risk transfer contracts. This
growth was partially offset by a lower level of U.S. primary mortgage insurance
in force on monthly premium policies, which resulted from the continued high
level of refinancing activity.
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 54.8% for the Arch MI U.S. portfolio of mortgage insurance
policies at June 30, 2021, reflecting the higher level of mortgage refinancing
activity, compared to 58.7% at December 31, 2020.
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 June 30,
                                                       2021                                          2020
                                          Amount                    %                   Amount                   %
Total new insurance written (NIW)
(1)                                  $       28,372                                 $     24,551

Credit quality (FICO):
>=740                                $       19,240                   67.8          $     15,851                   64.6
680-739                                       8,113                   28.6                 7,781                   31.7
620-679                                       1,019                    3.6                   919                    3.7

Total                                $       28,372                  100.0          $     24,551                  100.0

Loan-to-value (LTV):
95.01% and above                     $        1,484                    5.2          $      1,948                    7.9
90.01% to 95.00%                             13,936                   49.1                 9,403                   38.3
85.01% to 90.00%                              8,675                   30.6                 8,140                   33.2
85.00% and below                              4,277                   15.1                 5,060                   20.6
Total                                $       28,372                  100.0          $     24,551                  100.0

Monthly vs. single:
Monthly                              $       26,725                   94.2          $     23,391                   95.3
Single                                        1,647                    5.8                 1,160                    4.7
Total                                $       28,372                  100.0          $     24,551                  100.0

Purchase vs. refinance:
Purchase                             $       25,010                   88.2          $     14,956                   60.9
Refinance                                     3,362                   11.8                 9,595                   39.1
Total                                $       28,372                  100.0          $     24,551                  100.0

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



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(U.S. Dollars in millions)                                        Six Months Ended June 30,
                                                      2021                                          2020
                                          Amount                   %                   Amount                   %
Total new insurance written (NIW)
(1)                                  $      55,391                                 $     41,329

Credit quality (FICO):
>=740                                $      37,058                   66.9          $     25,920                   62.7
680-739                                     16,531                   29.8                13,568                   32.8
620-679                                      1,802                    3.3                 1,841                    4.5

Total                                $      55,391                  100.0          $     41,329                  100.0

Loan-to-value (LTV):
95.01% and above                     $       3,092                    5.6          $      3,616                    8.7
90.01% to 95.00%                            26,224                   47.3                16,602                   40.2
85.01% to 90.00%                            16,987                   30.7                13,469                   32.6
85.01% and below                             9,088                   16.4                 7,642                   18.5
Total                                $      55,391                  100.0          $     41,329                  100.0

Monthly vs. single:
Monthly                              $      51,714                   93.4          $     39,083                   94.6
Single                                       3,677                    6.6                 2,246                    5.4
Total                                $      55,391                  100.0          $     41,329                  100.0

Purchase vs. refinance:
Purchase                             $      45,515                   82.2          $     27,255                   65.9
Refinance                                    9,876                   17.8                14,074                   34.1
Total                                $      55,391                  100.0          $     41,329                  100.0


(1)Represents the original principal balance of all loans that received coverage
during the period.
Net Premiums Earned.
The following tables set forth our mortgage segment's net premiums earned by
underwriting location:
                                           Three Months Ended June 30,
                                         2021                              2020
                                  Amount                 %          Amount          %
Underwriting location:
United States            $      248,388                 74.3      $ 304,652        83.3
Other                            85,833                 25.7         61,061        16.7
Total                    $      334,221                100.0      $ 365,713       100.0


2021 Second Quarter versus 2020 Period. Net premiums earned for the 2021 second
quarter were 8.6% lower than in the 2020 second quarter, and reflected a lower
level of single premium policy terminations and a decrease in U.S. primary
mortgage insurance in force on monthly premium policies.
                                           Six Months Ended June 30,
                                        2021                             2020
                                 Amount                %          Amount          %

Underwriting location:
United States            $      510,938               76.2      $ 593,814        83.5
Other                           159,600               23.8        116,925        16.5
Total                    $      670,538              100.0      $ 710,739       100.0


Six Months Ended June 30, 2021 versus 2020 Period. Net premiums earned for the
six months ended June 30, 2021 were 5.7% lower than in the 2020 period,
primarily reflecting a lower level of single premiums earned, partially offset
by an increase in earnings from Australian single premium policy terminations.
Other Underwriting Income.
Other underwriting income, which is primarily related to GSE credit risk-sharing
transactions was $4.1 million for the 2021 second quarter, compared to $6.5
million for the 2020 second quarter.
Losses and Loss Adjustment Expenses.
The table below shows the components of the mortgage segment's loss ratio:
                                         Three Months Ended                 Six Months Ended
                                              June 30,                          June 30,
                                          2021              2020            2021             2020
Current year                                   15.9  %     61.4  %              19.1  %     41.9  %
Prior period reserve development              (12.9) %     (0.1) %              (8.1) %     (0.9) %
Loss ratio                                      3.0  %     61.3  %              11.0  %     41.0  %


Current Year Loss Ratio.
2021 Second Quarter versus 2020 Period. The mortgage segment's current year loss
ratio was 45.5 points lower in the 2021 second quarter than in the 2020 second
quarter. The mortgage segment's current year loss ratio was 22.8 points lower
for the six months ended June 30, 2021 than for the 2020 period. The lower
current year loss ratios for the 2021 period reflect decrease in loss
assumptions related to COVID-19 pandemic.
For the 2020 periods, the increase in incurred losses was primarily due to, the
financial stress related to the COVID-19 pandemic. Segregating estimated losses
due to COVID-19 from the overall mortgage segment estimated losses would require
the number of delinquencies specifically attributable to COVID-19. As this
analysis cannot be performed accurately, the Company is not reporting COVID-19
provisions separately from its overall loss provisions.
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Prior Period Reserve Development.
The mortgage segment's net favorable development was $43.1 million, or 12.9
points, for the 2021 second quarter, compared to $0.2 million, or 0.1 points,
for the 2020 second quarter, and $54.0 million, or 8.1 points, for the six
months ended June 30, 2021, compared to $6.3 million, or 0.9 points, for the
2020 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.
2021 Second Quarter versus 2020 Period. The underwriting expense ratio for the
mortgage segment was 23.5% in the 2021 second quarter, compared to 19.6% in the
2020 second quarter, with the increase primarily reflecting higher operating
expenses and, to a lesser extent, a decline in net premiums earned on U.S.
primary mortgage insurance business.
Six Months Ended June 30, 2021 versus 2020 period. The underwriting expense
ratio for the mortgage segment was 23.5% for the six months ended June 30, 2021,
compared to 21.9% for the 2020 period, with the increase primarily reflecting
higher operating expenses and, to a lesser extent, a decline in net premiums
earned on U.S. primary mortgage insurance business.
Corporate (Non-Underwriting) Segment
The corporate (non-underwriting) segment results include net investment income,
other income (loss), corporate expenses, transaction costs and other,
amortization of intangible assets, interest expense, items related to our
non-cumulative preferred shares, net realized gains or losses (which includes
changes in the allowance for credit losses on financial assets and net
impairment losses recognized in earnings), equity in net income or loss of
investment funds accounted for using the equity method, net foreign exchange
gains or losses, income or loss from operating affiliates and income taxes. Such
amounts exclude the results of the 'other' segment. See   note 1, "Basis of
Presentation and Recent Accounting Pronouncements,"   to our consolidated
financial statements for information about the change in presentation of income
or loss from operating affiliates.
Net Investment Income.
The components of net investment income were derived from the following sources:
                              Three Months Ended             Six Months Ended
                                   June 30,                      June 30,
                             2021           2020           2021           2020
Fixed maturities          $  77,709      $  91,491      $ 156,726      $ 193,254

