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OFFON

ARCH CAPITAL GROUP LTD.

(ACGL)
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ARCH CAPITAL GROUP LTD. MANAGEMENT'S DISCUSSION AND ANALYSIS OF FINANCIAL CONDITION AND RESULTS OF OPERATIONS (form 10-Q)

11/04/2021 | 02:34pm EST
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 $16.1 billion in capital at September 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


As we approach the end of 2021, our three areas of focus during the year have
remained constant. In our property and casualty segments of insurance and
reinsurance, we continue our growth in the sectors where rates allow for returns
that are substantially higher than our cost of capital. Our mortgage insurance
segment has transitioned, for the most part, from forbearance to recovery and is
producing results that made a significant contribution to our underwriting
income in the third quarter. We have also been keenly focused on actively
managing our investments and capital to enhance our returns over the long run.
The 2021 third 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. We believe that this time-tested strategy of protecting capital
through soft markets and increasing our writings in hard markets gives us the
best chance to generate superior risk adjusted returns over time. As long as
rate increases support returns above our required thresholds, we expect to
continue to grow our writings.
The trajectory and market acceptance of rate increases reinforce why we remain
optimistic that improved economics in the property casualty market will be
sustainable for some time. The property casualty industry is facing many degrees
of uncertainty, including heightened catastrophe activity, rising inflation,
COVID's ongoing influence on the global economy and perennially low interest
rates.
Rate improvements have enabled us to continue to expand writings in our property
casualty segments as we have been for two years now. Rate increases remain well
above the long-term loss cost trends and have spread to more lines than last
year. Overall, 2021 rates are up around 10% compared to 2020 and we currently
expect that the benefit of higher premium levels will be reflected well into
2022 and beyond. Positive rate increases have accelerated in lower limit
accounts which, until now, had lagged the increases in larger accounts. Our
early focus on Lloyd's and business in the UK has improved our scale and our
economics in this market. Some of our business lines that were most impacted by
COVID, like travel, are recapturing some of the lost volume as both business and
consumer travel increases.
In reinsurance, strong growth was observed across most of our lines of business,
but especially in our casualty and other specialty lines where strong rates
increases and growth in new accounts helped increase the top line. At less than
6% of our tangible equity, we remained underweight in property catastrophe
exposure and we will deploy more capital to the line if expected returns improve
meaningfully above our target. 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, delinquencies continue to be better
than our expectations at the beginning of the COVID-19 pandemic, as notices of
default have declined to pre-pandemic levels at September 30, 2021, which is
another indicator of improved conditions. Additionally, loans in forbearance
continue to decline as federal programs conclude and we remain optimistic that
most of these loans will ultimately cure.
In the 2021 third quarter, insurance in force for our U.S. primary mortgage
operations remained steady at $280.4 billion, while insurance in force for the
total mortgage segment was $457.7 billion. Overall, the market remains
competitive but rational and our mortgage business continues to generate returns
on capital in the mid teens. Mortgage originations continue at a pace similar to
last year's record origination volume and credit quality remains excellent.
Outside of the U.S., we increased our writings in Australia as a result of the
housing market remaining strong and due to our acquisition of Westpac's LMI
business.
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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 $5.1 billion of aggregate
reinsurance coverage at September 30, 2021.
FINANCIAL MEASURES


Management uses the following three key financial indicators in evaluating our
performance and measuring the overall growth in value generated for Arch
Capital's common shareholders:
Book Value per Share
Book value per share represents total common shareholders' equity available to
Arch divided by the number of common shares outstanding. Management uses growth
in book value per share as a key measure of the value generated for our common
shareholders each period and believes that book value per share is the key
driver of Arch Capital's share price over time. Book value per share is impacted
by, among other factors, our underwriting results, investment returns and share
repurchase activity, which has an accretive or dilutive impact on book value per
share depending on the purchase price.
Book value per share was $32.43 at September 30, 2021, compared to $32.02 at
June 30, 2021 and $28.75 at September 30, 2020. The 1.3% increase in book value
per share for the 2021 third quarter reflected strong underwriting returns,
which were impacted by a high level of losses from catastrophic events, along
with flat total return on investments for the period. The 12.8% increase in book
value per share over the trailing twelve months primarily reflected strong
underwriting results.
Operating Return on Average Common Equity
Operating return on average common equity ("Operating ROAE") represents
annualized after-tax operating income available to Arch common shareholders
divided by the average of beginning and ending common shareholders' equity
available to Arch during the period. After-tax operating income available to
Arch common shareholders, a non-GAAP financial measure as defined in Regulation
G, represents net income available to Arch common shareholders, excluding net
realized gains or losses (which includes changes in the allowance for credit
losses on financial assets and net impairment losses recognized in earnings)
equity in net income or loss of investment funds
accounted for using the equity method, net foreign exchange gains or losses,
transaction costs and other, loss on redemption of preferred shares and income
taxes. Management uses Operating ROAE as a key measure of the return generated
to common shareholders. See "Comment on Non-GAAP Financial Measures."
Our Operating ROAE was 9.3% for the 2021 third quarter, compared to 4.2% for the
2020 third quarter, and 10.1% for the nine months ended September 30, 2021,
compared to 3.9% for the 2020 period. Results for the 2021 third quarter
reflected a one-time gain of $95.7 million recognized from the Company's
previously disclosed acquisition of a 40% share of Greysbridge. Returns for the
2021 periods reflected strong underwriting returns and income from operating
affiliates, while the 2020 period reflected the impact of COVID-19 on
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 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 Third Quarter

                         0.01  %       (0.40) %
2020 Third Quarter                         2.30  %        2.41  %

Nine Months Ended September 30, 2021 1.50 % 0.87 % Nine Months Ended September 30, 2020 5.19 % 3.67 %




Total return for the 2021 third 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 2.68 years at September 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,
ARCH CAPITAL     43      2021 THIRD QUARTER FORM 10-Q


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generally we do not adjust the composition of the benchmark return index except
to incorporate changes to the mix of liability currencies and durations noted
above. The benchmark return index should not be interpreted as expressing a
preference for or aversion to any particular sector or sector weight. The index
is intended solely to provide, unlike many master indices that change based on
the size of their constituent indices, a relatively stable basket of investable
indices. At September 30, 2021, the benchmark return index had an average credit
quality of "Aa2" by Moody's Investors Service ("Moody's"), and an estimated
duration of 3.18 years.
The benchmark return index included weightings to the following indices:
                                                                   %
ICE BoAML 1-5 Year A - AAA U.S. Corporate Index                  13.00  %
ICE BoAML 5-10 Year A - AAA U.S. Corporate Index                 11.00
ICE BoAML 1-5 Year U.S. Treasury Index                           11.00
MSCI ACWI Net Total Return USD Index                              9.30
ICE BoAML 1-10 Year BBB U.S. Corporate Index                      5.00
JPM CLOIE Investment Grade                                        5.00
S&P/LSTA Leveraged Loan Total Return Index                       4.965
ICE BoAML U.S. Mortgage Backed Securities Index                   4.00
ICE BoAML AAA US Fixed Rate CMBS                                  4.00
ICE BoAML 1-5 Year U.K. Gilt Index                                4.00
ICE BoAML German Government 1-10 Year Index                       3.50
ICE BoAML 0-3 Year U.S. Treasury Index                            3.25
ICE BoAML 5-10 Year U.S. Treasury Index                           3.00
ICE BoAML 1-10 Year U.S. Municipal Securities Index               3.00
Bloomberg Barclays ABS Aaa Index                                  3.00
ICE BoAML 1-5 Year Australia Government Index                     2.75
ICE BoAML U.S. High Yield Constrained Index                       2.50
ICE BoAML 1-5 Year Canada Government Index                        2.00
ICE BofA CCC and Lower US High Yield Constrained Index            1.38
Bloomberg Barclays Global High Yield Index                        1.38

S&P DJ Global ex-US Select Real Estate Securities Net Index 0.825 FTSE Nareit All Mortgage Capped Index Total Return USD

           0.825
Bloomberg Barclays CMBS: Erisa Eligible Unhedged USD             0.825
ICE BoAML 15+ Year Canada Government Index                        0.50
Total                                                           100.00  %



COMMENT ON NON-GAAP FINANCIAL MEASURES



Throughout this filing, we present our operations in the way we believe will be
the most meaningful and useful to investors, analysts, rating agencies and
others who use our financial information in evaluating the performance of our
company. This presentation includes the use of after-tax operating income
available to Arch common shareholders, which is defined as net income available
to Arch common shareholders, excluding net realized gains or losses (which
includes changes in the allowance for credit losses on financial assets and net
impairment losses recognized in earnings), equity in net income or loss of
investment funds accounted for using the equity method, net foreign exchange
gains or losses, transaction costs and other, loss on redemption of preferred
shares and income taxes, and the use of annualized operating return on average
common equity. The presentation of after-tax operating income available to Arch
common shareholders and annualized operating return on average common equity are
non-GAAP financial measures as defined in Regulation G. The reconciliation of
such measures to net income available to Arch common shareholders and annualized
net income return on average common equity (the most directly comparable GAAP
financial measures) in accordance with Regulation G is included under "Results
of Operations" below.
We believe that net realized gains or losses, equity in net income or loss of
investment funds accounted for using the equity method, net foreign exchange
gains or losses, transaction costs and other and loss on redemption of preferred
shares in any particular period are not indicative of the performance of, or
trends in, our business. Although net realized gains or losses, equity in net
income or loss of investment funds accounted for using the equity method and net
foreign exchange gains or losses are an integral part of our operations, the
decision to realize investment gains or losses, the recognition of the change in
the carrying value of investments accounted for using the fair value option in
net realized gains or losses, the recognition of net impairment losses, the
recognition of equity in net income or loss of investment funds accounted for
using the equity method and the recognition of foreign exchange gains or losses
are independent of the insurance underwriting process and result, in large part,
from general economic and financial market conditions. Furthermore, certain
users of our financial information believe that, for many companies, the timing
of the realization of investment gains or losses is largely opportunistic. In
addition, changes in the allowance for credit losses and net impairment losses
recognized in earnings on the Company's investments represent
other-than-temporary declines in expected recovery values on securities without
actual realization. The use of the equity method on certain of our investments
in certain funds that invest in fixed maturity securities is driven by the
ownership structure of such funds
ARCH CAPITAL     44      2021 THIRD QUARTER FORM 10-Q


