The underwriting expense ratio 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.

Corporate and Non-Underwriting

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

Pre-tax net investment income for the 2021 third quarter was $0.22 per share, or $88.2 million, compared to $0.24 per share, or $99.9 million, for the 2020 third quarter. The annualized pre-tax investment income yield was 1.41% for the 2021 third quarter, compared to 1.76% for the 2020 third quarter, with the decrease primarily due to lower yields available in the financial markets. Total return, a non-GAAP measure, was 0.01% for the 2021 third quarter, compared to 2.30% for the 2020 third quarter, primarily as a result of the mark-to-market impacts of higher interest rates in the 2021 period. See 'Comments on Regulation G' for a discussion of non-GAAP financial measures.

Interest expense for the 2021 third quarter was $33.2 million, compared to $36.2 million for the 2020 third quarter. Interest expense primarily reflects amounts related to the Company's outstanding senior notes. Preferred dividends for the 2021 third quarter were $16.1 million, compared to $10.4 million for the 2020 third quarter, with the increase reflecting the impact of the issuance of series G preferred shares in June 2021. The proceeds from the preferred offering were used to redeem the Company's Series E preferred shares on September 30, 2021. As such, in accordance with GAAP, the Company recorded a loss of $15.1 million to remove original issuance costs related to the redeemed shares from additional paid-in capital. For additional information on the Company's capital structure, please refer to the Financial Supplement dated September 30, 2021.

On a pre-tax basis, 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. For both periods, such amounts were primarily unrealized and resulted from the effects of revaluing the Company's net insurance liabilities required to be settled in foreign currencies at each balance sheet date. Changes in the value of available-for-sale investments held in foreign currencies due to foreign currency rate movements are reflected as a direct increase or decrease to shareholders' equity and are not included in the consolidated statements of income. Although the Company generally attempts to match the currency of its projected liabilities with investments in the same currencies, the Company may elect to over or underweight one or more currencies from time to time, which could increase the Company's exposure to foreign currency fluctuations and increase the volatility of the Company's shareholders' equity.

The Company's effective tax rate on income before income taxes (based on the Company's estimated annual effective tax rate) was an expense of 1.0% for the 2021 third quarter, compared to an expense of 5.3% for the 2020 third quarter. The Company's effective tax rate on pre-tax operating income available to Arch common shareholders was a benefit of 0.7% for the 2021 third quarter, compared to an expense of 4.8% for the 2020 third quarter. The effective tax rates for the 2021 third quarter included discrete income tax benefits of $25.3 million which had the effect of decreasing the 2021 third quarter effective tax rate on operating income available to Arch common shareholders by 8.2%. The discrete tax items in the 2021 third quarter primarily relate to the partial release of a valuation allowance on certain U.K. deferred tax assets. The Company's effective tax rate may fluctuate from period to period based upon the relative mix of income or loss reported by jurisdiction, the level of catastrophic loss activity incurred, and the varying tax rates in each jurisdiction. The Company's quarterly tax provision is adjusted to reflect changes in its estimated annual effective tax rate, if any.

During the 2021 first quarter, the Company changed its presentation of 'income (loss) from operating affiliates' on its consolidated statements of income for all periods presented to reclass such item from 'other income (loss).' The Company also changed its presentation of 'investment in operating affiliates' on its consolidated balance sheet for all periods presented to reclass such item from 'other assets.' Income from operating affiliates for the 2021 third quarter was $124.1 million, or $0.31 per share, compared to income of $0.9 million, or $0.00 per share, for the 2020 third quarter. 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 Watford. In addition, the 'net realized gains (losses)' line on the Company's consolidated statements of income included a $33.1 million loss as a result of this transaction this quarter.

Conference Call

The Company will hold a conference call for investors and analysts at 11:00 a.m. Eastern Time on October 28, 2021. A live webcast of this call will be available via the Investors section of the Company's website at http://www.archgroup.com. A telephone replay of the conference call also will be available beginning on October 28, 2021 at 2:00 p.m. Eastern Time until November 4, 2021 at midnight Eastern Time. To access the replay, domestic callers should dial 855-859-2056, and international callers should dial 404-537-3406 (passcode 3440118 for all callers).

Please refer to the Company's Financial Supplement dated September 30, 2021, which is available via the Investors section of the Company's website at http://www.archgroup.com. The Financial Supplement provides additional detail regarding the financial performance of the Company. From time to time, the Company posts additional financial information and presentations to its website, including information with respect to its subsidiaries. Investors and other recipients of this information are encouraged to check the Company's website regularly for additional information regarding the Company.

Arch Capital Group Ltd., a publicly listed Bermuda exempted company with approximately $16.1 billion in capital at September 30, 2021, provides insurance, reinsurance and mortgage insurance on a worldwide basis through its wholly owned subsidiaries.

Comments on Regulation G

Throughout this release, the Company presents its operations in the way it believes will be the most meaningful and useful to investors, analysts, rating agencies and others who use the Company's financial information in evaluating the performance of the Company and that investors and such other persons benefit from having a consistent basis for comparison between quarters and for comparison with other companies within the industry. These measures may not, however, be comparable to similarly titled measures used by companies outside of the insurance industry. Investors are cautioned not to place undue reliance on these non-GAAP financial measures in assessing the Company's overall financial performance.

This presentation includes the use of "after-tax operating income or loss available to Arch common shareholders," which is defined as net income available to Arch common shareholders, excluding net realized gains or losses (which includes changes in the allowance for credit losses on financial assets and net impairment losses recognized in earnings), equity in net income or loss of investment funds accounted for using the equity method, net foreign exchange gains or losses, transaction costs and other and loss on redemption of preferred shares, net of 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 on page 2 of this release.

The Company believes 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, the Company's business performance. 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 the Company's 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 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 the Company's financial information believe that, for many companies, the timing of the realization of investment gains or losses is largely