Equity securities             8,282          6,023         13,932         11,653
Short-term investments          972            897          1,616          4,282

Other (1)                    21,026         17,825         36,585         38,304
Gross investment income     107,989        116,236        208,859        247,493
Investment expenses (2)     (18,559)       (15,205)       (40,700)       (33,434)
Net investment income     $  89,430      $ 101,031      $ 168,159        214,059


(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 0.30% of average invested assets for
the 2021 second quarter, compared to 0.28% for the 2020 second quarter, and
0.32% for the six months ended June 30, 2021, compared to 0.32% for the 2020
period.
The lower level of net investment income for the 2021 second quarter primarily
related to lower yields available in the financial market. The pre-tax
investment income yield, calculated based on amortized cost and on an annualized
basis, was 1.47% for the 2021 second quarter, compared to 1.92% for the 2020
second quarter, and 1.40% for the six months ended June 30, 2021, compared to
2.08% for the 2020 period.
Corporate Expenses.
Corporate expenses were $17.2 million for the 2021 second quarter, compared to
$16.9 million for the 2020 second quarter, and $40.6 million for the six months
ended June 30, 2021, compared to $35.1 million for the 2020 period. The increase
in corporate expenses was primarily due to higher incentive compensation costs.
Transaction Costs and Other.
Transaction costs and other were a benefit of $1.4 million for the 2021 second
quarter, compared to an expense of $1.0 million for the 2020 second quarter, and
a benefit of $0.2 million for the six months ended June 30, 2021, compared to an
expense of $3.6 million for the 2020 period. Amounts in the 2021 and 2020
periods are primarily related to acquisitions activity for the respective
period.
Amortization of Intangible Assets.
Amortization of intangible assets for the 2021 second quarter was $14.4 million,
compared to $16.5 million for the 2020
ARCH CAPITAL     55     2021 SECOND QUARTER FORM 10-Q


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second quarter, and $28.8 million for the six months ended June 30, 2021,
compared to $33.1 million for the 2020 period. Amounts in 2021 and 2020
primarily related to amortization of finite-lived intangible assets. See the
consolidated financial statements contained in our 2020 Form 10-K for
disclosures on our amortization pattern.
Interest Expense.
Interest expense was $31.4 million for the 2021 second quarter, compared to the
$25.1 million for the 2020 second quarter, and $65.6 million for the six months
ended June 30, 2021, compared to $50.4 million for the 2020 period.The higher
level of interest expense mainly resulted from the issuance of $1.0 billion of
3.635% senior notes on June 30, 2020.
Net Realized Gains or Losses.
We recorded net realized gains of $163.4 million for the 2021 second quarter,
compared to net realized gains of $385.1 million for the 2020 second quarter,
and net realized gains of $264.7 million for the six months ended June 30, 2021,
compared to net realized gains of $313.0 million for the 2020 period. Currently,
our portfolio is actively managed to maximize total return within certain
guidelines. The effect of financial market movements on the investment portfolio
will directly impact net realized gains and losses as the portfolio is adjusted
and rebalanced. Net realized gains or losses from the sale of fixed maturities
primarily results from our decisions to reduce credit exposure, to change
duration targets, to rebalance our portfolios or due to relative value
determinations.
Net realized gains or losses also include realized and unrealized contract gains
and losses on our derivative instruments, changes in the fair value of assets
accounted for using the fair value option and in the fair value of equities,
along with changes in the allowance for credit losses on financial assets and
net impairment losses recognized in earnings. See   note 7, "Investment
Information-Net Realized Gains (Losses),"   to our consolidated financial
statements for additional information. See   note 7, "Investment
Information-Allowance for Credit Losses,"   to our consolidated financial
statements for additional information.
Equity in Net Income (Loss) of Investment Funds Accounted for Using the Equity
Method.
We recorded $122.2 million of equity in net income related to investment funds
accounted for using the equity method in the 2021 second quarter, compared to a
loss of $65.1 million for the 2020 second quarter, and $193.9 million of income
for the six months ended June 30, 2021, compared to a loss of $69.3 million for
the 2020 period. Such investments are generally recorded on a one to three month
lag based on the availability of reports from the investment funds. Investment
funds accounted for using the equity method totaled $2.5 billion at June 30,
2021, compared to $2.0 billion at December 31, 2020. See   note 7, "Investment
Information-Investments Accounted For Using the Equity Method,"   to our
consolidated financial statements for additional information.
Net Foreign Exchange Gains or Losses.
Net foreign exchange losses for the 2021 second quarter were $17.9 million,
compared to net foreign exchange losses for the 2020 second quarter of $42.4
million. Net foreign exchange gains for the six months ended June 30, 2021 were
$3.6 million, compared to net foreign exchange gains for the 2020 period of
$20.9 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 7.1% for the 2021
second quarter, compared to 8.8% for the 2020 second quarter, and 7.5% for the
six months ended June 30, 2021, compared to 10.7% for the 2020 period. Such
amounts exclude the results of the 'other' segment. Our effective tax rate,
which is based upon the expected annual effective tax rate, may fluctuate from
period to period based on the relative mix of income or loss reported by
jurisdiction and the varying tax rates in each jurisdiction.
Income (loss) from operating affiliates.
We recorded $24.5 million of net income from our operating affiliates in the
2021 second quarter, compared to a loss of $3.2 million for the 2020 second
quarter, and $99.9 million of income for the six months ended June 30, 2021,
compared to $5.3 million for the 2020 period. Results for the 2021 period,
primarily reflected our acquisition of 29.5% of the common equity in Coface,
which included a one-time gain of $74.5 million. As a result of equity method
accounting rules, approximately $36 million of additional gain was deferred and
will generally be recognized over the next five years.
Other Segment
Through June 30, 2021, the 'other' segment included the results of Watford.
Pursuant to GAAP, Watford was considered a variable interest entity and we
concluded that we are the primary beneficiary of Watford. As such, we
consolidated the results of Watford in our consolidated financial statements
through June 30, 2021, although we only owned approximately 10% of Watford's
common equity. See   note 11, "Variable Interest Entities and Noncontrolling
Interests,"     note 4, "Segment Information,"   and   Note 16,
ARCH CAPITAL     56     2021 SECOND QUARTER FORM 10-Q