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(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. The loss on redemption of preferred shares related
to the redemption of the Company's Series E preferred shares in September 2021
and had no impact on shareholders' equity or cash flows. Due to these reasons,
we exclude net realized gains or losses, equity in net income or loss of
investment funds accounted for using the equity method, net foreign exchange
gains or losses, transaction costs and other and loss on redemption of preferred
shares from the calculation of after-tax operating income available to Arch
common shareholders.
We believe that showing net income available to Arch common shareholders
exclusive of the items referred to above reflects the underlying fundamentals of
our business since we evaluate the performance of and manage our business to
produce an underwriting profit. In addition to presenting net income available
to Arch common shareholders, we believe that this presentation enables investors
and other users of our financial information to analyze our performance in a
manner similar to how management analyzes performance. We also believe that this
measure follows industry practice and, therefore, allows the users of financial
information to compare our performance with our industry peer group. We believe
that the equity analysts and certain rating agencies which follow us and the
insurance industry as a whole generally exclude these items from their analyses
for the same reasons.
Our segment information includes the presentation of consolidated underwriting
income or loss and a subtotal of underwriting income or loss before the
contribution from the 'other' segment, through June 30, 2021. Such measures
represent the pre-tax profitability of our underwriting operations and include
net premiums earned plus other underwriting income, less losses and loss
adjustment expenses, acquisition expenses and other operating expenses. Other
operating expenses include those operating expenses that are incremental and/or
directly attributable to our individual underwriting operations. Underwriting
income or loss does not incorporate items included in our corporate
(non-underwriting) segment. While these measures are presented in   note 5,
"Segment Information,"   of the notes accompanying our consolidated financial
statements, they are considered non-GAAP financial measures when presented
elsewhere on a consolidated basis. The reconciliations of underwriting income or
loss to income before income taxes (the most directly comparable GAAP financial
measure) on a consolidated basis and a subtotal before the contribution from the
'other' segment through June 30, 2021, in accordance with Regulation G, is shown
in   note 5, "Segment Information"   to our consolidated financial statements.

We measure segment performance for our three underwriting segments based on
underwriting income or loss. We do not manage our assets by underwriting
segment, with the exception of goodwill and intangibles and, accordingly,
investment income and other non-underwriting related items are not allocated to
each underwriting segment. The 'other' segment includes the results of Watford
through June 30, 2021.
Along with consolidated underwriting income, we provide a subtotal of
underwriting income or loss before the contribution from the 'other' segment.
Through June 30, 2021, the 'other' segment included the results of Watford
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 were the primary beneficiary of Watford. As such, we
consolidated the results of Watford in our consolidated financial statements
through June 30, 2021. In the 2020 fourth quarter, Arch Capital, Watford, and
Greysbridge Ltd., a wholly-owned subsidiary of Arch Capital, entered into an
Agreement and Plan of Merger (as amended, the "Merger Agreement"). Arch Capital
assigned its rights under the Merger Agreement to Greysbridge Holdings Ltd.
("Greysbridge"). The merger and the related Greysbridge equity financing closed
on July 1, 2021. Effective July 1, 2021, Watford is wholly owned by Greysbridge,
and Greysbridge is owned 40% by Arch and 30% by certain funds managed by Kelso
and 30% by certain funds managed by Warburg. Based on the governing documents of
Greysbridge, we concluded that, while we retain significant influence over
Greysbridge, Greysbridge does not constitute a variable interest entity.
Accordingly, effective July 1, 2021, we no longer consolidate the results of
Watford in our consolidated financial statements and footnotes. See   note 12,
"Variable Interest Entities and Noncontrolling Interests"   and   note 5,
"Segment Information,"   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
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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.
RESULTS OF OPERATIONS


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

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

Equity in net (income) loss of
investment funds accounted for
using the equity method             (105,398)             (126,735)             (299,270)              (57,407)
Net foreign exchange (gains)
losses                               (36,078)               39,462               (39,522)               17,003
Transaction costs and other            1,036                 1,674                   889                 5,246
Loss on redemption of preferred
shares                                15,101                     -                15,101                     -
Income tax expense (1)                 6,236                17,010                32,100                48,088
After-tax operating income
available to Arch common
shareholders                    $    294,688          $    120,321          

$ 941,673 $ 326,691


Beginning common shareholders'
equity                          $ 12,706,072          $ 11,211,825          $ 12,325,886          $ 10,717,371
Ending common shareholders'
equity                          $ 12,557,526          $ 11,671,997          $ 12,557,526          $ 11,671,997
Average common shareholders'
equity                          $ 12,631,799          $ 11,441,911          

$ 12,441,706 $ 11,194,684


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


(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.
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Segment Information
We classify our businesses into three underwriting segments - insurance,
reinsurance and mortgage - and two other operating segments - corporate
(non-underwriting) and 'other.' Our insurance, reinsurance and mortgage segments
each have managers who are responsible for the overall profitability of their
respective segments and who are directly accountable to our chief operating
decision makers, the Chief Executive Officer of Arch Capital, the Chief
Financial Officer and Treasurer of Arch Capital and the President and Chief
Underwriting Officer of Arch Capital. The chief operating decision makers do not
assess performance, measure return on equity or make resource allocation
decisions on a line of business basis. Management measures segment performance
for our three underwriting segments based on underwriting income or loss. We do
not manage our assets by underwriting segment, with the exception of goodwill
and intangible assets, and, accordingly, investment income is not allocated to
each underwriting segment.
We determined our reportable segments using the management approach described in
accounting guidance regarding disclosures about segments of an enterprise and
related information. The accounting policies of the segments are the same as
those used for the preparation of our consolidated financial statements.
Intersegment business is allocated to the segment accountable for the
underwriting results.
Insurance Segment
The following tables set forth our insurance segment's underwriting results:
                                                                         

Three Months Ended September 30,

                                                                                                                 %
                                                                2021                     2020                  Change
Gross premiums written                                  $      1,596,619           $    1,206,328                 32.4
Premiums ceded                                                  (442,806)                (382,167)
Net premiums written                                           1,153,813                  824,161                 40.0
Change in unearned premiums                                     (215,143)                (105,007)
Net premiums earned                                              938,670                  719,154                 30.5
Other underwriting income (loss)                                       -                      (31)
Losses and loss adjustment expenses                             (668,630)                (525,321)
Acquisition expenses                                            (152,467)                (102,420)
Other operating expenses                                        (138,931)                (122,541)
Underwriting income (loss)                              $        (21,358)          $      (31,159)                31.5

                                                                                                               % Point
Underwriting Ratios                                                                                            Change
Loss ratio                                                          71.2   %                 73.0  %              (1.8)
Acquisition expense ratio                                           16.2   %                 14.2  %               2.0
Other operating expense ratio                                       14.8   %                 17.0  %              (2.2)
Combined ratio                                                     102.2   %                104.2  %              (2.0)



                                                                       

Nine Months Ended September 30,

                                                            2021                     2020                   % Change
Gross premiums written                               $     4,381,372           $    3,444,335                    27.2
Premiums ceded                                            (1,269,165)              (1,119,165)
Net premiums written                                       3,112,207                2,325,170                    33.8
Change in unearned premiums                                 (488,636)                (202,188)
Net premiums earned                                        2,623,571                2,122,982                    23.6
Other underwriting income                                          -                      (31)
Losses and loss adjustment expenses                       (1,750,257)              (1,550,632)
Acquisition expenses                                        (417,541)                (317,428)
Other operating expenses                                    (409,386)                (370,947)
Underwriting income (loss)                           $        46,387           $     (116,056)                  140.0

                                                                                                             % Point
Underwriting Ratios                                                                                          Change
Loss ratio                                                      66.7   %                 73.0  %                 (6.3)
Acquisition expense ratio                                       15.9   %                 15.0  %                  0.9
Other operating expense ratio                                   15.6   %                 17.5  %                 (1.9)
Combined ratio                                                  98.2   %                105.5  %                 (7.3)


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
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managers with unique expertise and niche products offering general liability,
commercial automobile, inland marine and property business with minimal
catastrophe exposure.
•Property, energy, marine and aviation: primary and excess general property
insurance coverages, including catastrophe-exposed property coverage, for
commercial clients. Coverages for marine include hull, war, specie and
liability. Aviation and standalone terrorism are also offered.
•Travel, accident and health: specialty travel and accident and related
insurance products for individual, group travelers, travel agents and suppliers,
as well as accident and health, which provides accident, disability and medical
plan insurance coverages for employer groups, medical plan members, students and
other participant groups.
•Other: includes alternative market risks (including captive insurance
programs), excess workers' compensation and employer's liability insurance
coverages for qualified self-insured groups, associations and trusts, and
contract and commercial surety coverages, including contract bonds (payment and
performance bonds) primarily for medium and large contractors and commercial
surety bonds for Fortune 1,000 companies and smaller transaction business
programs.
Premiums Written.
The following tables set forth our insurance segment's net premiums written by
major line of business:
                                                                    Three Months Ended September 30,
                                                           2021                                             2020
                                              Amount                      %                    Amount                    %
Property, energy, marine and aviation  $          215,062                   18.6          $      152,193                   18.5
Professional lines                                310,185                   26.9                 199,163                   24.2
Programs                                          196,048                   17.0                 123,768                   15.0
Construction and national accounts                 92,253                    8.0                  88,790                   10.8
Excess and surplus casualty                        98,320                    8.5                  78,889                    9.6
Travel, accident and health                        62,837                    5.4                  28,972                    3.5
Lenders products                                   38,905                    3.4                  60,830                    7.4
Other                                             140,203                   12.2                  91,556                   11.1
Total                                  $        1,153,813                  100.0          $      824,161                  100.0


2021 Third Quarter versus 2020 Period. Gross premiums written by the insurance
segment in the 2021 third quarter were 32.4% higher than in the 2020 third
quarter, while net premiums written were 40.0% higher. The higher level of net
premiums written reflected increases in most lines of business, due in part to
rate increases, new business opportunities and growth in existing accounts.
                                                                    Nine Months Ended September 30,
                                                          2021                                             2020
                                              Amount                     %                    Amount                    %
Property, energy, marine and aviation  $         593,322                   19.1          $      439,579                   18.9
Professional Lines                               803,392                   25.8                 526,180                   22.6
Programs                                         503,822                   16.2                 341,230                   14.7
Construction and national accounts               304,624                    9.8                 261,933                   11.3
Excess and surplus casualty                      258,259                    8.3                 209,011                    9.0
Travel, accident and health                      226,214                    7.3                 183,015                    7.9
Lenders products                                 114,151                    3.7                 117,812                    5.1
Other                                            308,423                    9.9                 246,410                   10.6
Total                                  $       3,112,207                  100.0          $    2,325,170                  100.0


