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 the Company's investments in certain funds that invest in fixed maturity securities is driven by the ownership structure of such funds (either limited partnerships or limited liability companies). In applying the equity method, these investments are initially recorded at cost and are subsequently adjusted based on the Company's proportionate share of the net income or loss of the funds (which include changes in the fair value of the underlying securities in the funds). This method of accounting is different from the way the Company accounts for its 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 costs related to acquisitions. The Company believes that transaction costs and other, due to their non-recurring nature, are not indicative of the performance of, or trends in, the Company's 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, the Company excludes net realized gains or losses, equity in net income or loss of investment funds accounted for using the equity method, net foreign exchange gains or losses and transaction costs and other from the calculation of after-tax operating income or loss available to Arch common shareholders.
The Company believes that showing net income available to Arch common shareholders exclusive of the items referred to above reflects the underlying fundamentals of the Company's business since the Company evaluates the performance of and manages its business to produce an underwriting profit. In addition to presenting net income available to Arch common shareholders, the Company believes that this presentation enables investors and other users of the Company's financial information to analyze the Company's performance in a manner similar to how the Company's management analyzes performance. The Company also believes that this measure follows industry practice and, therefore, allows the users of the Company's financial information to compare the Company's performance with its industry peer group. The Company believes that the equity analysts and certain rating agencies which follow the Company and the insurance industry as a whole generally exclude these items from their analyses for the same reasons.
The Company's segment information includes the presentation of consolidated underwriting income or loss and a subtotal of underwriting income or loss before the contribution from the 'other' segment. Such measures represent the pre-tax profitability of its 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 the Company's individual underwriting operations. Underwriting income or loss does not incorporate items included in the Company's corporate (non-underwriting) segment. While these measures are presented in the Segment Information footnote to the Company's Consolidated Financial Statements, they are considered non-GAAP financial measures when presented elsewhere on a consolidated basis. The reconciliations of underwriting income or loss to income before income taxes (the most directly comparable GAAP financial measure) on a consolidated basis and a subtotal before the contribution from the 'other' segment, in accordance with Regulation G, is shown on the following pages.
Management measures segment performance for its three underwriting segments based on underwriting income or loss. The Company does not manage its assets by underwriting segment and, accordingly, investment income and other non-underwriting related items are not allocated to each underwriting segment. As noted earlier, the 'other' segment includes the results of Watford through June 30, 2021.
Along with consolidated underwriting income, the Company provides a subtotal of underwriting income or loss before the contribution from the 'other' segment and believes that this presentation enables investors and other users of the Company's financial information to analyze the Company's underwriting performance in a manner similar to how the Company's management analyzes performance. Pursuant to GAAP, Watford was considered a variable interest entity and the Company concluded that it was the primary beneficiary of Watford through June 30, 2021. As such, the Company consolidated the results of Watford in its consolidated financial statements. The Company's presentation of information on a 'core' basis enabled investors and other users of the Company's financial information to analyze the Company's performance in a manner similar to how the Company's management analyzed performance. In the 2020 fourth quarter, Arch Capital, Watford, and Greysbridge Ltd., a wholly-owned subsidiary of Arch Capital ("Greysbridge"), entered into an Agreement and Plan of Merger (as amended, the "Merger Agreement") pursuant to which, among other things, Arch Capital agreed to acquire all of the common shares of Watford Holdings Ltd. not owned by Arch. Arch Capital assigned its rights under the Merger Agreement to 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 the Company, 30% by certain investment funds managed by Kelso & Company and 30% by certain investment funds managed by Warburg Pincus LLC. Based on the governing documents of Greysbridge, the Company has concluded that, while it retains significant influence over Greysbridge, Greysbridge does not constitute a variable interest entity of which the Company is the primary beneficiary. Accordingly, effective July 1, 2021, Arch no longer consolidates the results of Watford in its consolidated financial statements and footnotes.
In addition, the Company's segment information includes the use of a combined ratio excluding catastrophic activity and prior year development, for the insurance and reinsurance segments, and a combined ratio excluding prior year development, for the mortgage segment. These ratios are non-GAAP financial measures as defined in Regulation G. The reconciliation of such measures to the combined ratio (the most directly comparable GAAP financial measure) in accordance with Regulation G are shown on the individual segment pages. The Company's management utilizes the adjusted combined ratios excluding current accident year catastrophic events and favorable or adverse development in prior year loss reserves in its analysis of the underwriting performance of each of its 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. Management uses total return on investments as a key measure of the return generated to Arch common shareholders, and compares the return generated by the Company's investment portfolio against benchmark returns during the periods presented.
The following tables summarize the Company's results by segment for the 2021 third quarter and 2020 third quarter and a reconciliation of underwriting income or loss to income or loss before income taxes and net income or loss available to Arch common shareholders:
(U.S. Dollars
in thousands) Three Months Ended
September 30, 2021
-------------------------------------------------------------------------------------------
Insurance Reinsurance Mortgage Sub-total Other Total
-------------- -------------- ------------ ----------------- ------- -----------------
Gross premiums
written (1) $1,596,619 $1,251,760 $360,934 $ 3,207,415 $-- $ 3,207,415
Premiums ceded (442,806) (630,371) (60,207) (1,131,486) -- (1,131,486)
---------- ---------- -------- ------------- --- -------------
Net premiums
written 1,153,813 621,389 300,727 2,075,929 -- 2,075,929
Change in
unearned
premiums (215,143) 57,313 11,238 (146,592) -- (146,592)
---------- ---------- -------- ------------- --- -------------
Net premiums
earned 938,670 678,702 311,965 1,929,337 -- 1,929,337
Other
underwriting
income (loss) -- 3,293 3,981 7,274 -- 7,274
Losses and loss
adjustment
expenses (668,630) (545,846) (11,543) (1,226,019) -- (1,226,019)
Acquisition