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  "    Subsequent Event,    "   to our consolidated financial statements for
additional information on Watford.
CRITICAL ACCOUNTING POLICIES,
ESTIMATES AND RECENT ACCOUNTING PRONOUNCEMENTS


Critical accounting policies, estimates and recent accounting pronouncements are
discussed in Management's Discussion and Analysis of Financial Condition and
Results of Operations contained in our 2020 Form 10-K, updated where applicable
in the notes accompanying our consolidated financial statements, including

note 1, "Basis of Presentation and Recent Accounting Pronouncements." FINANCIAL CONDITION




Investable Assets
At June 30, 2021, total investable assets held by Arch were $27.3 billion,
excluding the $2.9 billion included in the 'other' segment (i.e., attributable
to Watford).
Investable Assets Held by Arch
The following table summarizes the fair value of the investable assets held by
Arch:
                                                              Estimated                   % of
Investable assets (1):                                        Fair Value                 Total
June 30, 2021
Fixed maturities (2)                                      $    18,022,113                    66.0
Short-term investments (2)                                      2,380,016                     8.7
Cash                                                              884,857                     3.2
Equity securities (2)                                           1,633,579                     6.0
Other investments (2)                                           1,512,317                     5.5
Other investable assets (3)                                       500,000                     1.8
Investments accounted for using the equity method               2,539,124                     9.3

Securities transactions entered into but not settled at the balance sheet date

                                           (180,592)                   (0.7)
Total investable assets held by Arch                      $    27,291,414                   100.0

Average effective duration (in years)                                2.31
Average S&P/Moody's credit ratings (4)                                AA/Aa2
Embedded book yield (5)                                              1.45  %

December 31, 2020
Fixed maturities (2)                                      $    18,771,296                    69.9
Short-term investments (2)                                      2,063,240                     7.7
Cash                                                              694,997                     2.6
Equity securities (2)                                           1,436,104                     5.3
Other investments (2)                                           1,480,347                     5.5
Other investable assets (3)                                       500,000                     1.9
Investments accounted for using the equity method               2,047,889                     7.6

Securities transactions entered into but not settled at the balance sheet date

                                           (137,578)                   (0.5)
Total investable assets held by Arch                      $    26,856,295                   100.0

Average effective duration (in years)                                3.01
Average S&P/Moody's credit ratings (4)                                AA/Aa2
Embedded book yield (5)                                              1.56  %


(1)In securities lending transactions, we receive collateral in excess of the
fair value of the securities pledged. For purposes of this table, we have
excluded the collateral received under securities lending, at fair value and
included the securities pledged under securities lending, at fair value.
(2)Includes investments carried as available for sale, at fair value and at fair
value under the fair value option.
(3)Represents participation interests in a receivable of a reverse repurchase
agreement.
(4)Average credit ratings on our investment portfolio on securities with ratings
by Standard & Poor's Rating Services ("S&P") and Moody's Investors Service
("Moody's").
(5)Before investment expenses.
At June 30, 2021, approximately $18.5 billion, or 67.9%, of total investable
assets held by Arch were internally managed, compared to $19.2 billion, or
71.4%, at December 31, 2020.
ARCH CAPITAL     57     2021 SECOND QUARTER FORM 10-Q


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The following table summarizes our fixed maturities and fixed maturities pledged
under securities lending agreements ("Fixed Maturities") by type:
                                            Estimated          % of
                                            Fair Value        Total
June 30, 2021
Corporate bonds                           $  7,375,350        40.9

Residential mortgage backed securities 374,565 2.1 Municipal bonds

                                413,709         2.3

Commercial mortgage backed securities 267,574 1.5 U.S. government and government agencies 4,855,595 26.9 Non-U.S. government securities

               2,308,403        12.8
Asset backed securities                      2,426,917        13.5
Total                                     $ 18,022,113       100.0

December 31, 2020
Corporate bonds                           $  8,039,745        42.8

Residential mortgage backed securities 616,619 3.3 Municipal bonds

                                492,734         2.6

Commercial mortgage backed securities 390,990 2.1 U.S. government and government agencies 5,354,863 28.5 Non-U.S. government securities

               2,310,157        12.3
Asset backed securities                      1,566,188         8.3
Total                                     $ 18,771,296       100.0


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


                                                                        % of
                                           Estimated Fair Value        Total
June 30, 2021
U.S. government and gov't agencies (1)    $           5,221,296        29.0
AAA                                                   3,432,285        19.0
AA                                                    2,004,442        11.1
A                                                     3,268,661        18.1
BBB                                                   2,896,453        16.1
BB                                                      544,730         3.0
B                                                       330,639         1.8
Lower than B                                             48,230         0.3
Not rated                                               275,377         1.5
Total                                     $          18,022,113       100.0

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


(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:
                                                                                       % of
                                                                     Gross         Total Gross
                                                                   Unrealized       Unrealized
Severity of gross unrealized losses:    Estimated Fair Value         Losses           Losses
June 30, 2021
0-10%                                  $           7,387,667      $  (68,781)         92.0
10-20%                                                28,039          (4,166)          5.6
20-30%                                                 1,999            (553)          0.7
Greater than 30%                                       1,326          (1,239)          1.7
Total                                  $           7,419,031      $  (74,739)        100.0