Nine Months Ended September 30, 2021 versus 2020 Period. Gross premiums written
by the insurance segment for the nine months ended September 30, 2021 were 27.2%
higher than in the 2020 period, while net premiums written were 33.8% 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 September 30,
                                                          2021                                             2020
                                              Amount                     %                    Amount                    %
Property, energy, marine and aviation  $         187,905                   20.0          $      133,827                   18.6
Professional lines                               249,007                   26.5                 168,502                   23.4
Programs                                         137,299                   14.6                 104,861                   14.6
Construction and national accounts                94,523                   10.1                  95,386                   13.3
Excess and surplus casualty                       84,048                    9.0                  69,978                    9.7
Travel, accident and health                       56,102                    6.0                  36,726                    5.1
Lenders products                                  33,030                    3.5                  33,401                    4.6
Other                                             96,756                   10.3                  76,473                   10.6
Total                                  $         938,670                  100.0          $      719,154                  100.0


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                                                                    Nine Months Ended September 30,
                                                          2021                                             2020
                                              Amount                     %                    Amount                    %
Property, energy, marine and aviation  $         512,880                   19.5          $      365,791                   17.2
Professional Lines                               662,776                   25.3                 475,014                   22.4
Programs                                         369,113                   14.1                 322,203                   15.2
Construction and national accounts               293,043                   11.2                 286,691                   13.5
Excess and surplus casualty                      232,314                    8.9                 196,041                    9.2
Travel, accident and health                      168,378                    6.4                 166,218                    7.8
Lenders products                                 119,507                    4.6                  81,855                    3.9
Other                                            265,560                   10.1                 229,169                   10.8
Total                                  $       2,623,571                  100.0          $    2,122,982                  100.0


Net premiums written are primarily earned on a pro rata basis over the terms of
the policies for all products, usually 12 months. Net premiums earned reflect
changes in net premiums written over the previous five quarters. Net premiums
earned in the 2021 third quarter were 30.5% higher than in the 2020 third
quarter. Net premiums earned for the nine months ended September 30, 2021 were
23.6% higher than in the 2020 period.
Losses and Loss Adjustment Expenses.
The table below shows the components of the insurance segment's loss ratio:
                                                    Three Months Ended                                          Nine Months Ended
                                                      September 30,                                               September 30,
                                             2021                             2020                       2021                        2020
Current year                                            71.7  %                    73.3  %                     67.2  %                    73.3  %
Prior period reserve
development                                             (0.5) %                    (0.3) %                     (0.5) %                    (0.3) %
Loss ratio                                              71.2  %                    73.0  %                     66.7  %                    73.0  %


Current Year Loss Ratio.
2021 Third Quarter versus 2020 Period. The insurance segment's current year loss
ratio in the 2021 third quarter was 1.6 points lower than in the 2020 third
quarter. The 2021 third quarter loss ratio reflected 12.2 points of current year
catastrophic activity, primarily related to Hurricane Ida and other global
events, compared to 10.3 points of catastrophic activity for the 2020 third
quarter, which included exposure to the COVID-19 global pandemic. The insurance
segment's current year loss ratio for the nine months ended September 30, 2021
was 6.1 points lower than in the 2020 period and reflected 7.0 points of current
year catastrophic activity, compared to 9.9 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.
Prior Period Reserve Development.
The insurance segment's net favorable development was $5.1 million, or 0.5
points, for the 2021 third quarter, compared to $2.3 million, or 0.3 points, for
the 2020 third quarter, and $13.1 million, or 0.5 points for the nine months
ended September 30, 2021, compared to $5.9 million, or 0.3 points, for the 2020
period. See   note 6, "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 Third Quarter versus 2020 Period. The insurance segment's underwriting
expense ratio was 31.0% in the 2021 third quarter, consistent with 31.2% in the
2020 third quarter.
Nine Months Ended September 30, 2021 versus 2020 Period. The insurance segment's
underwriting expense ratio was 31.5% for the nine months ended September 30,
2021, compared to 32.5% 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 September 30,
                                                                                                           %
                                                         2021                     2020                   Change
Gross premiums written                           $      1,251,760           $    1,004,590                   24.6
Premiums ceded                                           (630,371)                (400,388)
Net premiums written                                      621,389                  604,202                    2.8
Change in unearned premiums                                57,313                  (49,704)
Net premiums earned                                       678,702                  554,498                   22.4
Other underwriting income (loss)                            3,293                      298
Losses and loss adjustment expenses                      (545,846)                (422,084)
Acquisition expenses                                     (129,450)                 (85,388)
Other operating expenses                                  (45,647)                 (41,818)
Underwriting income (loss)                       $        (38,948)          $        5,506                 (807.4)

                                                                                                         % Point
Underwriting Ratios                                                                                      Change
Loss ratio                                                   80.4   %                 76.1  %                 4.3
Acquisition expense ratio                                    19.1   %                 15.4  %                 3.7
Other operating expense ratio                                 6.7   %                  7.5  %                (0.8)
Combined ratio                                              106.2   %                 99.0  %                 7.2


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                                                                 Nine 

Months Ended September 30,

                                                     2021                     2020                   % Change
Gross premiums written                        $     4,080,840           $    2,934,174                    39.1
Premiums ceded                                     (1,535,607)                (967,698)
Net premiums written                                2,545,233                1,966,476                    29.4
Change in unearned premiums                          (484,607)                (388,321)
Net premiums earned                                 2,060,626                1,578,155                    30.6
Other underwriting income                               3,148                    1,767
Losses and loss adjustment expenses                (1,494,539)              (1,235,586)
Acquisition expenses                                 (381,060)                (255,516)
Other operating expenses                             (150,856)                (125,831)
Underwriting income (loss)                    $        37,319           $  
   (37,011)                  200.8

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


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
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 September 30,

                                                         2021                                             2020
                                             Amount                     %                    Amount                    %
Property excluding property
catastrophe                           $         237,025                   38.1          $      223,880                   37.1
Property catastrophe                             (7,125)                  (1.1)                 42,125                    7.0
Other specialty                                 167,006                   26.9                 159,969                   26.5
Casualty                                        187,066                   30.1                 142,401                   23.6
Marine and aviation                              19,159                    3.1                  27,839                    4.6
Other                                            18,258                    2.9                   7,988                    1.3
Total                                 $         621,389                  100.0          $      604,202                  100.0


2021 Third Quarter versus 2020 Period. Gross premiums written by the reinsurance
segment in the 2021 third quarter were 24.6% higher than in the 2020 third
quarter, while net premiums written were 2.8% higher. The lower level of growth
in net premiums written compared to gross premiums written primarily reflected a
higher level of premiums ceded due to a one-time $161.2 million adjustment,
resulting from retrocessions to Watford following its ownership change on July
1, 2021. Absent this item, the growth in net premiums written would have been
29.5%, consistent with the level of growth in gross premiums written, reflecting
increases in most lines of business, due in part to new business opportunities
and rate increases.
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                                                                   Nine 

Months Ended September 30,

                                                         2021                                             2020
                                             Amount                     %                    Amount                    %
Property excluding property
catastrophe                           $         778,959                   30.6          $      546,443                   27.8
Property catastrophe                            197,724                    7.8                 248,893                   12.7
Other Specialty                                 747,662                   29.4                 562,296                   28.6
Casualty                                        631,212                   24.8                 438,330                   22.3
Marine and aviation                             131,045                    5.1                 109,996                    5.6
Other                                            58,631                    2.3                  60,518                    3.1
Total                                 $       2,545,233                  100.0          $    1,966,476                  100.0


Nine Months Ended September 30, 2021 versus 2020 Period. Gross premiums written
by the reinsurance segment for the nine months ended September 30, 2021 were
39.1% higher than in the 2020 period, while net premiums written were 29.4%
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 September 30,

                                                         2021                                             2020
                                             Amount                     %                    Amount                    %
Property excluding property
catastrophe                           $         210,280                   31.0          $      163,081                   29.4
Property catastrophe                             61,107                    9.0                  69,524                   12.5
Other specialty                                 195,649                   28.8                 141,201                   25.5
Casualty                                        159,697                   23.5                 136,421                   24.6
Marine and aviation                              29,818                    4.4                  26,744                    4.8
Other                                            22,151                    3.3                  17,527                    3.2
Total                                 $         678,702                  100.0          $      554,498                  100.0


                                                                   Nine

Months Ended September 30,

                                                         2021                                             2020
                                             Amount                     %                    Amount                    %
Property excluding property
catastrophe                           $         600,842                   29.2          $      399,752                   25.3
Property catastrophe                            225,285                   10.9                 177,750                   11.3
Other Specialty                                 571,364                   27.7                 467,592                   29.6
Casualty                                        492,574                   23.9                 404,248                   25.6
Marine and aviation                             112,699                    5.5                  76,562                    4.9
Other                                            57,862                    2.8                  52,251                    3.3
Total                                 $       2,060,626                  100.0          $    1,578,155                  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 third quarter were 22.4% higher than in the 2020 third quarter, and reflect
changes in net premiums written over the previous five quarters. For the nine
months ended September 30, 2021, net premiums earned were 30.6% higher than in
the 2020 period.
Other Underwriting Income (Loss).
Other underwriting income for the 2021 third quarter was $3.3 million, compared
to an income of $0.3 million for the 2020 third quarter, and an income of $3.1
million for the nine months ended September 30, 2021, compared to an income of
$1.8 million for the 2020 period.

