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Table of Contents

UNITED STATES
SECURITIES AND EXCHANGE COMMISSION
Washington, D.C. 20549
___________________________________________
FORM 10-Q
______________________________________________________________________________________
☒ Quarterly report pursuant to Section 13 or 15(d) of the Securities Exchange Act of 1934 for the quarterly period ended June 30, 2023
or
☐ Transition report pursuant to Section 13 or 15(d) of the Securities Exchange Act of 1934 for the transition period from _______ to _______
Commission File Number: 001-15811
_________________________________________
MARKEL GROUP INC.
(Exact name of registrant as specified in its charter)
___________________________________________________________________________________

Virginia |  | 54-1959284
(State or other jurisdiction of incorporation or organization) |  | (I.R.S. Employer Identification No.)

4521 Highwoods Parkway, Glen Allen, Virginia 23060-6148
(Address of principal executive offices) (Zip Code)
(804) 747-0136
(Registrant's telephone number, including area code)
Securities registered pursuant to Section 12(b) of the Act:

Title of each class |  | Trading Symbol(s) |  | Name of exchange on which registered
Common Stock, no par value |  | MKL |  | New York Stock Exchange

Indicate by check mark whether the registrant (1) has filed all reports required to be filed by Section 13 or 15(d) of the Securities Exchange Act of 1934 during the preceding 12 months (or for such shorter period that the registrant was required to file such reports), and (2) has been subject to such filing requirements for the past 90 days. Yes x No ☐
Indicate by check mark whether the registrant has submitted electronically every Interactive Data File required to be submitted pursuant to Rule 405 of Regulation S-T (§232.405 of this chapter) during the preceding 12 months (or for such shorter period that the registrant was required to submit such files). Yes x No ☐
Indicate by check mark whether the registrant is a large accelerated filer, an accelerated filer, a non-accelerated filer, a smaller reporting company, or an emerging growth company. See the definitions of "large accelerated filer," "accelerated filer," "smaller reporting company," and "emerging growth company" in Rule 12b-2 of the Exchange Act.

Large accelerated filer | x | Accelerated filer | ☐ | Non-accelerated filer | ☐
Smaller reporting company | ☐ | Emerging growth company | ☐ |  |

If an emerging growth company, indicate by check mark if the registrant has elected not to use the extended transition period for complying with any new or revised financial accounting standards provided pursuant to Section 13(a) of the Exchange Act. ☐
Indicate by check mark whether the registrant is a shell company (as defined in Rule 12b-2 of the Exchange Act). Yes ☐ No x
Number of shares of the registrant's common stock outstanding at July 26, 2023: 13,264,492

Table of Contents
Markel Group Inc.
Form 10-Q
Index

|  | Page Number
PART I. FINANCIAL INFORMATION |
Item 1. | Financial Statements |
| Consolidated Balance Sheets—June 30, 2023 and December 31, 2022 | 3
| Consolidated Statements of Income (Loss) and Comprehensive Income (Loss)—Quarters and Six Months Ended June 30, 2023 and 2022 | 4
| Consolidated Statements of Changes in Equity—Quarters and Six Months Ended June 30, 2023 and 2022 | 5
| Condensed Consolidated Statements of Cash Flows—Six Months Ended June 30, 2023 and 2022 | 7
| Notes to Consolidated Financial Statements | 8
Item 2. | Management's Discussion and Analysis of Financial Condition and Results of Operations | 30
Item 3. | Quantitative and Qualitative Disclosures About Market Risk | 50
Item 4. | Controls and Procedures | 51
PART II. OTHER INFORMATION |
Item 1. | Legal Proceedings | 51
Item 2. | Unregistered Sales of Equity Securities and Use of Proceeds | 52
Item 5. | Other Information | 52
Item 6. | Exhibits | 53
Signatures | 55

2

Table of Contents
PART I. FINANCIAL INFORMATION
Item 1. Financial Statements
MARKEL GROUP INC. AND SUBSIDIARIES
CONSOLIDATED BALANCE SHEETS