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


The following table summarizes our top ten exposures to fixed income corporate
issuers by fair value at June 30, 2021, excluding guaranteed amounts and covered
bonds:
                                                                            Credit
                                              Estimated Fair Value        Rating (1)
Bank of America Corporation                  $             373,742               A-/A2
JPMorgan Chase & Co.                                       372,381               A-/A2
Citigroup Inc.                                             288,574             BBB+/A3
Morgan Stanley                                             253,549             BBB+/A1
Wells Fargo & Company                                      247,222             BBB+/A2
The Goldman Sachs Group, Inc.                              185,647             BBB+/A2
Nestlé S.A.                                                129,191             AA-/Aa3
Amazon.com, Inc.                                           118,047               AA/A1
Nippon Telegraph and Telephone Corporation                  95,958                A/A1
AT&T Inc.                                                   92,795            BBB/Baa2
Total                                        $           2,157,106

(1)Average credit ratings as assigned by S&P and Moody's, respectively. ARCH CAPITAL 58 2021 SECOND QUARTER FORM 10-Q

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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
Jun 30, 2021
RMBS           $ 336,784      $          14,716      $                23,065      $   374,565
CMBS              28,917                213,655                       25,002          267,574
ABS                    -              2,206,453                      220,464        2,426,917
Total          $ 365,701      $       2,434,824      $               268,531      $ 3,069,056

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

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


                          June 30,        December 31,
                            2021              2020
Equities (1)            $   864,688      $    676,437
Exchange traded funds
Fixed income (2)            304,723           341,139
Equity and other (3)        464,168           418,528
Total                   $ 1,633,579      $  1,436,104

(1)Primarily in consumer non-cyclical, consumer cyclical, technology, communications and financial stocks at June 30, 2021. (2)Primarily in corporate, MBS and municipal strategies at June 30, 2021. (3)Primarily in utilities, large cap stocks and foreign equities at June 30, 2021.



The following table summarizes our other investments and other investable
assets:
                                   June 30,        December 31,
                                     2021              2020
Lending                          $   638,786      $    572,636
Term loan investments                474,859           380,193
Energy                                84,891            65,813
Credit related funds                  73,171            90,780
Investment grade fixed income        110,375           138,646
Infrastructure                        32,109           165,516
Private equity                        70,878            48,750
Real estate                           27,248            18,013
Total fair value option          $ 1,512,317      $  1,480,347

Other investable assets          $   500,000      $    500,000

Total other investments          $ 2,012,317      $  1,980,347


For details on our investments accounted for using the equity method, see   note
7, "Investment Information-Investments Accounted For Using the Equity Method,"
to our consolidated financial statements.
Our investment strategy allows for the use of derivative instruments. We utilize
various derivative instruments such as futures contracts to enhance investment
performance, replicate investment positions or manage market exposures and
duration risk that would be allowed under our investment guidelines if
implemented in other ways. See   note 9, "Derivative Instruments,"   to our
consolidated financial statements for additional disclosures related to
derivatives.
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.
Investable Assets in the 'Other' Segment
Investable assets in the 'other' segment are managed by Watford. The board of
directors of Watford establishes its investment policies and guidelines. A
significant amount of Watford's investments are accounted for using the fair
value option with changes in the carrying value of such investments recorded in
net realized gains or losses.
The following table summarizes investable assets in the 'other' segment:
                                                          June 30,          

December 31,


                                                            2021            

2020


Investments accounted for using the fair value
option:
Other investments                                    $       858,155          $        851,538
Fixed maturities                                             578,280                   455,163
Short-term investments                                       478,711                   418,690
Equity securities                                             69,773                    64,994
Total                                                      1,984,919                 1,790,385
Fixed maturities available for sale, at fair value           625,422                   613,503
Equity securities, at fair value                              97,623                    52,410
Cash                                                         349,202                   211,451
Securities sold but not yet purchased                        (28,068)                  (21,679)

Securities transactions entered into but not settled at the balance sheet date

                                    (97,055)                   11,542

Total investable assets included in 'other' segment $ 2,932,043

  $      2,657,612



ARCH CAPITAL     59     2021 SECOND QUARTER FORM 10-Q

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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                 Six Months Ended
                                June 30,                          June 30,
                         2021             2020             2021             2020
Premiums written:
Direct               $ 1,909,893      $ 1,485,627      $ 3,802,138      $ 3,174,425
Assumed                1,376,398          832,065        2,881,359        1,976,097
Ceded                   (886,767)        (649,381)      (1,775,516)      (1,344,965)
Net                  $ 2,399,524      $ 1,668,311      $ 4,907,981      $ 3,805,557

Premiums earned:
Direct               $ 1,795,899      $ 1,559,222      $ 3,508,824      $ 3,105,047
Assumed                1,091,968          746,188        2,039,582        1,507,262
Ceded                   (766,958)        (640,056)      (1,479,075)      (1,202,511)
Net                  $ 2,120,909      $ 1,665,354      $ 4,069,331      $ 3,409,798

Losses and LAE:
Direct               $ 1,046,579      $ 1,162,958      $ 2,032,512      $ 2,148,041
Assumed                  554,256          508,108        1,221,567        1,053,977
Ceded                   (441,004)        (440,544)        (891,148)        (856,077)
Net                  $ 1,159,831      $ 1,230,522      $ 2,362,931      $ 2,345,941


See   note 6, "Allowance for Expected Credit Losses,"   to our consolidated
financial statements for information about our reinsurance recoverables and
related allowance for credit losses.
Bellemeade Re
We have entered into various aggregate excess of loss mortgage reinsurance
agreements with various special purpose reinsurance companies domiciled in
Bermuda (the "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
June 30, 2021:
                                                                                           June 30, 2021
                                                   Initial Coverage                                        Remaining
                                                     at Issuance             Current Coverage           Retention, Net
Bellemeade 2017-1 Ltd. (1)                        $       368,114          $         145,573          $        125,297
Bellemeade 2018-1 Ltd. (2)                                374,460                    250,095                   123,173
Bellemeade 2018-3 Ltd. (3)                                506,110                    302,563                   126,127
Bellemeade 2019-1 Ltd. (4)                                341,790                    219,256                   102,017
Bellemeade 2019-2 Ltd. (5)                                621,022                    398,316                   156,718
Bellemeade 2019-3 Ltd. (6)                                700,920                    528,084                   176,565
Bellemeade 2019-4 Ltd. (7)                                577,267                    468,737                   113,415
Bellemeade 2020-1 Ltd. (8)                                528,540                     18,843                   747,799
Bellemeade 2020-2 Ltd. (9)                                449,167                    328,375                   232,481
Bellemeade 2020-3 Ltd. (10)                               451,816                    451,816                   163,905
Bellemeade 2020-4 Ltd. (11)                               337,013                    281,750                   138,183
Bellemeade 2021-1 Ltd. (12)                               643,577                    643,577                   166,199
Bellemeade 2021-2 Ltd. (13)                               616,017                    616,017                   152,734
Total                                             $     6,515,813          $       4,653,002          $      2,524,613