Losses and Loss Adjustment Expenses.
The table below shows the components of the reinsurance segment's loss ratio:
                                                        Three Months Ended                                      Nine Months Ended
                                                          September 30,                                           September 30,
                                                  2021                           2020                     2021                      2020
Current year                                                91.1  %                  83.7  %                   78.3  %                  84.2  %
Prior period reserve development                           (10.7) %                  (7.6) %                   (5.8) %                  (5.9) %
Loss ratio                                                  80.4  %                  76.1  %                   72.5  %                  78.3  %


Current Year Loss Ratio.
2021 Third Quarter versus 2020 Period. The reinsurance segment's current year
loss ratio in the 2021 third quarter was 7.4 points higher than in the 2020
third quarter. The 2021 third quarter loss ratio reflected 34.6 points of
current year catastrophic activity, primarily related to Hurricane Ida, European
floods and other global events. The 2020 third quarter included 26.1 points of
catastrophic activity, which included exposure to the COVID-19 pandemic.
Nine Months Ended September 30, 2021 versus 2020 Period. The reinsurance
segment's current year loss ratio for the nine months ended September 30, 2021
was 5.9 points lower than in the 2020 period and reflected 20.1 points of
current year catastrophic activity, compared to 21.6 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 $72.3 million, or 10.7
points, for the 2021 third quarter, compared to $42.0 million, or 7.6 points,
for the 2020 third quarter, and $119.6 million, or 5.8 points, for the nine
months ended September 30, 2021, compared to $93.8 million, or 5.9 points, for
the 2020 period. See   note 6, "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 Third Quarter versus 2020 Period. The underwriting expense ratio for the
reinsurance segment was 25.8% in the
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2021 third quarter, compared to 22.9% in the 2020 third quarter, with the
increase primarily resulting from changes in mix of business to lines with
higher acquisition costs and a higher level of expenses related to favorable
development of prior year loss reserves.
Nine Months Ended September 30, 2021 versus 2020 Period. The underwriting
expense ratio for the reinsurance segment was 25.8% for the nine months ended
September 30, 2021, compared to 24.2% 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 Lenders Mortgage Indemnity Limited ("ALMI")
and participation in various GSE credit risk-sharing products primarily through
Arch Re Bermuda.
The following tables set forth our mortgage segment's underwriting results.
                                                                        

Three Months Ended September 30,

                                                             2021                     2020                   % Change
Gross premiums written                                $       360,934           $      346,248                    4.2
Premiums ceded                                                (60,207)                 (47,783)
Net premiums written                                          300,727                  298,465                    0.8
Change in unearned premiums                                    11,238                   52,944
Net premiums earned                                           311,965                  351,409                  (11.2)
Other underwriting income                                       3,981                    4,600
Losses and loss adjustment expenses                           (11,543)                (153,055)
Acquisition expenses                                          (24,098)                 (35,716)
Other operating expenses                                      (46,254)                 (36,708)
Underwriting income                                   $       234,051           $      130,530                   79.3

                                                                                                             % Point
Underwriting Ratios                                                                                           Change
Loss ratio                                                        3.7   %                 43.6  %               (39.9)
Acquisition expense ratio                                         7.7   %                 10.2  %                (2.5)
Other operating expense ratio                                    14.8   %                 10.4  %                 4.4
Combined ratio                                                   26.2   %                 64.2  %               (38.0)


                                                                       

Nine Months Ended September 30,

                                                            2021                     2020                   % Change
Gross premiums written                               $     1,143,691           $    1,084,337                     5.5
Premiums ceded                                              (171,923)                (136,154)
Net premiums written                                         971,768                  948,183                     2.5
Change in unearned premiums                                   10,735                  113,965
Net premiums earned                                          982,503                1,062,148                    (7.5)
Other underwriting income                                     15,026                   15,649
Losses and loss adjustment expenses                          (85,112)                (444,721)
Acquisition expenses                                         (84,297)                (108,304)
Other operating expenses                                    (143,697)                (120,178)
Underwriting income                                  $       684,423           $      404,594                    69.2

                                                                                                             % Point
Underwriting Ratios                                                                                          Change
Loss ratio                                                       8.7   %                 41.9  %                (33.2)
Acquisition expense ratio                                        8.6   %                 10.2  %                 (1.6)
Other operating expense ratio                                   14.6   %                 11.3  %                  3.3
Combined ratio                                                  31.9   %                 63.4  %                (31.5)


Premiums Written.
The following tables set forth our mortgage segment's net premiums written by
underwriting location (i.e., where the business is underwritten):
                                             Three Months Ended September 30,
                                             2021                                  2020
                                      Amount                     %          Amount          %
Underwriting location:
United States            $         221,315                      73.6      $ 245,971        82.4
Other                               79,412                      26.4         52,494        17.6
Total                    $         300,727                     100.0      $ 298,465       100.0


2021 Third Quarter versus 2020 Period. Gross premiums written by the mortgage
segment in the 2021 third quarter were 4.2% higher than in the 2020 third
quarter, while net premiums written were 0.8% higher. The increase in gross
premiums written reflected growth in Australian single premium mortgage
insurance partially as a result of the previously disclosed acquisition of
Westpac Lenders Mortgage Insurance Limited. The lower increase in net premiums
written reflected a higher level of premiums ceded on U.S. primary mortgage
insurance.
                                            Nine Months Ended September 30,
                                            2021                                 2020
                                     Amount                    %          Amount          %

Underwriting location:
United States            $        703,489                     72.4      $ 771,203        81.3
Other                             268,279                     27.6        176,980        18.7
Total                    $        971,768                    100.0      $ 948,183       100.0


Nine Months Ended September 30, 2021 versus 2020 Period. Gross premiums written
by the mortgage segment for the nine months ended September 30, 2021 were 5.5%
higher than in the 2020 period, while net premiums written for the nine months
ended September 30, 2021 were 2.5% higher
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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 57.7% for the Arch MI U.S. portfolio of mortgage insurance
policies at September 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 September 30,

                                                        2021                                           2020
                                           Amount                     %                   Amount                   %
Total new insurance written (NIW)
(1)                                  $         27,841                                 $     32,787

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

Total                                $         27,841                  100.0          $     32,787                  100.0

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

Monthly vs. single:
Monthly                              $         26,515                   95.2          $     31,928                   97.4
Single                                          1,326                    4.8                   859                    2.6
Total                                $         27,841                  100.0          $     32,787                  100.0

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


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

(U.S. Dollars in millions)                                       Nine Months Ended September 30,
                                                        2021                                           2020
                                           Amount                     %                   Amount                   %
Total new insurance written (NIW)
(1)                                  $         83,232                                 $     74,116

Credit quality (FICO):
>=740                                $         54,572                   65.6          $     47,080                   63.5
680-739                                        25,543                   30.7                24,130                   32.6
620-679                                         3,117                    3.7                 2,906                    3.9

Total                                $         83,232                  100.0          $     74,116                  100.0

Loan-to-value (LTV):
95.01% and above                     $          4,646                    5.6          $      6,177                    8.3
90.01% to 95.00%                               40,464                   48.6                30,569                   41.2
85.01% to 90.00%                               25,381                   30.5                23,521                   31.7
85.01% and below                               12,741                   15.3                13,849                   18.7
Total                                $         83,232                  100.0          $     74,116                  100.0

Monthly vs. single:
Monthly                              $         78,229                   94.0          $     71,011                   95.8
Single                                          5,003                    6.0                 3,105                    4.2
Total                                $         83,232                  100.0          $     74,116                  100.0

Purchase vs. refinance:
Purchase                             $         71,226                   85.6          $     51,511                   69.5
Refinance                                      12,006                   14.4                22,605                   30.5
Total                                $         83,232                  100.0          $     74,116                  100.0


(1)Represents the original principal balance of all loans that received coverage
during the period.
Net Premiums Earned.
The following tables set forth our mortgage segment's net premiums earned by
underwriting location:
                                             Three Months Ended September 30,
                                             2021                                  2020
                                      Amount                     %          Amount          %
Underwriting location:
United States            $         236,892                      75.9      $ 290,451        82.7
Other                               75,073                      24.1         60,958        17.3
Total                    $         311,965                     100.0      $ 351,409       100.0


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

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                                            Nine Months Ended September 30,
                                           2021                                2020
                                    Amount                  %           Amount           %

Underwriting location:
United States            $       747,830                   76.1      $   884,265        83.3
Other                            234,673                   23.9          177,883        16.7
Total                    $       982,503                  100.0      $ 1,062,148       100.0


Nine Months Ended September 30, 2021 versus 2020 Period. Net premiums earned for
the nine months ended September 30, 2021 were 7.5% 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 $4.0 million for the 2021 third quarter, compared to $4.6
million for the 2020 third quarter.
Losses and Loss Adjustment Expenses.
The table below shows the components of the mortgage segment's loss ratio:
                                                    Three Months Ended                                Nine Months Ended
                                                      September 30,                                     September 30,
                                               2021                    2020                     2021                     2020
Current year                                       18.2  %                 44.9  %                   18.8  %                 42.9  %
Prior period reserve development                  (14.5) %                 (1.3) %                  (10.1) %                 (1.0) %
Loss ratio                                          3.7  %                 43.6  %                    8.7  %                 41.9  %


Current Year Loss Ratio.
2021 Third Quarter versus 2020 Period. The mortgage segment's current year loss
ratio was 26.7 points lower in the 2021 third quarter than in the 2020 third
quarter. The mortgage segment's current year loss ratio was 24.1 points lower
for the nine months ended September 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, primarily driven by lower
delinquencies.
For the 2020 periods, the increase in incurred losses was primarily due to, the
financial stress related to the COVID-19 pandemic. Segregating estimated losses
due to COVID-19 from the overall mortgage segment estimated losses would require
the number of delinquencies specifically attributable to COVID-19. As this
analysis cannot be performed accurately, the Company is not reporting COVID-19
provisions separately from its overall loss provisions.
Prior Period Reserve Development.
The mortgage segment's net favorable development was $45.1 million, or 14.5
points, for the 2021 third quarter, compared to $4.5 million, or 1.3 points, for
the 2020 third quarter, and $99.1 million, or 10.1 points, for the nine months
ended September 30, 2021, compared to $10.8 million, or 1.0 points, for the 2020
period. See   note 6, "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 Third Quarter versus 2020 Period. The underwriting expense ratio for the
mortgage segment was 22.5% in the 2021 third quarter, compared to 20.6% in the
2020 third quarter, with the increase primarily due to a lower level in net
premiums earned on U.S. primary mortgage insurance business.
Nine Months Ended September 30, 2021 versus 2020 Period. The underwriting
expense ratio for the mortgage segment was 23.2% for the nine months ended
September 30, 2021, compared to 21.5% for the 2020 period, with the increase
primarily due to a lower level 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.
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Net Investment Income.
The components of net investment income were derived from the following sources:
                              Three Months Ended            Nine Months Ended
                                September 30,                 September 30,
                              2021           2020          2021           2020
Fixed maturities          $   75,964      $ 84,608      $ 232,690      $ 277,862