| June 30, 2023 |  | December 31, 2022
(dollars in thousands) | (unaudited) |  |
ASSETS |  |  |
Investments, at estimated fair value: |  |  |
Fixed maturity securities, available-for-sale (amortized cost of $13,653,557 in 2023 and $12,805,887 in 2022) | $ | 12,745,692 |  |  | $ | 11,856,835 |
Equity securities (cost of $3,282,591 in 2023 and $3,100,040 in 2022) | 8,688,860 |  |  | 7,671,912 |
Short-term investments, available-for-sale (estimated fair value approximates cost) | 2,039,061 |  |  | 2,669,262 |
Total Investments | 23,473,613 |  |  | 22,198,009 |
Cash and cash equivalents | 4,305,884 |  |  | 4,137,432 |
Restricted cash and cash equivalents | 935,045 |  |  | 1,084,081 |
Receivables | 3,695,172 |  |  | 2,961,056 |
Reinsurance recoverables | 8,296,043 |  |  | 8,446,745 |
Deferred policy acquisition costs | 1,013,304 |  |  | 925,483 |
Prepaid reinsurance premiums | 2,486,203 |  |  | 2,066,114 |
Goodwill | 2,626,588 |  |  | 2,638,838 |
Intangible assets | 1,677,621 |  |  | 1,747,464 |
Other assets | 3,674,660 |  |  | 3,586,037 |
Total Assets | $ | 52,184,133 |  |  | $ | 49,791,259 |
LIABILITIES AND EQUITY |  |  |
Unpaid losses and loss adjustment expenses | $ | 21,374,813 |  |  | $ | 20,947,898 |
Life and annuity benefits | 643,572 |  |  | 650,721 |
Unearned premiums | 7,072,182 |  |  | 6,220,748 |
Payables to insurance and reinsurance companies | 972,194 |  |  | 669,742 |
Senior long-term debt and other debt (estimated fair value of $3,299,000 in 2023 and $3,541,000 in 2022) | 3,813,917 |  |  | 4,103,629 |
Other liabilities | 3,603,932 |  |  | 3,461,482 |
Total Liabilities | 37,480,610 |  |  | 36,054,220 |
Redeemable noncontrolling interests | 464,442 |  |  | 523,154 |
Commitments and contingencies |  |  |
Shareholders' equity: |  |  |
Preferred stock | 591,891 |  |  | 591,891 |
Common stock | 3,515,362 |  |  | 3,493,893 |
Retained earnings | 10,818,989 |  |  | 9,832,804 |
Accumulated other comprehensive loss | (740,743) |  |  | (767,494) |
Total Shareholders' Equity | 14,185,499 |  |  | 13,151,094 |
Noncontrolling interests | 53,582 |  |  | 62,791 |
Total Equity | 14,239,081 |  |  | 13,213,885 |
Total Liabilities and Equity | $ | 52,184,133 |  |  | $ | 49,791,259 |

See accompanying notes to consolidated financial statements.
3

Table of Contents
MARKEL GROUP INC. AND SUBSIDIARIES
CONSOLIDATED STATEMENTS OF INCOME (LOSS) AND COMPREHENSIVE INCOME (LOSS)
(Unaudited)