(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 June 2020, covering in-force policies issued between July 1,
2019 and December 31, 2019. $450 million was directly funded by Bellemeade
2020-1 Ltd. with an additional $79 million of capacity provided directly to Arch
MI U.S. by a separate panel of reinsurers.
(9)  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.
(10)  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.
(11) 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.
(12) 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.
(13) 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.
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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 June 30, 2021 and December 31, 2020, our Loss Reserves, net of unpaid losses
and loss adjustment expenses recoverable, by type and by operating segment were
as follows:
                              June 30,        December 31,
                                2021              2020
Insurance segment:
Case reserves              $  2,100,109      $  2,051,640
IBNR reserves                 4,117,169         3,889,823
Total net reserves            6,217,278         5,941,463
Reinsurance segment:
Case reserves                 1,523,486         1,560,523
Additional case reserves        432,516           280,472
IBNR reserves                 2,435,575         2,253,953
Total net reserves            4,391,577         4,094,948
Mortgage segment:
Case reserves                   704,314           631,921
IBNR reserves                   266,690           271,702
Total net reserves              971,004           903,623
Other segment:
Case reserves                   682,341           566,587
Additional case reserves         47,774            32,321
IBNR reserves                   740,654           660,132
Total net reserves            1,470,769         1,259,040
Total:
Case reserves                 5,010,250         4,810,671
Additional case reserves        480,290           312,793
IBNR reserves                 7,560,088         7,075,610
Total net reserves         $ 13,050,628      $ 12,199,074

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


                                          June 30,        December 31,
                                            2021              2020
Insurance segment:
Professional lines (1)                  $ 1,516,878      $  1,482,820

Construction and national accounts 1,470,201 1,395,067 Excess and surplus casualty (2)

             859,662           816,495
Programs                                    748,015           699,354
Property, energy, marine and aviation       500,880           517,692
Travel, accident and health                  96,345            98,910
Lenders products                             64,560            48,946
Other (3)                                   960,737           882,179
Total net reserves                      $ 6,217,278      $  5,941,463


(1)Includes professional liability, executive assurance and healthcare business.
(2)Includes casualty and contract binding business.
(3)Includes alternative markets, excess workers' compensation and surety
business.
At June 30, 2021 and December 31, 2020, the reinsurance segment's Loss Reserves
by major line of business, net of unpaid losses and loss adjustment expenses
recoverable, were as follows:
                                            June 30,        December 31,
                                              2021              2020
Reinsurance segment:
Casualty (1)                              $ 2,024,591      $  1,995,849
Other specialty (2)                           955,770           917,178
Property excluding property catastrophe       668,339           594,033
Marine and aviation                           215,345           204,205
Property catastrophe                          410,034           268,858
Other (3)                                     117,498           114,825
Total net reserves                        $ 4,391,577      $  4,094,948


(1)Includes executive assurance, professional liability, workers' compensation,
excess motor, healthcare and other.
(2)Includes non-excess motor, surety, accident and health, workers' compensation
catastrophe, agriculture, trade credit and other.
(3)Includes life, casualty clash and other.
At June 30, 2021 and December 31, 2020, the mortgage segment's Loss Reserves by
major line of business, net of unpaid losses and loss adjustment expenses
recoverable, were as follows:
                                        June 30,       December 31,
                                          2021             2020

U.S. primary mortgage insurance (1) $ 713,135 $ 649,748 Other

                                    257,869            253,875
Total net reserves                     $ 971,004      $     903,623

(1) At June 30, 2021, 28.0% represents policy years 2011 and prior and the remainder from later policy years. At December 31, 2020, 28.3% of total net reserves represent policy years 2011 and prior and the remainder from later policy years.



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Mortgage Operations Supplemental Information
The mortgage segment's insurance in force ("IIF") and risk in force ("RIF") were
as follows at June 30, 2021 and December 31, 2020:
(U.S. Dollars in millions)               June 30, 2021                   December 31, 2020
                                       Amount            %               Amount              %
Insurance In Force (IIF) (1):
U.S. primary mortgage insurance   $      277,887        65.8      $          280,579        66.2
Mortgage reinsurance                      32,666         7.7                  31,220         7.4
Other (2)                                111,884        26.5                 111,740        26.4
Total                             $      422,437       100.0      $          423,539       100.0

Risk In Force (RIF) (3):
U.S. primary mortgage insurance   $       69,587        90.3      $           70,522        90.5
Mortgage reinsurance                       2,245         2.9                   2,226         2.9
Other (2)                                  5,188         6.7                   5,146         6.6
Total                             $       77,020       100.0      $           77,894       100.0


(1)Represents the aggregate dollar amount of each insured mortgage loan's
current principal balance.
(2)Includes GSE credit risk-sharing transactions and international insurance
business.
(3)Represents the aggregate dollar amount of each insured mortgage loan's
current principal balance multiplied by the insurance coverage percentage
specified in the policy for insurance policies issued and after contract limits
and/or loss ratio caps for credit risk-sharing or reinsurance transactions.
The IIF and RIF for our U.S. primary mortgage insurance business by policy year
were as follows at June 30, 2021:
(U.S. Dollars in millions)              IIF                       RIF               Delinquency
                                Amount          %          Amount         %          Rate (1)
Policy year:
2011 and prior                $  12,591         4.5      $  2,839         4.1            9.75  %
2012                              2,261         0.8           587         0.8            3.00  %
2013                              5,635         2.0         1,563         2.2            2.95  %
2014                              6,288         2.3         1,729         2.5            3.52  %
2015                             11,208         4.0         3,017         4.3            3.19  %
2016                             18,500         6.7         4,958         7.1            4.11  %
2017                             17,577         6.3         4,574         6.6            4.87  %
2018                             19,044         6.9         4,827         6.9            6.25  %
2019                             34,944        12.6         8,727        12.5            4.02  %
2020                             95,419        34.3        23,316        33.5            0.88  %
2021                             54,420        19.6        13,450        19.3            0.10  %
Total                         $ 277,887       100.0      $ 69,587       100.0            3.11  %