Equity securities              9,867         6,659         23,799         18,312
Short-term investments         1,858         1,162          3,474          5,444

Other (1)                     19,114        24,594         55,699         62,898
Gross investment income      106,803       117,023        315,662        364,516
Investment expenses (2)      (18,608)      (17,166)       (59,308)       (50,600)
Net investment income     $   88,195      $ 99,857      $ 256,354        313,916


(1)  Amounts include dividends and other distributions on investment funds, term
loan investments, funds held balances, cash balances and other items.
(2)  Investment expenses were approximately 0.32% of average invested assets for
the 2021 third quarter, compared to 0.32% for the 2020 third quarter, and 0.32%
for the nine months ended September 30, 2021, compared to 0.31% for the 2020
period.
The lower level of net investment income for the 2021 third 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 1.41% for the 2021 third quarter, compared to 1.76% for the 2020
third quarter, and 1.40% for the nine months ended September 30, 2021, compared
to 1.94% for the 2020 period.
Corporate Expenses.
Corporate expenses were $18.6 million for the 2021 third quarter, compared to
$16.3 million for the 2020 third quarter, and $59.3 million for the nine months
ended September 30, 2021, compared to $51.4 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 $1.0 million for the 2021 third quarter,
compared to $1.7 million for the 2020 third quarter, and $0.8 million for the
nine months ended September 30, 2021, compared to $5.2 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 third quarter was $20.1 million,
compared to $16.7 million for the 2020 third quarter, and $48.9 million for the
nine months ended
September 30, 2021, compared to $49.8 million for the 2020 period. Amounts in
2021 and 2020 primarily related to amortization of finite-lived intangible
assets. The increase in amortization of intangible assets expense was a result
of acquisitions closed during the 2021 third quarter.
Interest Expense.
Interest expense was $33.2 million for the 2021 third quarter, compared to the
$36.2 million for the 2020 third quarter, and $98.8 million for the nine months
ended September 30, 2021, compared to $86.6 million for the 2020 period.The
higher level of interest expense in 2021 period mainly resulted from the
issuance of $1.0 billion of 3.635% senior notes on June 30, 2020.
Loss on Redemption of Preferred Shares.
In September 2021, we redeemed all 5.25% Series E preferred shares and, in
accordance with GAAP, we recorded a loss of $15.1 million to remove original
issuance costs related to the redeemed shares from additional paid-in capital.
Such adjustment had no impact on total shareholders' equity or cash flows.

Net Realized Gains or Losses.
We recorded net realized losses of $25.0 million for the 2021 third quarter,
compared to net realized gains of $211.0 million for the 2020 third quarter, and
net realized gains of $239.7 million for the nine months ended September 30,
2021, compared to net realized gains of $524.0 million for the 2020 period. In
addition, 2021 third quarter included $33.1 million loss as a result of
deconsolidation of Watford in our financial statements following the close of
the transaction. Currently, our portfolio is actively managed to maximize total
return within certain guidelines. The effect of financial market movements on
the investment portfolio will directly impact net realized gains and losses as
the portfolio is adjusted and rebalanced. Net realized gains or losses from the
sale of fixed maturities primarily results from our decisions to reduce credit
exposure, to change duration targets, to rebalance our portfolios or due to
relative value determinations.
Net realized gains or losses also include realized and unrealized contract gains
and losses on our derivative instruments, changes in the fair value of assets
accounted for using the fair value option and in the fair value of equities,
along with changes in the allowance for credit losses on financial assets and
net impairment losses recognized in earnings. See   note 8, "Investment
Information-Net Realized Gains (Losses),"   to our consolidated financial
statements for additional information. See   note 8, "Investment
Information-Allowance for Credit Losses,"   to our consolidated financial
statements for additional information.
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Equity in Net Income (Loss) of Investment Funds Accounted for Using the Equity
Method.
We recorded $105.4 million of equity in net income related to investment funds
accounted for using the equity method in the 2021 third quarter, compared to
income of $126.7 million for the 2020 third quarter, and $299.3 million of
income for the nine months ended September 30, 2021, compared to income of $57.4
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 $2.7 billion at
September 30, 2021, compared to $2.0 billion at December 31, 2020. See   note 8,
"Investment Information-Investments Accounted For Using the Equity Method," 

to

our consolidated financial statements for additional information.
Net Foreign Exchange Gains or Losses.
Net foreign exchange gains for the 2021 third quarter were $36.1 million,
compared to net foreign exchange losses for the 2020 third quarter of $38.7
million. Net foreign exchange gains for the nine months ended September 30, 2021
were $39.7 million, compared to net foreign exchange losses for the 2020 period
of $17.8 million. Amounts in both periods were primarily unrealized and resulted
from the effects of revaluing our net insurance liabilities required to be
settled in foreign currencies at each balance sheet date.
Income Tax Expense.
Our income tax provision on income (loss) before income taxes, including income
(loss) from operating affiliates, resulted in an expense of 1.0% for the 2021
third quarter, compared to 5.4% for the 2020 third quarter, and 5.8% for the
nine months ended September 30, 2021, compared to 8.3% for the 2020 period. The
effective tax rates for the 2021 third quarter and nine months ended September
30, 2021 included discrete income tax benefits of $25.3 million and $28.7
million, respectively. The discrete tax items primarily related to the partial
release of a valuation allowance on certain U.K. deferred tax assets in the
third quarter. 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 $124.1 million of net income from our operating affiliates in the
2021 third quarter, compared to income of $0.9 million for the 2020 third
quarter, and $224.1 million of income for the nine months ended September 30,
2021, compared to $6.3 million for the 2020 period. Results for the 2021 third
quarter reflected a one-time gain of $95.7 million recognized from the Company's
previously disclosed
acquisition of a 40% share of Greysbridge. Results for 2021 period, primarily
include income from our investment in Coface, Greysbridge and Premia.
Other Segment
Through June 30, 2021, the 'other' segment included the results of Watford.
Pursuant to GAAP, Watford was considered a variable interest entity and we
concluded that we were the primary beneficiary of Watford. As such, we
consolidated the results of Watford in our consolidated financial statements
through June 30, 2021. In July 2021, we announced the completion of the
previously disclosed acquisition of Watford by Greysbridge. Based on the
governing documents of Greysbridge, the Company has concluded that, while it
retains significant influence over Watford, Watford no longer constitutes a
variable interest entity. Accordingly, effective July 1, 2021, Arch no longer
consolidates the results of Watford in its consolidated financial statements.
See   note 12, "Variable Interest Entities and Noncontrolling Interests"   and
  note 5, "Segment Information"   to our consolidated financial statements for
additional information on Watford.
CRITICAL ACCOUNTING POLICIES,
ESTIMATES AND RECENT ACCOUNTING PRONOUNCEMENTS


Critical accounting policies, estimates and recent accounting pronouncements are
discussed in Management's Discussion and Analysis of Financial Condition and
Results of Operations contained in our 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." ARCH CAPITAL 56 2021 THIRD QUARTER FORM 10-Q

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FINANCIAL CONDITION


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
September 30, 2021
Fixed maturities (2)                                      $    17,182,370                    63.0
Short-term investments (2)                                      3,185,646                    11.7
Cash                                                            1,137,721                     4.2
Equity securities (2)                                           1,815,163                     6.7
Other investments (2)                                           1,489,759                     5.5
Other investable assets (3)                                             -                       -
Investments accounted for using the equity method               2,741,293                    10.0

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

                                           (273,512)                   (1.0)
Total investable assets held by Arch                      $    27,278,440                   100.0

Average effective duration (in years)                                2.68
Average S&P/Moody's credit ratings (4)                               AA-/Aa3
Embedded book yield (5)                                              1.54  %

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

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

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

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


(1)In securities lending transactions, we receive collateral in excess of the
fair value of the securities pledged. For purposes of this table, we have
excluded the collateral received under securities lending, at fair value and
included the securities pledged under securities lending, at fair value. In
September 2021, the Company terminated its securities lending program.
(2)Includes investments carried as available for sale, at fair value and at fair
value under the fair value option.
(3)Represents participation interests in a receivable of a reverse repurchase
agreement.
(4)Average credit ratings on our investment portfolio on securities with ratings
by Standard & Poor's Rating Services ("S&P") and Moody's Investors Service
("Moody's").
(5)Before investment expenses.
At September 30, 2021, approximately $18.4 billion, or 67.3%, of total
investable assets held by Arch were internally managed, compared to $19.2
billion, or 71.4%, at December 31, 2020.
The following table summarizes our fixed maturities and fixed maturities pledged
under securities lending agreements ("Fixed Maturities") by type:
                                            Estimated          % of
                                            Fair Value        Total
September 30, 2021
Corporate bonds                           $  6,777,943        39.4

Residential mortgage backed securities 405,797 2.4 Municipal bonds

                                382,722         2.2

Commercial mortgage backed securities 579,424 3.4 U.S. government and government agencies 4,460,515 26.0 Non-U.S. government securities

               1,883,563        11.0
Asset backed securities                      2,692,406        15.7
Total                                     $ 17,182,370       100.0

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

Residential mortgage backed securities 616,619 3.3 Municipal bonds

                                492,734         2.6

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

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


The following table provides the credit quality distribution of our Fixed Maturities. 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
September 30, 2021
U.S. government and gov't agencies (1)    $           4,830,467        28.1
AAA                                                   3,257,679        19.0
AA                                                    2,217,452        12.9
A                                                     2,773,104        16.1
BBB                                                   2,807,788        16.3
BB                                                      522,357         3.0
B                                                       348,036         2.0
Lower than B                                             43,751         0.3
Not rated                                               381,736         2.2
Total                                     $          17,182,370       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. ARCH CAPITAL 57 2021 THIRD QUARTER FORM 10-Q