| Quarter Ended June 30, |  | Six Months Ended June 30,
| 2023 |  | 2022 |  | 2023 |  | 2022
(dollars in thousands, except per share data) |  |  |  |  |  |  |
OPERATING REVENUES |  |  |  |  |  |  |
Earned premiums | $ | 2,031,143 |  |  | $ | 1,833,104 |  |  | $ | 3,998,847 |  |  | $ | 3,592,874 |
Net investment income | 169,693 |  |  | 96,795 |  |  | 329,028 |  |  | 189,099 |
Net investment gains (losses) | 484,527 |  |  | (1,554,643) |  |  | 857,090 |  |  | (1,913,042) |
Products revenues | 784,882 |  |  | 776,959 |  |  | 1,362,808 |  |  | 1,258,580 |
Services and other revenues | 672,291 |  |  | 639,992 |  |  | 1,238,152 |  |  | 1,270,932 |
Total Operating Revenues | 4,142,536 |  |  | 1,792,207 |  |  | 7,785,925 |  |  | 4,398,443 |
OPERATING EXPENSES |  |  |  |  |  |  |
Losses and loss adjustment expenses | 1,187,876 |  |  | 1,058,810 |  |  | 2,360,890 |  |  | 2,031,182 |
Underwriting, acquisition and insurance expenses | 697,887 |  |  | 609,469 |  |  | 1,373,592 |  |  | 1,199,834 |
Products expenses | 651,469 |  |  | 697,718 |  |  | 1,167,225 |  |  | 1,145,537 |
Services and other expenses | 590,817 |  |  | 557,481 |  |  | 1,071,436 |  |  | 1,147,372 |
Amortization of intangible assets | 44,423 |  |  | 45,523 |  |  | 88,822 |  |  | 91,572 |
Total Operating Expenses | 3,172,472 |  |  | 2,969,001 |  |  | 6,061,965 |  |  | 5,615,497 |
Operating Income (Loss) | 970,064 |  |  | (1,176,794) |  |  | 1,723,960 |  |  | (1,217,054) |
Interest expense | (47,221) |  |  | (50,050) |  |  | (96,659) |  |  | (99,742) |
Net foreign exchange gains (losses) | (14,976) |  |  | 105,067 |  |  | (47,904) |  |  | 128,071 |
Income (Loss) Before Income Taxes | 907,867 |  |  | (1,121,777) |  |  | 1,579,397 |  |  | (1,188,725) |
Income tax (expense) benefit | (191,937) |  |  | 238,953 |  |  | (325,668) |  |  | 257,089 |
Net Income (Loss) | 715,930 |  |  | (882,824) |  |  | 1,253,729 |  |  | (931,636) |
Net income attributable to noncontrolling interests | (20,419) |  |  | (32,972) |  |  | (69,566) |  |  | (35,901) |
Net Income (Loss) to Shareholders | 695,511 |  |  | (915,796) |  |  | 1,184,163 |  |  | (967,537) |
Preferred stock dividends | (18,000) |  |  | (18,000) |  |  | (18,000) |  |  | (18,000) |
Net Income (Loss) to Common Shareholders | $ | 677,511 |  |  | $ | (933,796) |  |  | $ | 1,166,163 |  |  | $ | (985,537) |
OTHER COMPREHENSIVE INCOME (LOSS) |  |  |  |  |  |  |
Change in net unrealized gains (losses) on available-for-sale investments, net of taxes: |  |  |  |  |  |  |
Net holding gains (losses) arising during the period | $ | (134,991) |  |  | $ | (362,392) |  |  | $ | 26,215 |  |  | $ | (883,592) |
Reclassification adjustments for net losses included in net income (loss) | 405 |  |  | 1,261 |  |  | 3,399 |  |  | 1,698 |
Change in net unrealized gains (losses) on available-for-sale investments, net of taxes | (134,586) |  |  | (361,131) |  |  | 29,614 |  |  | (881,894) |
Change in discount rate for life and annuity benefits, net of taxes | 3,224 |  |  | 63,198 |  |  | (5,828) |  |  | 123,891 |
Change in foreign currency translation adjustments, net of taxes | 361 |  |  | (4,275) |  |  | 2,940 |  |  | (5,523) |
Change in net actuarial pension loss, net of taxes | 18 |  |  | 373 |  |  | 36 |  |  | 1,505 |
Total Other Comprehensive Income (Loss) | (130,983) |  |  | (301,835) |  |  | 26,762 |  |  | (762,021) |
Comprehensive Income (Loss) | 584,947 |  |  | (1,184,659) |  |  | 1,280,491 |  |  | (1,693,657) |
Comprehensive income attributable to noncontrolling interests | (20,398) |  |  | (33,029) |  |  | (69,577) |  |  | (35,945) |
Comprehensive Income (Loss) to Shareholders | $ | 564,549 |  |  | $ | (1,217,688) |  |  | $ | 1,210,914 |  |  | $ | (1,729,602) |
NET INCOME (LOSS) PER COMMON SHARE |  |  |  |  |  |  |
Basic | $ | 50.20 |  |  | $ | (69.15) |  |  | $ | 87.50 |  |  | $ | (75.56) |
Diluted | $ | 50.09 |  |  | $ | (69.15) |  |  | $ | 87.34 |  |  | $ | (75.56) |

See accompanying notes to consolidated financial statements.
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MARKEL GROUP INC. AND SUBSIDIARIES
CONSOLIDATED STATEMENTS OF CHANGES IN EQUITY
(Unaudited)

Quarter Ended June 30, 2023 | Preferred Stock |  | Common Stock |  | Retained Earnings |  | Accumulated Other Comprehensive Loss |  | Total Shareholders' Equity |  | Noncontrolling Interests |  | Total Equity |  | Redeemable Noncontrolling Interests
(dollars in thousands) |  |  |  |  |  |  |  |  |  |  |  |  |  |  |
March 31, 2023 | $ | 591,891 |  |  | $ | 3,506,972 |  |  | $ | 10,255,401 |  |  | $ | (609,781) |  |  | $ | 13,744,483 |  |  | $ | 44,838 |  |  | $ | 13,789,321 |  |  | $ | 491,883 |
Net income |  |  |  |  | 695,511 |  |  | — |  |  | 695,511 |  |  | 8,745 |  |  | 704,256 |  |  | 11,674 |
Other comprehensive loss |  |  |  |  | — |  |  | (130,962) |  |  | (130,962) |  |  | — |  |  | (130,962) |  |  | (21) |
Comprehensive Income |  |  |  |  |  |  |  |  | 564,549 |  |  | 8,745 |  |  | 573,294 |  |  | 11,653 |
Repurchase of common stock | — |  |  | — |  |  | (105,197) |  |  | — |  |  | (105,197) |  |  | — |  |  | (105,197) |  |  | — |
Preferred stock dividends | — |  |  | — |  |  | (18,000) |  |  | — |  |  | (18,000) |  |  | — |  |  | (18,000) |  |  | — |
Restricted stock awards expensed | — |  |  | 4,830 |  |  | — |  |  | — |  |  | 4,830 |  |  | — |  |  | 4,830 |  |  | — |
Adjustment of redeemable noncontrolling interests | — |  |  | — |  |  | (5,758) |  |  | — |  |  | (5,758) |  |  | — |  |  | (5,758) |  |  | 5,758 |
Purchase of noncontrolling interests | — |  |  | 3,931 |  |  | — |  |  | — |  |  | 3,931 |  |  | — |  |  | 3,931 |  |  | (36,431) |
Other | — |  |  | (371) |  |  | (2,968) |  |  | — |  |  | (3,339) |  |  | (1) |  |  | (3,340) |  |  | (8,421) |
June 30, 2023 | $ | 591,891 |  |  | $ | 3,515,362 |  |  | $ | 10,818,989 |  |  | $ | (740,743) |  |  | $ | 14,185,499 |  |  | $ | 53,582 |  |  | $ | 14,239,081 |  |  | $ | 464,442 |