(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, 2020:
(U.S. Dollars in millions)              IIF                       RIF               Delinquency
                                Amount          %          Amount         %          Rate (1)
Policy year:
2011 and prior                $  14,588         5.2      $  3,327         4.7           11.36  %
2012                              3,651         1.3           992         1.4            2.98  %
2013                              7,546         2.7         2,107         3.0            3.30  %
2014                              8,261         2.9         2,273         3.2            4.06  %
2015                             15,032         5.4         4,048         5.7            3.72  %
2016                             24,958         8.9         6,648         9.4            4.77  %
2017                             24,748         8.8         6,413         9.1            5.52  %
2018                             27,304         9.7         6,918         9.8            6.76  %
2019                             48,304        17.2        12,001        17.0            4.61  %
2020                            106,187        37.8        25,795        36.6            0.76  %

Total                         $ 280,579       100.0      $ 70,522       100.0            4.19  %


(1)Represents the ending percentage of loans in default.
The following tables provide supplemental disclosures on risk in force for our
U.S. primary mortgage insurance business at June 30, 2021 and December 31, 2020:
(U.S. Dollars in millions)                         June 30, 2021                                December 31, 2020
                                           Amount                   %                     Amount                     %
Credit quality (FICO):
>=740                                 $      41,156                   59.1          $         40,774                   57.8
680-739                                      23,663                   34.0                    24,498                   34.7
620-679                                       4,401                    6.3                     4,837                    6.9
<620                                            367                    0.5                       413                    0.6
Total                                 $      69,587                  100.0          $         70,522                  100.0
Weighted average FICO score                     745                                              743

Loan-to-value (LTV):
95.01% and above                      $       7,975                   11.5          $          8,643                   12.3
90.01% to 95.00%                             37,619                   54.1                    37,877                   53.7
85.01% to 90.00%                             19,784                   28.4                    20,013                   28.4
85.00% and below                              4,209                    6.0                     3,989                    5.7
Total                                 $      69,587                  100.0          $         70,522                  100.0
Weighted average LTV                           92.8  %                                          92.8  %

Total RIF, net of external
reinsurance                           $      55,557                                 $         56,658


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(U.S. Dollars in millions)           June 30, 2021                   December 31, 2020
                                   Amount            %               Amount              %
Total RIF by State:
Texas                         $        5,560         8.0      $            5,636         8.0
California                             5,324         7.7                   5,261         7.5
Florida                                3,367         4.8                   3,632         5.2
Minnesota                              2,973         4.3                   2,520         3.6
North Carolina                         2,924         4.2                   2,622         3.7
Georgia                                2,886         4.1                   2,959         4.2
Illinois                               2,832         4.1                   2,762         3.9
Massachusetts                          2,459         3.5                   2,464         3.5
Virginia                               2,372         3.4                   2,526         3.6
Ohio                                   2,229         3.2                   2,264         3.2
Other                                 36,661        52.7                  37,876        53.7
Total                         $       69,587       100.0      $           70,522       100.0

The following table provides supplemental disclosures for our U.S. primary mortgage insurance business related to insured loans and loss metrics: (U.S. Dollars in thousands, except policy, loan and

                 Six Months Ended
claim count)                                                            June 30,
                                                             2021                      2020
Roll-forward of insured loans in default:
Beginning delinquent number of loans                            52,234                    20,163
New notices                                                     18,415                    67,793
Cures                                                          (32,924)                  (22,205)
Paid claims                                                       (406)                   (1,084)

Ending delinquent number of loans (1)                           37,319                    64,667

Ending number of policies in force (1)                       1,199,918                 1,259,328

Delinquency rate (1)                                              3.11  %                   5.14  %

Losses:
Number of claims paid                                              406                     1,084
Total paid claims                                     $         15,297          $         46,139
Average per claim                                     $           37.7          $           42.6
Severity (2)                                                      81.0  %                   94.3  %
Average case reserve per default (in thousands)       $           19.5          $            6.9


(1)Includes first lien primary and pool policies.
(2)Represents total paid claims divided by RIF of loans for which claims were
paid.
The risk to capital ratio, which represents total current (non-delinquent) risk
in force, net of reinsurance, divided by total statutory capital, for Arch MI
U.S. was approximately 8.5 to 1 at June 30, 2021, compared to 9.3 to 1 at
December 31, 2020.
Shareholders' Equity and Book Value per Share
The following table presents the calculation of book value per share:
(U.S. dollars in thousands, except                                        June 30,               December 31,
share data)                                                                 2021                     2020
Total shareholders' equity available to Arch                         $    13,986,072          $    13,105,886
Less preferred shareholders' equity                                        1,280,000                  780,000
Common shareholders' equity available to Arch                        $    12,706,072          $    12,325,886
Common shares and common share equivalents outstanding, net of
treasury shares (1)                                                      396,771,251              406,720,642
Book value per share                                                 $         32.02          $         30.31

(1)Excludes the effects of 17,717,327 and 17,839,333 stock options and 759,926 and 1,153,784 restricted stock units outstanding at June 30, 2021 and December 31, 2020, respectively.

LIQUIDITY




This section does not include information specific to Watford. We do not
guarantee or provide credit support for Watford, and our financial exposure to
Watford is limited to our investment in Watford's senior notes, common and
preferred shares and counterparty credit risk (mitigated by collateral) arising
from reinsurance transactions with Watford.
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 six months ended June 30, 2021, Arch Capital received dividends of
$563.7 million from Arch Re Bermuda, our Bermuda-based reinsurer and insurer,
which can pay approximately $3.2 billion to Arch Capital during the remainder of
2021 without providing an affidavit to the Bermuda Monetary Authority ("BMA").
In June 2021, Arch Capital completed a $500.0 million underwritten public
offering of 20.0 million depositary shares, each of which represents a 1/1,000th
interest in a share of its 4.550% Non-Cumulative Preferred Shares.   See