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The following table provides information on the severity of the unrealized loss
position as a percentage of amortized cost for all Fixed Maturities which were
in an unrealized loss position:
                                                                                       % of
                                                                     Gross         Total Gross
                                                                   Unrealized       Unrealized
Severity of gross unrealized losses:    Estimated Fair Value         Losses           Losses
September 30, 2021
0-10%                                  $           9,287,536      $ (106,042)         93.6
10-20%                                                27,315          (4,173)          3.7
20-30%                                                 8,233          (2,034)          1.8
Greater than 30%                                         993          (1,088)          1.0
Total                                  $           9,324,077      $ (113,337)        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 September 30, 2021, excluding guaranteed amounts and
covered bonds:
                                                               Credit
                                 Estimated Fair Value        Rating (1)
Bank of America Corporation     $             359,893               A-/A2
JPMorgan Chase & Co.                          294,411               A-/A2
Citigroup Inc.                                247,892             BBB+/A3
Wells Fargo & Company                         231,542             BBB+/A1
Morgan Stanley                                215,424             BBB+/A1
The Goldman Sachs Group, Inc.                 180,324             BBB+/A2
Dai-ichi Life Holdings, Inc.                  111,418              AA-/A1
Apple Inc.                                    111,280             AA+/Aa1
Westpac Banking Corporation                   107,389             AA-/Aa3
Nestlé S.A.                                    83,838             AA-/Aa3
Total                           $           1,943,411

(1)Average credit ratings as assigned by S&P and Moody's, respectively. The following table provides information on our structured securities, which includes residential mortgage-backed securities ("RMBS"), commercial mortgage-backed securities ("CMBS") and asset-backed securities ("ABS"):

                Agencies       Investment Grade       Below Investment Grade          Total
Sep 30, 2021
RMBS           $ 345,175      $          48,301      $                12,321      $   405,797
CMBS              24,779                502,218                       52,427          579,424
ABS                    -              2,374,981                      317,425        2,692,406
Total          $ 369,954      $       2,925,500      $               382,173      $ 3,677,627

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:

                         September 30,       December 31,
                              2021               2020
Equities (1)            $      856,837      $    676,437
Exchange traded funds
Fixed income (2)               348,613           341,139
Equity and other (3)           609,713           418,528
Total                   $    1,815,163      $  1,436,104


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

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

Other investable assets                       -           500,000

Total other investments          $    1,489,759      $  1,980,347


For details on our investments accounted for using the equity method, see   note
8, "Investment Information-Investments Accounted For Using the Equity Method,"
to our consolidated financial statements.
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Our investment strategy allows for the use of derivative instruments. We utilize
various derivative instruments such as futures contracts to enhance investment
performance, replicate investment positions or manage market exposures and
duration risk that would be allowed under our investment guidelines if
implemented in other ways. See   note 10, "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 9, "Fair Value,"   to our
consolidated financial statements for a summary of our financial assets and
liabilities measured at fair value, segregated by level in the fair value
hierarchy.
Reinsurance
The effects of reinsurance on written and earned premiums and losses and loss
adjustment expenses ("LAE") with unaffiliated reinsurers were as follows:
                           Three Months Ended                Nine Months Ended
                             September 30,                     September 30,
                         2021             2020             2021             2020
Premiums written:
Direct               $ 1,993,098      $ 1,667,449      $ 5,795,236      $ 4,841,874
Assumed                1,214,317        1,013,583        4,095,676        2,989,680
Ceded                 (1,131,486)        (806,888)      (2,907,002)      (2,151,853)
Net                  $ 2,075,929      $ 1,874,144      $ 6,983,910      $ 5,679,701

Premiums earned:
Direct               $ 1,754,462      $ 1,618,583      $ 5,263,286      $ 4,723,630
Assumed                1,129,434          880,024        3,169,016        2,387,286
Ceded                   (954,559)        (727,515)      (2,433,634)      (1,930,026)
Net                  $ 1,929,337      $ 1,771,092      $ 5,998,668      $ 5,180,890

Losses and LAE:
Direct               $ 1,101,793      $ 1,131,696      $ 3,134,305      $ 3,279,737
Assumed                  961,285          635,199        2,182,852        1,689,176
Ceded                   (837,059)        (550,622)      (1,728,207)      (1,406,699)
Net                  $ 1,226,019      $ 1,216,273      $ 3,588,950      $ 3,562,214


See   note 7, "Allowance for Expected Credit Losses,"   to our consolidated
financial statements for information about our reinsurance recoverables and
related allowance for credit losses.
Bellemeade Re
We have entered into aggregate excess of loss mortgage reinsurance agreements
with various special purpose reinsurance companies domiciled in Bermuda (the
"Bellemeade Agreements"). For the respective coverage periods, we will retain
the first layer of the respective aggregate losses and the special purpose
reinsurance companies will provide second layer coverage up to the outstanding
coverage amount. We will then retain losses in excess of the outstanding
coverage limit. The aggregate excess of loss reinsurance coverage generally
decreases over a ten-year period as the underlying covered mortgages amortize,
unless provisional call options embedded within certain of the Bellemeade
Agreements are executed or if pre-defined delinquency triggering events occur.
The following table summarizes the respective coverages and retentions at
September 30, 2021:
                                                                                         September 30, 2021
                                                   Initial Coverage                                        Remaining
                                                     at Issuance             Current Coverage           Retention, Net
Bellemeade 2017-1 Ltd. (1)                        $       368,114          $         145,573          $        124,777
Bellemeade 2018-1 Ltd. (2)                                374,460                    228,938                   121,411
Bellemeade 2018-3 Ltd. (3)                                506,110                    302,563                   126,578
Bellemeade 2019-1 Ltd. (4)                                341,790                    210,529                    98,340
Bellemeade 2019-2 Ltd. (5)                                621,022                    398,316                   156,085
Bellemeade 2019-3 Ltd. (6)                                700,920                    491,634                   178,759
Bellemeade 2019-4 Ltd. (7)                                577,267                    468,737                   113,674
Bellemeade 2020-2 Ltd. (8)                                449,167                    268,468                   227,140
Bellemeade 2020-3 Ltd. (9)                                451,816                    405,881                   159,615
Bellemeade 2020-4 Ltd. (10)                               337,013                    238,480                   133,872
Bellemeade 2021-1 Ltd. (11)                               643,577                    643,577                   157,685
Bellemeade 2021-2 Ltd. (12)                               616,017                    616,017                   146,956
Bellemeade 2021-3 Ltd. (13)                               639,391                    639,391                   145,790
Total                                             $     6,626,664          $       5,058,104          $      1,890,682


(1)  Issued in October 2017, covering in-force policies issued between January
1, 2017 and June 30, 2017.
(2)  Issued in April 2018, covering in-force policies issued between July 1,
2017 and December 31, 2017.
(3)  Issued in October 2018, covering in-force policies issued between January
1, 2018 and June 30, 2018.
(4)  Issued in March 2019, covering in-force policies primarily issued between
2005-2008 under United Guaranty Residential Insurance Company ("UGRIC"); as well
as policies issued through 2015 under both UGRIC and Arch Mortgage Insurance
Company.
(5)  Issued in April 2019, covering in-force policies issued between July 1,
2018 and December 31, 2018.
(6)  Issued in July 2019, covering in-force policies issued in 2016.
(7)  Issued in October 2019, covering in-force policies issued between January
1, 2019 and June 30, 2019.
(8)  Issued in September 2020, covering in-force policies issued between January
1, 2020 and May 31, 2020. $423 million was directly funded by Bellemeade 2020-2
Ltd. with an additional $26 million of capacity provided directly to Arch MI
U.S. by a separate panel of reinsurers.
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(9)  Issued in November 2020, covering in-force policies issued between June 1,
2020 and August 31, 2020. $418 million was directly funded by Bellemeade 2020-3
Ltd. with an additional $34 million of capacity provided directly to Arch MI
U.S. by a separate panel of reinsurers.
(10) Issued in December 2020, covering in-force policies issued between July 1,
2019 and December 31, 2019. $321 million was directly funded by Bellemeade
2020-4 Ltd. with an additional $16 million of capacity provided directly to Arch
MI U.S. by a separate panel of reinsurers.
(11) Issued in March 2021, covering in-force policies issued between September
1, 2020 and November 30, 2020. $580 million was directly funded by Bellemeade Re
2021-1 Ltd. with an additional $64 million capacity provided directly to Arch MI
U.S. by a separate panel of reinsurers.
(12) Issued in June 2021, covering in-force policies issued between December 1,
2020 and March 31, 2021. $523 million was directly funded by Bellemeade Re
2021-2 Ltd. via insurance-linked notes, with an additional $93 million capacity
provided directly to Arch MI U.S. by a separate panel of reinsurers.
(13) Issued in September 2021, covering in-force policies issued between April
1, 2021 and June 30, 2021. $508 million was directly funded by Bellemeade Re
2021-3 Ltd. via insurance-linked notes, with an additional $131 million capacity
provided directly to Arch MI U.S. by a separate panel of reinsurers.
Reserve for Losses and Loss Adjustment Expenses
We establish reserve for losses and loss adjustment expenses ("Loss Reserves")
which represent estimates involving actuarial and statistical projections, at a
given point in time, of our expectations of the ultimate settlement and
administration costs of losses incurred. Estimating Loss Reserves is inherently
difficult. We utilize actuarial models as well as available historical insurance
industry loss ratio experience and loss development patterns to assist in the
establishment of Loss Reserves. Actual losses and loss adjustment expenses paid
will deviate, perhaps substantially, from the reserve estimates reflected in our
financial statements.
At September 30, 2021 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:
                            September 30,      December 31,
                                2021               2020
Insurance segment:
Case reserves              $   2,147,930      $  2,051,640
IBNR reserves                  4,341,016         3,889,823
Total net reserves             6,488,946         5,941,463
Reinsurance segment:
Case reserves                  1,562,072         1,560,523
Additional case reserves         549,476           280,472
IBNR reserves                  2,617,728         2,253,953
Total net reserves             4,729,276         4,094,948
Mortgage segment:
Case reserves                    731,671           631,921
IBNR reserves                    266,007           271,702
Total net reserves               997,678           903,623
Other segment:
Case reserves                          -           566,587
Additional case reserves               -            32,321
IBNR reserves                          -           660,132
Total net reserves                     -         1,259,040
Total:
Case reserves                  4,441,673         4,810,671
Additional case reserves         549,476           312,793
IBNR reserves                  7,224,751         7,075,610
Total net reserves         $  12,215,900      $ 12,199,074

At September 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:

                                         September 30,       December 31,
                                              2021               2020
Insurance segment:
Professional lines (1)                  $    1,587,042      $  1,482,820
Construction and national accounts           1,468,668         1,395,067
Excess and surplus casualty (2)                903,966           816,495
Programs                                       760,273           699,354
Property, energy, marine and aviation          599,431           517,692
Travel, accident and health                     93,632            98,910
Lenders products                                70,520            48,946
Other (3)                                    1,005,414           882,179
Total net reserves                      $    6,488,946      $  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.
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At September 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:
                                           September 30,       December 31,
                                                2021               2020
Reinsurance segment:
Casualty (1)                              $    2,079,990      $  1,995,849
Other specialty (2)                            1,093,611           917,178
Property excluding property catastrophe          669,922           594,033
Marine and aviation                              231,203           204,205
Property catastrophe                             526,356           268,858
Other (3)                                        128,194           114,825
Total net reserves                        $    4,729,276      $  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 September 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:
                                        September 30,       December 31,
                                             2021               2020

U.S. primary mortgage insurance (1) $ 726,636 $ 649,748 Other

                                         271,042            253,875
Total net reserves                     $      997,678      $     903,623


(1) At September 30, 2021, 27.9% 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.