Six Months Ended June 30, 2023 | Preferred Stock |  | Common Stock |  | Retained Earnings |  | Accumulated Other Comprehensive Loss |  | Total Shareholders' Equity |  | Noncontrolling Interests |  | Total Equity |  | Redeemable Noncontrolling Interests
(dollars in thousands) |  |  |  |  |  |  |  |  |  |  |  |  |  |  |
December 31, 2022 | $ | 591,891 |  |  | $ | 3,493,893 |  |  | $ | 9,832,804 |  |  | $ | (767,494) |  |  | $ | 13,151,094 |  |  | $ | 62,791 |  |  | $ | 13,213,885 |  |  | $ | 523,154 |
Net income |  |  |  |  | 1,184,163 |  |  | — |  |  | 1,184,163 |  |  | 53,438 |  |  | 1,237,601 |  |  | 16,128 |
Other comprehensive income |  |  |  |  | — |  |  | 26,751 |  |  | 26,751 |  |  | — |  |  | 26,751 |  |  | 11 |
Comprehensive Income |  |  |  |  |  |  |  |  | 1,210,914 |  |  | 53,438 |  |  | 1,264,352 |  |  | 16,139 |
Repurchase of common stock | — |  |  | — |  |  | (187,161) |  |  | — |  |  | (187,161) |  |  | — |  |  | (187,161) |  |  | — |
Preferred stock dividends | — |  |  | — |  |  | (18,000) |  |  | — |  |  | (18,000) |  |  | — |  |  | (18,000) |  |  | — |
Restricted stock awards expensed | — |  |  | 26,528 |  |  | — |  |  | — |  |  | 26,528 |  |  | — |  |  | 26,528 |  |  | — |
Adjustment of redeemable noncontrolling interests | — |  |  | — |  |  | 7,715 |  |  | — |  |  | 7,715 |  |  | — |  |  | 7,715 |  |  | (7,715) |
Purchase of noncontrolling interests | — |  |  | (4,688) |  |  | — |  |  | — |  |  | (4,688) |  |  | — |  |  | (4,688) |  |  | (49,477) |
Redemption of Markel CATCo Re noncontrolling interests | — |  |  | — |  |  | — |  |  | — |  |  | — |  |  | (62,646) |  |  | (62,646) |  |  | — |
Other | — |  |  | (371) |  |  | (532) |  |  | — |  |  | (903) |  |  | (1) |  |  | (904) |  |  | (17,659) |
June 30, 2023 | $ | 591,891 |  |  | $ | 3,515,362 |  |  | $ | 10,818,989 |  |  | $ | (740,743) |  |  | $ | 14,185,499 |  |  | $ | 53,582 |  |  | $ | 14,239,081 |  |  | $ | 464,442 |

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MARKEL GROUP INC. AND SUBSIDIARIES
CONSOLIDATED STATEMENTS OF CHANGES IN EQUITY
(Unaudited)