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We expect that our liquidity needs, including our anticipated (re)insurance
obligations and operating and capital expenditure needs, for the next twelve
months, 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.
Cash Flows
The following table summarizes our cash flows from operating, investing and
financing activities, excluding amounts related to the 'other' segment (i.e.,
Watford). See   note 11, "Variable Interest Entities and Noncontrolling
Interests,"   for cash flows related to Watford.
                                                                   Six Months Ended
                                                                       June 30,
                                                                2021             2020
Total cash provided by (used for):
Operating activities                                        $ 1,565,718      $ 1,234,383
Investing activities                                         (1,174,033)      (1,888,221)
Financing activities                                              8,352          824,990

Effects of exchange rate changes on foreign currency cash (9,868)

(15,384)


Increase (decrease) in cash and restricted cash             $   390,169

$ 155,768





•Cash provided by operating activities for the six months ended June 30, 2021
reflected a higher level of premiums collected than in the 2020 period.
•Cash used for investing activities for the six months ended June 30, 2021 was
lower than in the 2020 period. Activity for the six months ended June 30, 2021
reflected our $546.3 million purchase of a 29.5% interest in Coface, while the
2020 period reflected a higher level of securities purchased, and the investing
of proceeds from our issuance of the senior notes.
•Cash used for financing activities for the six months ended June 30, 2021 was
lower than cash used in the 2020 period, reflecting $485.8 million inflow from
issuance of preferred shares and $485.3 million of repurchases under our share
repurchase program. Activity for the 2020 period primarily reflected the
issuance of $1.0 billion of our senior notes and $75.5 million of repurchases
under our share repurchase program.
CAPITAL RESOURCES


This section does not include information specific to Watford. We do not
guarantee or provide credit support for Watford, and our financial exposure to
Watford is limited to our investment in Watford's senior notes, common and
preferred shares and counterparty credit risk (mitigated by collateral) arising
from reinsurance transactions with Watford.
The following table provides an analysis of our capital structure:
(U.S. dollars in thousands, except            Jun 30,           Dec 31,
share data)                                     2021              2020

Senior notes                               $  2,723,903      $  2,723,423

Shareholders' equity available to Arch: Series E non-cumulative preferred shares $ 450,000 $ 450,000 Series F non-cumulative preferred shares 330,000

           330,000
Series G non-cumulative preferred shares        500,000                 -
Common shareholders' equity                  12,706,072        12,325,886
Total                                      $ 13,986,072      $ 13,105,886

Total capital available to Arch            $ 16,709,975      $ 15,829,309

Debt to total capital (%)                          16.3              17.2
Preferred to total capital (%)                      7.7               4.9
Debt and preferred to total capital (%)            24.0              22.1


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
June 30, 2021 with an estimated PMIER sufficiency ratio of 196%, compared to
173% at December 31, 2020.
Arch Capital, through its subsidiaries, provides financial support to certain of
its insurance subsidiaries and affiliates, through certain reinsurance
arrangements beneficial to the ratings of such subsidiaries. Historically, our
insurance, reinsurance and mortgage insurance subsidiaries have entered into
separate reinsurance arrangements with Arch Re Bermuda covering individual lines
of business. The reinsurance agreements between our U.S.-based property casualty
insurance and reinsurance subsidiaries and Arch Re Bermuda were canceled on a
cutoff basis as of January 1,
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2018. In 2019, certain reinsurance agreements between our insurance subsidiaries
and Arch Re Bermuda were reinstated.
GUARANTOR INFORMATION


The below table provides a description of our senior notes payable at June 30,
2021, excluding amounts attributable to the 'other' segment (i.e., Watford):
                        Interest       Principal        Carrying
    Issuer/Due          (Fixed)         Amount           Amount
Arch Capital:
May 1, 2034              7.350  %    $   300,000      $   297,426
June 30, 2050            3.635  %        1,000,000          988,609
Arch-U.S.:
Nov. 1, 2043 (1)         5.144  %          500,000          495,003
Arch Finance:
Dec. 15, 2026 (1)        4.011  %          500,000          497,420
Dec. 15, 2046 (1)        5.031  %          450,000          445,445
Total                                $ 2,750,000      $ 2,723,903


(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):


                                                              June 30, 2021                            December 31, 2020
                                                    Arch Capital           Arch-U.S.           Arch Capital           Arch-U.S.
Assets
Total investments                                  $        508          $   373,784          $        172          $   396,547
Cash                                                     15,239               27,434                18,932               11,368

Investment in operating affiliates                        7,294                    -                 7,731                    -
Due from subsidiaries and affiliates                          -              225,006                     -              201,515

Other assets                                             15,244               27,568                10,659               34,405
Total assets                                       $     38,285          $   653,792          $     37,494          $   643,835

Liabilities

Senior notes                                          1,286,035              495,003             1,285,867              494,944

Due to subsidiaries and affiliates                            -              551,760                     -              586,805
Other liabilities                                        20,172               42,582                23,270               41,876
Total liabilities                                  $  1,306,207          $ 1,089,345          $  1,309,137          $ 1,123,625

Non-cumulative preferred shares                    $  1,280,000                    -          $    780,000                    -


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                                                            Six Months Ended                      Year Ended
                                                             June 30, 2021                     December 31, 2020
                                                                 Arch Capital          Arch-U.S.           Arch Capital          Arch-U.S.

Revenues

Net investment income                                          $         796          $   5,007          $          53          $  18,084
Net realized gains (losses)                                                -             70,522                 (2,110)            26,096

Equity in net income (loss) of investments
accounted for using the equity method                                      -             10,678                      -              2,507

Total revenues                                                           796             86,207                 (2,057)            46,687

Expenses

Corporate expenses                                                    37,021              3,007                 65,566              7,227

Interest expense                                                      29,369             23,567                 40,445             47,566
Net foreign exchange (gains) losses                                        6                  -                      3                  -
Total expenses                                                        66,396             26,574                106,014             54,793

Income (loss) before income taxes and income
(loss) from operating affiliates                                     (65,600)            59,633               (108,071)            (8,106)
Income tax (expense) benefit                                               -            (14,731)                     -              2,689

Income (loss) from operating affiliates                                 (317)                 -                   (437)                 -

Net income available to Arch                                         (65,917)            44,902               (108,508)            (5,417)
Preferred dividends                                                  (22,069)                 -                (41,612)                 -

Net income available to Arch common shareholders               $     (87,986)         $  44,902          $    (150,120)         $  (5,417)