Mortgage Operations Supplemental Information
The mortgage segment's insurance in force ("IIF") and risk in force ("RIF") were
as follows at September 30, 2021 and December 31, 2020:
(U.S. Dollars in millions)                             September 30, 2021                                 December 31, 2020
                                                 Amount                      %                      Amount                      %
Insurance In Force (IIF) (1):
U.S. primary mortgage insurance           $          280,379                   61.3          $          280,579                   66.2
U.S. credit risk transfer (CRT) and other
(2)                                                  108,203                   23.6                     103,535                   24.4
International mortgage
insurance/reinsurance (3)                             69,127                   15.1                      39,425                    9.3
Total                                     $          457,709                  100.0          $          423,539                  100.0

Risk In Force (RIF) (4):
U.S. primary mortgage insurance           $           70,320                   84.8          $           70,522                   90.5
U.S. credit risk transfer (CRT) and other
(2)                                                    4,817                    5.8                       4,699                    6.0
International mortgage
insurance/reinsurance (3)                              7,803                    9.4                       2,673                    3.4
Total                                     $           82,940                  100.0          $           77,894                  100.0


(1)Represents the aggregate dollar amount of each insured mortgage loan's
current principal balance.
(2)Includes all CRT transactions, which are predominantly with GSEs, and other
U.S. reinsurance transactions.
(3)International mortgage insurance and reinsurance with risk primarily located
in Australia, which reflects WLMI acquisition in the 2021 third quarter and to
lesser extent Europe and Asia.
(4)The aggregate dollar amount of each insured mortgage loan's current principal
balance multiplied by the insurance coverage percentage specified in the policy
for insurance policies issued and after contract limits and/or loss ratio caps
for risk-sharing or reinsurance.


The IIF and RIF for our U.S. primary mortgage insurance business by policy year
were as follows at September 30, 2021:
(U.S. Dollars in millions)              IIF                       RIF               Delinquency
                                Amount          %          Amount         %          Rate (1)
Policy year:
2011 and prior                $  11,888         4.2      $  2,672         3.8            9.51  %
2012                              1,974         0.7           505         0.7            2.76  %
2013                              4,876         1.7         1,342         1.9            2.72  %
2014                              5,454         1.9         1,501         2.1            3.37  %
2015                              9,810         3.5         2,637         3.8            2.92  %
2016                             16,150         5.8         4,324         6.1            3.64  %
2017                             15,001         5.4         3,910         5.6            4.50  %
2018                             16,193         5.8         4,105         5.8            5.75  %
2019                             29,860        10.6         7,463        10.6            3.58  %
2020                             88,737        31.6        21,777        31.0            0.91  %
2021                             80,436        28.7        20,084        28.6            0.19  %
Total                         $ 280,379       100.0      $ 70,320       100.0            2.67  %

(1)Represents the ending percentage of loans in default. ARCH CAPITAL 61 2021 THIRD QUARTER FORM 10-Q

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The IIF and RIF for our U.S. primary mortgage insurance business by policy year
were as follows at December 31, 2020:
(U.S. Dollars in millions)              IIF                       RIF               Delinquency
                                Amount          %          Amount         %          Rate (1)
Policy year:
2011 and prior                $  14,588         5.2      $  3,327         4.7           11.36  %
2012                              3,651         1.3           992         1.4            2.98  %
2013                              7,546         2.7         2,107         3.0            3.30  %
2014                              8,261         2.9         2,273         3.2            4.06  %
2015                             15,032         5.4         4,048         5.7            3.72  %
2016                             24,958         8.9         6,648         9.4            4.77  %
2017                             24,748         8.8         6,413         9.1            5.52  %
2018                             27,304         9.7         6,918         9.8            6.76  %
2019                             48,304        17.2        12,001        17.0            4.61  %
2020                            106,187        37.8        25,795        36.6            0.76  %

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


(1)Represents the ending percentage of loans in default.
The following tables provide supplemental disclosures on risk in force for our
U.S. primary mortgage insurance business at September 30, 2021 and December 31,
2020:
(U.S. Dollars in millions)                        September 30, 2021                                December 31, 2020
                                             Amount                     %                     Amount                     %
Credit quality (FICO):
>=740                                 $         41,927                    59.6          $         40,774                   57.8
680-739                                         23,732                    33.7                    24,498                   34.7
620-679                                          4,323                     6.1                     4,837                    6.9
<620                                               338                     0.5                       413                    0.6
Total                                 $         70,320                   100.0          $         70,522                  100.0
Weighted average FICO score                        745                                               743

Loan-to-value (LTV):
95.01% and above                      $          7,708                    11.0          $          8,643                   12.3
90.01% to 95.00%                                38,378                    54.6                    37,877                   53.7
85.01% to 90.00%                                19,980                    28.4                    20,013                   28.4
85.00% and below                                 4,254                     6.0                     3,989                    5.7
Total                                 $         70,320                   100.0          $         70,522                  100.0
Weighted average LTV                              92.8   %                                          92.8  %

Total RIF, net of external
reinsurance                           $         54,847                                  $         56,658


(U.S. Dollars in millions)           September 30, 2021                   December 31, 2020
                                     Amount               %               Amount              %
Total RIF by State:
Texas                         $             5,590         7.9      $            5,636         8.0
California                                  5,451         7.8                   5,261         7.5
Florida                                     3,344         4.8                   3,632         5.2
Minnesota                                   2,936         4.2                   2,520         3.6
North Carolina                              2,921         4.2                   2,622         3.7
Illinois                                    2,920         4.2                   2,762         3.9
Georgia                                     2,908         4.1                   2,959         4.2
Massachusetts                               2,519         3.6                   2,464         3.5
Virginia                                    2,412         3.4                   2,526         3.6
Ohio                                        2,263         3.2                   2,264         3.2
Other                                      37,056        52.7                  37,876        53.7
Total                         $            70,320       100.0      $           70,522       100.0

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

                 Nine Months Ended
claim count)                                                          September 30,
                                                             2021                      2020
Roll-forward of insured loans in default:
Beginning delinquent number of loans                            52,234                    20,163
New notices                                                     26,483                    87,760
Cures                                                          (46,334)                  (48,234)
Paid claims                                                       (613)                   (1,327)

Ending delinquent number of loans (1)                           31,770                    58,362

Ending number of policies in force (1)                       1,188,768                 1,245,408

Delinquency rate (1)                                              2.67  %                   4.69  %

Losses:
Number of claims paid                                              613                     1,327
Total paid claims                                     $         22,848          $         55,559
Average per claim                                     $           37.3          $           41.9
Severity (2)                                                      80.2  %                   93.3  %
Average case reserve per default (in thousands)       $           23.5          $           10.1


(1)Includes first lien primary and pool policies.
(2)Represents total paid claims divided by RIF of loans for which claims were
paid.
The risk to capital ratio, which represents total current (non-delinquent) risk
in force, net of reinsurance, divided by total statutory capital, for Arch MI
U.S. was approximately 8.6 to 1 at September 30, 2021, compared to 9.3 to 1 at
December 31, 2020.
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Shareholders' Equity and Book Value per Share
The following table presents the calculation of book value per share:
(U.S. dollars in thousands, except                                      September 30,             December 31,
share data)                                                                 2021                      2020
Total shareholders' equity available to Arch                         $     13,387,526          $    13,105,886
Less preferred shareholders' equity                                           830,000                  780,000
Common shareholders' equity available to Arch                        $     12,557,526          $    12,325,886
Common shares and common share equivalents outstanding, net of
treasury shares (1)                                                       387,257,752              406,720,642
Book value per share                                                 $          32.43          $         30.31

(1)Excludes the effects of 17,419,530 and 17,839,333 stock options and 739,407 and 1,153,784 restricted stock units outstanding at September 30, 2021 and December 31, 2020, respectively.

LIQUIDITY



Liquidity is a measure of our ability to access sufficient cash flows to meet
the short-term and long-term cash requirements of our business operations.
Arch Capital is a holding company whose assets primarily consist of the shares
in its subsidiaries. Generally, Arch Capital depends on its available cash
resources, liquid investments and dividends or other distributions from its
subsidiaries to make payments, including the payment of debt service obligations
and operating expenses it may incur and any dividends or liquidation amounts
with respect to our preferred and common shares.