Quarter Ended June 30, 2022 | Preferred Stock |  | Common Stock |  | Retained Earnings |  | Accumulated Other Comprehensive Loss |  | Total Shareholders' Equity |  | Noncontrolling Interests |  | Total Equity |  | Redeemable Noncontrolling Interests
(dollars in thousands) |  |  |  |  |  |  |  |  |  |  |  |  |  |  |
March 31, 2022 | $ | 591,891 |  |  | $ | 3,469,449 |  |  | $ | 10,277,639 |  |  | $ | (238,166) |  |  | $ | 14,100,813 |  |  | $ | 5,554 |  |  | $ | 14,106,367 |  |  | $ | 480,351 |
Net income (loss) |  |  |  |  | (915,797) |  |  | — |  |  | (915,797) |  |  | 25,989 |  |  | (889,808) |  |  | 6,983 |
Other comprehensive income (loss) |  |  |  |  | — |  |  | (301,892) |  |  | (301,892) |  |  | — |  |  | (301,892) |  |  | 57 |
Comprehensive Income (Loss) |  |  |  |  |  |  |  |  | (1,217,689) |  |  | 25,989 |  |  | (1,191,700) |  |  | 7,040 |
Repurchase of common stock | — |  |  | — |  |  | (46,995) |  |  | — |  |  | (46,995) |  |  | — |  |  | (46,995) |  |  | — |
Preferred stock dividends | — |  |  | — |  |  | (18,000) |  |  | — |  |  | (18,000) |  |  | — |  |  | (18,000) |  |  | — |
Restricted stock awards expensed | — |  |  | 4,406 |  |  | — |  |  | — |  |  | 4,406 |  |  | — |  |  | 4,406 |  |  | — |
Adjustment of redeemable noncontrolling interests | — |  |  | — |  |  | (7,498) |  |  | — |  |  | (7,498) |  |  | — |  |  | (7,498) |  |  | 7,498 |
Redemption of Markel CATCo Re noncontrolling interests | — |  |  | — |  |  | — |  |  | — |  |  | — |  |  | (22,261) |  |  | (22,261) |  |  | — |
Other | — |  |  | 4,298 |  |  | 267 |  |  | — |  |  | 4,565 |  |  | 1,843 |  |  | 6,408 |  |  | 489 |
June 30, 2022 | $ | 591,891 |  |  | $ | 3,478,153 |  |  | $ | 9,289,616 |  |  | $ | (540,058) |  |  | $ | 12,819,602 |  |  | $ | 11,125 |  |  | $ | 12,830,727 |  |  | $ | 495,378 |

Six Months Ended June 30, 2022 | Preferred Stock |  | Common Stock |  | Retained Earnings |  | Accumulated Other Comprehensive Income (Loss) |  | Total Shareholders' Equity |  | Noncontrolling Interests |  | Total Equity |  | Redeemable Noncontrolling Interests
(dollars in thousands) |  |  |  |  |  |  |  |  |  |  |  |  |  |  |
December 31, 2021 | $ | 591,891 |  |  | $ | 3,441,079 |  |  | $ | 10,444,895 |  |  | $ | 222,007 |  |  | $ | 14,699,872 |  |  | $ | 22,860 |  |  | $ | 14,722,732 |  |  | $ | 461,378 |
Net income (loss) |  |  |  |  | (967,538) |  |  | — |  |  | (967,538) |  |  | 25,416 |  |  | (942,122) |  |  | 10,485 |
Other comprehensive income (loss) |  |  |  |  | — |  |  | (762,065) |  |  | (762,065) |  |  | — |  |  | (762,065) |  |  | 44 |
Comprehensive Income (Loss) |  |  |  |  |  |  |  |  | (1,729,603) |  |  | 25,416 |  |  | (1,704,187) |  |  | 10,529 |
Repurchase of common stock | — |  |  | — |  |  | (126,291) |  |  | — |  |  | (126,291) |  |  | — |  |  | (126,291) |  |  | — |
Preferred stock dividends | — |  |  | — |  |  | (18,000) |  |  | — |  |  | (18,000) |  |  | — |  |  | (18,000) |  |  | — |
Restricted stock awards expensed | — |  |  | 32,870 |  |  | — |  |  | — |  |  | 32,870 |  |  | — |  |  | 32,870 |  |  | — |
Adjustment of redeemable noncontrolling interests | — |  |  | — |  |  | (44,438) |  |  | — |  |  | (44,438) |  |  | — |  |  | (44,438) |  |  | 44,438 |
Adjustment to Metromont purchase price allocation | — |  |  | — |  |  | — |  |  | — |  |  | — |  |  | — |  |  | — |  |  | (18,681) |
Disposition of Velocity | — |  |  | — |  |  | — |  |  | — |  |  | — |  |  | (22,059) |  |  | (22,059) |  |  | — |
Redemption of Markel CATCo Re noncontrolling interests | — |  |  | — |  |  | — |  |  | — |  |  | — |  |  | (22,261) |  |  | (22,261) |  |  | — |
Other | — |  |  | 4,204 |  |  | 988 |  |  | — |  |  | 5,192 |  |  | 7,169 |  |  | 12,361 |  |  | (2,286) |
June 30, 2022 | $ | 591,891 |  |  | $ | 3,478,153 |  |  | $ | 9,289,616 |  |  | $ | (540,058) |  |  | $ | 12,819,602 |  |  | $ | 11,125 |  |  | $ | 12,830,727 |  |  | $ | 495,378 |