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 six months
ended June 30, 2021, Arch Capital repurchased 13.1 million shares under the
share repurchase program with an aggregate purchase price of $485.3 million.
Since the inception of the share repurchase program through June 30, 2021, Arch
Capital has repurchased 402.3 million common shares for an aggregate purchase
price of $4.54 billion. At June 30, 2021, approximately $431.2 million of share
repurchases were available under the program, which may be effected from time to
time in open market or privately negotiated transactions through December 31,
2021. The timing and amount of the repurchase transactions under this program
will depend on a variety of factors, including market conditions and corporate
and regulatory considerations.
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 July 1, 2021, our modeled peak zone
catastrophe exposure was a windstorm affecting the Northeastern U.S., with a net
probable maximum pre-tax loss of $676 million, followed by windstorms affecting
the Florida Tri-County and the Gulf of Mexico regions with net probable maximum
pre-tax losses of $669 and $662 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
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hurricanes. As of July 1, 2021, our modeled peak zone earthquake exposure (San
Francisco earthquake) represented approximately 75% of our peak zone catastrophe
exposure, and our modeled peak zone international exposure (UK windstorm) was
substantially less than both our peak zone windstorm and earthquake exposures.
Effective July 1, 2021, our insurance operations had in effect a reinsurance
program which provided coverage for certain property-catastrophe related losses
equal to $279 million in excess of various retentions per occurrence.
We also have significant exposure to losses due to mortgage defaults resulting
from severe economic events in the future. For our U.S. mortgage insurance
business, we have developed a proprietary risk model ("Realistic Disaster
Scenario" or "RDS") that simulates the maximum loss resulting from a severe
economic downturn impacting the housing market. The RDS models the collective
impact of adverse conditions for key economic indicators, the most significant
of which is a decline in home prices. The RDS model projects paths of future
home prices, unemployment rates, income levels and interest rates and assumes
correlation across states and geographic regions. The resulting future
performance of our in-force portfolio is then estimated under the economic
stress scenario, reflecting loan and borrower information.
Currently, we seek to limit our modeled RDS loss from a severe economic event to
approximately 25% of tangible shareholders' equity available to Arch. We reserve
the right to change this threshold at any time. Based on in-force exposure
estimated as of July 1, 2021, our modeled RDS loss was approximately 6% 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 2020 Form 10-K.
OFF-BALANCE SHEET ARRANGEMENTS


Off-balance sheet arrangements are discussed in Management's Discussion and
Analysis of Financial Condition and Results of Operations contained in our 2020
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 June 30, 2021. 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. We have not included Watford in the
following analyses as we do not guarantee or provide credit support for Watford,
and our financial exposure to Watford is limited to our investment in Watford's
senior notes, common and preferred shares and counterparty credit risk
(mitigated by collateral) arising from reinsurance transactions.
An analysis of material changes in market risk exposures at June 30, 2021 that
affect the quantitative and qualitative disclosures presented in our 2020
Form 10-K (see section captioned "Management's Discussion and Analysis of
Financial Condition and Results of Operations-Market Sensitive Instruments and
Risk Management") were as follows:
Investment Market Risk
Fixed Income Securities. We invest in interest rate sensitive securities,
primarily debt securities. We consider the effect of interest rate movements on
the fair value of our fixed maturities, fixed maturities pledged under
securities lending agreements, short-term investments and certain of our other
investments, equity securities and investment funds accounted for using the
equity method which invest in fixed income securities (collectively, "Fixed
Income Securities") and the corresponding change in unrealized appreciation. As
interest rates rise, the fair value of our Fixed Income
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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                             Interest Rate Shift in Basis Points
billions)                        -100          -50            -           +50           +100
Jun 30, 2021
Total fair value              $ 25.83       $ 25.45       $ 25.08      $ 24.70       $ 24.33
Change from base                  3.0  %        1.5  %                    (1.5) %       (3.0) %
Change in unrealized value    $  0.75       $  0.38                    $ (0.38)      $ (0.75)

Dec 31, 2020
Total fair value              $ 25.82       $ 25.44       $ 25.07      $ 24.69       $ 24.31
Change from base                  3.0  %        1.5  %                    (1.5) %       (3.0) %
Change in unrealized value    $  0.75       $  0.38                    $ (0.38)      $ (0.75)


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.
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                           Credit Spread Shift in Percentage Points
billions)                        -100           -50            -           +50           +100
Jun 30, 2021
Total fair value              $  25.55       $ 25.33       $ 25.08      $ 24.83       $ 24.60
Change from base                   1.9  %        1.0  %                    (1.0) %       (1.9) %
Change in unrealized value    $   0.48       $  0.25                    $ (0.25)      $ (0.48)

Dec 31, 2020
Total fair value              $  25.54       $ 25.32       $ 25.07      $ 24.82       $ 24.59
Change from base                   1.9  %        1.0  %                    (1.0) %       (1.9) %
Change in unrealized value    $   0.48       $  0.25                    $ 

(0.25) $ (0.48)




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 June 30, 2021, our portfolio's VaR was estimated to be 6.1%
compared to an estimated 4.3% at December 31, 2020. 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 June 30, 2021 and December 31, 2020, the fair value of our
investments in equity securities (excluding securities included in Fixed Income
Securities above) totaled $1.3 billion and $1.1 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
$132.9 million and $109.5 million at June 30, 2021 and December 31, 2020,
respectively, and would have decreased book value per share by approximately
$0.33 and $0.27, respectively. An immediate hypothetical 10% increase in the
value of each position would increase the fair value of such investments by
approximately $132.9 million and $109.5 million at June 30, 2021 and
December 31, 2020, respectively, and would have increased book value per share
by approximately $0.33 and $0.27, respectively.
Investment-Related Derivatives. At June 30, 2021, the notional value of all
derivative instruments (excluding to-be-announced mortgage backed securities
which are included in the fixed income securities analysis above and foreign
currency forward contracts which are included in the foreign currency exchange
risk analysis below) was $7.5 billion, compared to $8.6 billion at December 31,
2020. If the underlying exposure of each investment-related derivative held at
June 30, 2021 depreciated by 100 basis points, it would have resulted in a
reduction in net income of approximately $75.0 million, and a decrease in book
value per share of approximately $0.19 per share, compared to $85.7 million and
$0.21 per share, respectively, on investment-related derivatives held at
December 31, 2020. If the underlying exposure of each investment-related
derivative held at June 30, 2021 appreciated by 100 basis points, it would have
resulted in an increase in net income of approximately $75.0 million, and an
increase in book value per share of approximately $0.19 per share, compared to
$85.7 million and $0.21 per share, respectively, on
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investment-related derivatives held at December 31, 2020. 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."
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:

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