For the nine months ended September 30, 2021, Arch Capital received dividends of
$1.4 billion from Arch Re Bermuda, our Bermuda-based reinsurer and insurer,
which can pay approximately $2.3 billion to Arch Capital during the remainder of
2021 without providing an affidavit to the Bermuda Monetary Authority ("BMA").
For the nine months ended September 30, 2021, Arch-U.S. received $200.0 million
of dividends from Arch U.S. MI Holdings Inc., a subsidiary of Arch-U.S., which
received a total of $300.0 million of ordinary and extraordinary dividends, $140
million from United Guaranty Residential Insurance Company ("UGRIC") and $160
million from Arch Mortgage Insurance Company ("AMIC"). UGRIC and AMIC have
minimal ordinary dividend capacity remaining for the remainder of 2021.
In June 2021, Arch Capital completed a $500.0 million underwritten public
offering of 20.0 million depositary shares, each of which represents a 1/1,000th
interest in a
share of its 4.550% Non-Cumulative Preferred Shares.   See note 3, "Share
Transactions."
We expect that our liquidity needs, including our anticipated (re)insurance
obligations and operating and capital expenditure needs, for 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.
                                                                  Nine Months Ended
                                                                    September 30,
                                                                2021             2020
Total cash provided by (used for):
Operating activities                                        $ 2,580,697      $ 2,198,037
Investing activities                                         (1,184,436)      (2,850,392)
Financing activities                                           (895,943)         845,612

Effects of exchange rate changes on foreign currency cash (30,501)

(2,878)

Increase (decrease) in cash and restricted cash             $   469,817     

$ 190,379




•Cash provided by operating activities for the nine months ended September 30,
2021 reflected a higher level of premiums collected than in the 2020 period.
•Cash used for investing activities for the nine months ended September 30, 2021
was lower than in the 2020 period. Activity for the nine months ended September
30, 2021 reflected cash used to purchase our non-controlling interest in Coface
and Watford, while the 2020 period reflected a higher level of securities
purchased, and the investing of proceeds from our issuance of the senior notes.
•Cash used for financing activities for the nine months ended September 30, 2021
reflected $485.8 million inflow from issuance of preferred shares, $450.0
million related to redemption of our Series E preferred shares and $872.2
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.
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CAPITAL RESOURCES


The following table provides an analysis of our capital structure: (U.S. dollars in thousands, except

            Sep 30,           Dec 31,
share data)                                     2021              2020

Senior notes                               $  2,724,149      $  2,723,423

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

           330,000
Series G non-cumulative preferred shares        500,000                 -
Common shareholders' equity                  12,557,526        12,325,886
Total                                      $ 13,387,526      $ 13,105,886

Total capital available to Arch            $ 16,111,675      $ 15,829,309

Debt to total capital (%)                          16.9              17.2
Preferred to total capital (%)                      5.2               4.9
Debt and preferred to total capital (%)            22.1              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
September 30, 2021 with an estimated PMIER sufficiency ratio of 195%, 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, 2018. In 2019, certain
reinsurance agreements between our insurance subsidiaries and Arch Re Bermuda
were reinstated.
GUARANTOR INFORMATION


The below table provides a description of our senior notes payable at
September 30, 2021:
                        Interest       Principal        Carrying
    Issuer/Due          (Fixed)         Amount           Amount
Arch Capital:
May 1, 2034              7.350  %    $   300,000      $   297,457
June 30, 2050            3.635  %        1,000,000          988,665
Arch-U.S.:
Nov. 1, 2043 (1)         5.144  %          500,000          495,033
Arch Finance:
Dec. 15, 2026 (1)        4.011  %          500,000          497,527
Dec. 15, 2046 (1)        5.031  %          450,000          445,467
Total                                $ 2,750,000      $ 2,724,149


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

                                                            September 30, 2021                         December 31, 2020
                                                    Arch Capital           Arch-U.S.           Arch Capital           Arch-U.S.
Assets
Total investments                                  $        135          $   565,314          $        172          $   396,547
Cash                                                     10,796               10,386                18,932               11,368

Investment in operating affiliates                        7,099                    -                 7,731                    -
Due from subsidiaries and affiliates                          -              200,786                     -              201,515

Other assets                                             10,281               36,601                10,659               34,405
Total assets                                       $     28,311          $   813,087          $     37,494          $   643,835

Liabilities

Senior notes                                          1,286,122              495,033             1,285,867              494,944

Due to subsidiaries and affiliates                            4              507,103                     -              586,805
Other liabilities                                        37,226               55,132                23,270               41,876
Total liabilities                                  $  1,323,352          $ 1,057,268          $  1,309,137          $ 1,123,625

Non-cumulative preferred shares                    $    830,000                    -          $    780,000                    -


                                                           Nine Months Ended                      Year Ended
                                                           September 30, 2021                  December 31, 2020
                                                                 Arch Capital          Arch-U.S.           Arch Capital          Arch-U.S.

Revenues

Net investment income                                          $       1,160          $   9,392          $          53          $  18,084
Net realized gains (losses)                                                -             66,147                 (2,110)            26,096

Equity in net income (loss) of investments
accounted for using the equity method                                      -             13,726                      -              2,507

Total revenues                                                         1,160             89,265                 (2,057)            46,687

Expenses

Corporate expenses                                                    54,726              4,438                 65,566              7,227

Interest expense                                                      44,055             35,455                 40,445             47,566
Net foreign exchange (gains) losses                                        7                  -                      3                  -
Total expenses                                                        98,788             39,893                106,014             54,793

Income (loss) before income taxes and income
(loss) from operating affiliates                                     (97,628)            49,372               (108,071)            (8,106)
Income tax (expense) benefit                                               -            (12,843)                     -              2,689

Income (loss) from operating affiliates                                 (443)                 -                   (437)                 -

Net income available to Arch                                         (98,071)            36,529               (108,508)            (5,417)
Preferred dividends                                                  (38,159)                 -                (41,612)                 -
Loss on redemption of preferred shares                               (15,101)                 -                      -                  -
Net income (loss) available to Arch common
shareholders                                                   $    (151,331)         $  36,529          $    (150,120)         $  (5,417)



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SHARE REPURCHASE PROGRAM


The board of directors of Arch Capital has authorized the investment in Arch
Capital's common shares through a share repurchase program. For the nine months
ended September 30, 2021, Arch Capital repurchased 22.8 million shares under the
share repurchase program with an aggregate purchase price of $872.2 million.
Since the inception of the share repurchase program through September 30, 2021,
Arch Capital has repurchased 412.0 million common shares for an aggregate
purchase price of $4.92 billion. At September 30, 2021, approximately $44.3
million of share repurchases were available under the program. On October 8,
2021, the board of directors of ACGL increased the aggregate purchase amount
authorized under the share repurchase program to $1.5 billion, which may be
effected from time to time in open market or privately negotiated transactions
through December 31, 2022. The timing and amount of the repurchase transactions
under this program will depend on a variety of factors, including market
conditions and corporate and regulatory considerations. We will continue to
monitor our share price and, depending upon results of operations, market
conditions and the development of the economy, as well as other factors, we will
consider share repurchases on an opportunistic basis.   See note 17, "Subsequent
Event."
CATASTROPHIC EVENTS AND SEVERE ECONOMIC EVENTS


We have large aggregate exposures to natural and man-made catastrophic events,
pandemic events like COVID-19 and severe economic events. Natural catastrophes
can be caused by various events, including hurricanes, floods, windstorms,
earthquakes, hailstorms, tornadoes, explosions, severe winter weather, fires,
droughts and other natural disasters. Man-made catastrophic events may include
acts of war, acts of terrorism and political instability. Catastrophes can also
cause losses in non-property business such as mortgage insurance, workers'
compensation or general liability. In addition to the nature of property
business, we believe that economic and geographic trends affecting insured
property, including inflation, property value appreciation and geographic
concentration, tend to generally increase the size of losses from catastrophic
events over time.
Our models employ both proprietary and vendor-based systems and include
cross-line correlations for property, marine, offshore energy, aviation, workers
compensation and personal accident. We seek to limit the probable maximum
pre-tax loss to a specific level for severe catastrophic events. Currently, we
seek to limit our 1-in-250 year return period net probable maximum loss from a
severe catastrophic event in any geographic zone to approximately 25% of
tangible shareholders' equity available to Arch (total shareholders'
equity available to Arch less goodwill and intangible assets). We reserve the
right to change this threshold at any time.
Based on in-force exposure estimated as of October 1, 2021, our modeled peak
zone catastrophe exposure was a windstorm affecting the Florida Tri-County, with
a net probable maximum pre-tax loss of $671 million, followed by windstorms
affecting the Northeastern U.S. and the Gulf of Mexico regions with net probable
maximum pre-tax losses of $650 and $661 million, respectively. Our exposures to
other perils, such as U.S. earthquake and international events, were less than
the exposures arising from U.S. windstorms and hurricanes. As of October 1,
2021, 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 $276 million in excess of various retentions per occurrence.
We also have significant exposure to losses due to mortgage defaults resulting
from severe economic events in the future. For our U.S. mortgage insurance
business, we have developed a proprietary risk model ("Realistic Disaster
Scenario" or "RDS") that simulates the maximum loss resulting from a severe
economic downturn impacting the housing market. The RDS models the collective
impact of adverse conditions for key economic indicators, the most significant
of which is a decline in home prices. The RDS model projects paths of future
home prices, unemployment rates, income levels and interest rates and assumes
correlation across states and geographic regions. The resulting future
performance of our in-force portfolio is then estimated under the economic
stress scenario, reflecting loan and borrower information.
Currently, we seek to limit our modeled RDS loss from a severe economic event to
approximately 25% of tangible shareholders' equity available to Arch. We reserve
the right to change this threshold at any time. Based on in-force exposure
estimated as of October 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
ARCH CAPITAL     66      2021 THIRD QUARTER FORM 10-Q


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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 September 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.
An analysis of material changes in market risk exposures at September 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 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
Sept. 30, 2021
Total fair value              $ 25.29       $ 25.00       $ 24.67      $ 24.35       $ 24.06
Change from base                  2.5  %        1.3  %                    (1.3) %       (2.5) %
Change in unrealized value    $  0.62       $  0.32                    $ (0.32)      $ (0.62)

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.
ARCH CAPITAL     67      2021 THIRD QUARTER FORM 10-Q


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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
Sept. 30, 2021
Total fair value              $  25.24       $ 24.97       $ 24.67      $ 24.38       $ 24.11
Change from base                   2.3  %        1.2  %                    (1.2) %       (2.3) %
Change in unrealized value    $   0.57       $  0.30                    $ (0.30)      $ (0.57)

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 September 30, 2021, our portfolio's VaR was
estimated to be 3.2% 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 September 30, 2021 and December 31, 2020, the fair value
of our investments in equity securities (excluding securities included in Fixed
Income Securities above) totaled $1.5 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 $146.7 million and $109.5 million at September 30, 2021 and
December 31, 2020, respectively, and would have decreased book value per share
by approximately $0.38 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 $146.7 million and $109.5 million at September 30,
2021 and December 31, 2020, respectively, and would have increased book value
per share by approximately $0.38 and $0.27, respectively.
Investment-Related Derivatives. At September 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 $6.8 billion, compared to $8.6 billion at December 31,
2020. If the underlying exposure of each investment-related derivative held at
September 30, 2021 depreciated by 100 basis points, it would have resulted in a
reduction in net income of approximately $68.2 million, and a decrease in book
value per share of approximately $0.18 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 September 30, 2021 appreciated by 100 basis points, it would
have resulted in an increase in net income of approximately $68.2 million, and
an increase in book value per share of approximately $0.18 per share, compared
to $85.7 million and $0.21 per share, respectively, on investment-related
derivatives held at December 31, 2020. See   note 10, "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
10, "Derivative Instruments,"   to our consolidated financial statements for
additional information.

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