See accompanying notes to consolidated financial statements.
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MARKEL GROUP INC. AND SUBSIDIARIES
CONDENSED CONSOLIDATED STATEMENTS OF CASH FLOWS
(Unaudited)

| Six Months Ended June 30,
| 2023 |  | 2022
| (dollars in thousands)
OPERATING ACTIVITIES |  |  |
Net income (loss) | $ | 1,253,729 |  |  | $ | (931,636) |
Adjustments to reconcile net income (loss) to net cash provided by operating activities | (245,108) |  |  | 1,852,625 |
Net Cash Provided By Operating Activities | 1,008,621 |  |  | 920,989 |
INVESTING ACTIVITIES |  |  |
Proceeds from sales, maturities, calls and prepayments of fixed maturity securities | 993,834 |  |  | 370,028 |
Cost of fixed maturity securities purchased | (1,771,986) |  |  | (889,888) |
Proceeds from sales of equity securities | 138,702 |  |  | 146,116 |
Cost of equity securities purchased | (293,322) |  |  | (209,576) |
Net change in short-term investments | 675,339 |  |  | (256,698) |
Cost of other investments purchased | (83,490) |  |  | (18,251) |
Additions to property and equipment | (79,443) |  |  | (110,544) |
Consolidation of Markel CATCo Re, net | — |  |  | 629,955 |
Distributions to Markel CATCo Re noncontrolling interests for buy-out transaction | — |  |  | (169,380) |
Proceeds from sales of subsidiaries, net | 41,302 |  |  | 109,505 |
Other | 5,503 |  |  | (4,628) |
Net Cash Used By Investing Activities | (373,561) |  |  | (403,361) |
FINANCING ACTIVITIES |  |  |
Additions to senior long-term debt and other debt | 356,085 |  |  | 529,051 |
Repayment of senior long-term debt and other debt | (646,264) |  |  | (387,165) |
Advance funding for repayment of senior long-term debt | — |  |  | (350,000) |
Repurchases of common stock | (187,161) |  |  | (126,291) |
Dividends paid on preferred stock | (18,000) |  |  | (18,000) |
Redemption of Markel CATCo Re noncontrolling interests | (88,997) |  |  | — |
Purchase of noncontrolling interests | (21,665) |  |  | 7,492 |
Other | (23,879) |  |  | (41,796) |
Net Cash Used By Financing Activities | (629,881) |  |  | (386,709) |
Effect of foreign currency rate changes on cash, cash equivalents, restricted cash and restricted cash equivalents | 14,237 |  |  | (100,549) |
Increase in cash, cash equivalents, restricted cash and restricted cash equivalents | 19,416 |  |  | 30,370 |
Cash, cash equivalents, restricted cash and restricted cash equivalents at beginning of period | 5,221,513 |  |  | 4,880,947 |
CASH, CASH EQUIVALENTS, RESTRICTED CASH AND RESTRICTED CASH EQUIVALENTS AT END OF PERIOD | $ | 5,240,929 |  |  | $ | 4,911,317 |

See accompanying notes to consolidated financial statements.
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MARKEL GROUP INC. AND SUBSIDIARIES
NOTES TO CONSOLIDATED FINANCIAL STATEMENTS
1. Summary of Significant Accounting Policies
Markel Group Inc., formerly Markel Corporation, is a holding company comprised of a diverse group of companies and investments with specialty insurance at its core. Effective May 26, 2023, Markel Corporation changed its name to Markel Group Inc. (Markel Group). Through its wholly owned subsidiary, Markel Ventures, Inc. (Markel Ventures), Markel Group owns controlling interests in businesses that operate in a variety of industries. See note 2 for details regarding reportable segments.
a) Basis of Presentation. The consolidated balance sheet as of June 30, 2023 and the related consolidated statements of income (loss) and comprehensive income (loss) and changes in equity for the quarters and six months ended June 30, 2023 and 2022, and the condensed consolidated statements of cash flows for the six months ended June 30, 2023 and 2022 are unaudited. In the opinion of management, all adjustments necessary for fair presentation of such consolidated financial statements have been included. Except for the adjustments described in note 1 c), such adjustments consist only of normal, recurring items. Interim results are not necessarily indicative of results of operations for the entire year. The consolidated balance sheet as of December 31, 2022 was derived from Markel Group's audited annual consolidated financial statements.
The accompanying consolidated financial statements have been prepared in accordance with United States (U.S.) generally accepted accounting principles (GAAP) and include the accounts of Markel Group and its consolidated subsidiaries, as well as variable interest entities (VIEs) that meet the requirements for consolidation (the Company). All significant intercompany balances and transactions have been eliminated in consolidation. The Company consolidates the results of its Markel Ventures subsidiaries on a one-month lag, with the exception of significant transactions or events that occur during the intervening period. Certain prior period amounts have been reclassified to conform to the current period presentation.
The preparation of financial statements in accordance with U.S. GAAP requires management to make estimates and assumptions that affect the reported amounts of assets, liabilities, revenues and expenses and the disclosure of contingent assets and liabilities. Actual results may differ materially from the estimates and assumptions used in preparing the consolidated financial statements.
The consolidated financial statements and notes are presented as permitted by Form 10-Q and do not contain certain information included in the Company's annual consolidated financial statements and notes. The following accounting policy was updated to reflect an accounting standard that became effective January 1, 2023. See note 1 c). For a more complete description of the Company's business and accounting policies, readers are urged to review the Company's 2022 Annual Report on Form 10-K.
b) Life and Annuity Benefits. The Company has a run-off block of life and annuity reinsurance contracts that subject the Company to mortality, longevity and morbidity risks. Effective January 1, 2023, the Company adopted Financial Accounting Standards Board (FASB) Accounting Standards Update (ASU) No. 2018-12, Financial Services—Insurance (Topic 944): Targeted Improvements to the Accounting for Long-Duration Contracts and restated all prior periods presented to reflect the new accounting standard. The primary component of the Company's liabilities for life and annuity benefits is the present value of the liability for future policyholder benefits. The cash flow assumptions used to determine the policyholder benefit reserves are reviewed and updated, as necessary, at least annually. Interest accretion for the reserves is calculated using the discount rate locked-in at contract inception. Policy benefit reserves are remeasured each period using current discount rates, based on yields for upper-medium grade fixed maturity securities, with the impact of changes in the discount rate included in other comprehensive income, net of taxes. All other results attributable to the run-off of life and annuity reinsurance contracts are included in services and other revenues and services and other expenses in the consolidated statements of income and comprehensive income. Investment income earned on the investments that support the policy benefit reserves are included in net investment income. Because of the uncertainty in the assumptions used to estimate reserves for life and annuity benefit obligations and the long-term nature of these reinsurance contracts, the ultimate liability may be greater or less than the estimated liability. See note 9 for further details regarding life and annuity benefits.
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c) Recent Accounting Pronouncements
Accounting Standards Adopted
Effective January 1, 2023, the Company adopted ASU No. 2018-12 and several ASUs issued as amendments to ASU No. 2018-12. This standard requires insurance companies with long duration contracts to: (1) review and, if there is a change, update the assumptions used to measure expected cash flows at least annually; (2) update the discount rate assumption at each reporting date; and (3) enhance certain qualitative and quantitative disclosures. ASU No. 2018-12 was applied using a modified retrospective approach that required restatement of prior periods presented, including a cumulative adjustment recorded to accumulated other comprehensive income as of January 1, 2021 (the transition date) as a result of updating the discount rate assumption. At the transition date, the adoption of ASU 2018-12 had no impact on retained earnings but resulted in a decrease to accumulated other comprehensive income, net of taxes, of $15.3 million, which was comprised of the following corresponding adjustments to life and annuity benefits and deferred tax liabilities.

(dollars in thousands) | January 1, 2021
Reverse reserve deficiency adjustment related to unrealized gains on underlying investment portfolio of available-for-sale securities | $ | 119,548 |
Apply updated discount rate to the liability for future policyholder benefits | (138,865) |
Increase in life and annuity benefits | (19,317) |
Decrease in deferred tax liability | 4,057 |
Decrease in accumulated other comprehensive income, net of taxes | $ | (15,260) |

The impact of changes in the discount rate on the liability for future policyholder benefits following the transition date are included in other comprehensive income (loss) in the respective periods and, combined with the transition adjustment, resulted in the following cumulative changes to the Company's previously presented consolidated balance sheets.

| December 31,
(dollars in thousands) | 2022 |  | 2021
Decrease (increase) in life and annuity benefits | $ | 113,396 |  |  | $ | (19,759) |
Decrease (increase) in deferred tax liability | (23,813) |  |  | 4,149 |
Increase (decrease) in accumulated other comprehensive income (loss), net of taxes | $ | 89,583 |  |  | $ | (15,610) |

Changes in the discount rate on the liability for future policyholder benefits also resulted in an increase, or benefit, of $63.2 million and $79.2 million to the other comprehensive loss previously presented for the quarter and six months ended June 30, 2022, which was comprised of the following adjustments.

(dollars in thousands) | Quarter Ended June 30, 2022 |  | Six Months Ended June 30, 2022
Reverse benefit included in change in net unrealized gains (losses) on available-for-sale-investments, net of taxes, related to reversal of previously recognized reserve deficiency adjustment | $ | — |  |  | $ | (44,682) |
Change in discount rate for life and annuity benefits, net of taxes | 63,198 |  |  | 123,891 |
Increase in other comprehensive loss, net of taxes | $ | 63,198 |  |  | $ | 79,209 |

The adoption of other provisions of this ASU did not have a material impact on the Company's financial position, results of operations or cash flows for any of the periods presented.
Effective January 1, 2023, the Company adopted ASU No. 2021-08, Business Combinations (Topic 805): Accounting for Contract Assets and Contract Liabilities from Contracts with Customer s. ASU No. 2021-08 requires contract assets and liabilities accounted for under FASB Accounting Standards Codification (ASC) 606, Revenue from Contracts with Customers, to be recorded at the acquisition date as if the acquirer entered into those contracts itself on the contract inception dates, rather than at fair value. At adoption, ASU No. 2021-08 did not impact the Company's financial position, results of operations or cash flows, but prospectively, this ASU will impact amounts recorded by the Company for assets acquired and liabilities assumed in conjunction with certain acquisitions.
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2. Segment Reporting Disclosures
The chief operating decision maker reviews the Company's ongoing underwriting operations on a global basis in the following two segments: Insurance and Reinsurance. In determining how to allocate resources and assess the performance of the Company's underwriting results, management considers many factors, including the nature of the insurance product sold, the type of account written and the type of customer served. The Insurance segment includes all direct business and facultative placements written on a risk-bearing basis within the Company's underwriting operations. The Reinsurance segment includes all treaty reinsurance written on a risk-bearing basis within the Company's underwriting operations. All investing activities related to the Company's insurance operations are included in the Investing segment.
The Company's other insurance operations primarily consist of the results of the Company's insurance-linked securities operations and program services business. Other insurance operations also include results for lines of business discontinued prior to, or in conjunction with, acquisitions, including development on asbestos and environmental loss reserves and results attributable to the run-off of life and annuity reinsurance business, which are monitored separately from the Company's ongoing underwriting operations. For purposes of segment reporting, none of these other insurance operations are considered to be reportable segments.
The Company's chief operating decision maker reviews and assesses Markel Ventures' performance in the aggregate, as a single operating segment. The Markel Ventures segment primarily consists of controlling interests in a diverse portfolio of businesses that operate in various industries.
Segment profit for each of the Company's underwriting segments is measured by underwriting profit. The property and casualty insurance industry commonly defines underwriting profit as earned premiums net of losses and loss adjustment expenses and underwriting, acquisition and insurance expenses. Underwriting profit does not replace operating income or net income computed in accordance with U.S. GAAP as a measure of profitability. Underwriting profit or loss provides a basis for management to evaluate the Company's underwriting performance. Segment profit for the Company's underwriting segments may also include other revenues and expenses that are attributable to the Company's underwriting operations that are not captured in underwriting profit. Segment profit for the Investing segment is measured by income from the Company's investment portfolio, which is comprised of net investment income and net investment gains. Segment profit for the Investing segment also includes income from equity method investments, which is included within services and other revenues. Segment profit for the Markel Ventures segment is measured by operating income.
For management reporting purposes, the Company allocates assets to its underwriting operations and to its Investing and Markel Ventures segments and certain of its other operations, including its insurance-linked securities and program services operations. Underwriting assets include assets attributed to the Company's Insurance and Reinsurance segments, discontinued underwriting lines of business, as well as assets that are not specifically allocated to the Company's other operations. Generally, the Company manages its underwriting assets in the aggregate and therefore does not allocate assets to individual underwriting segments.
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a) The following tables summarize the Company's segment disclosures.

| Quarter Ended June 30, 2023
(dollars in thousands) | Insurance |  | Reinsurance |  | Investing |  | Markel Ventures |  | Other (1) |  | Consolidated
Gross premium volume | $ | 2,455,403 |  |  | $ | 281,100 |  |  | $ | — |  |  | $ | — |  |  | $ | 1,051,682 |  |  | $ | 3,788,185 |
Net written premiums | 1,946,528 |  |  | 261,496 |  |  | — |  |  | — |  |  | (331) |  |  | 2,207,693 |
Earned premiums | 1,763,186 |  |  | 268,288 |  |  | — |  |  | — |  |  | (331) |  |  | 2,031,143 |
Losses and loss adjustment expenses: |  |  |  |  |  |  |  |  |  |  |
Current accident year | (1,079,450) |  |  | (176,317) |  |  | — |  |  | — |  |  | — |  |  | (1,255,767) |
Prior accident years | 61,562 |  |  | 7,974 |  |  | — |  |  | — |  |  | (1,645) |  |  | 67,891 |
Underwriting, acquisition and insurance expenses: |  |  |  |  |  |  |  |  |  |  |
Amortization of policy acquisition costs | (367,145) |  |  | (71,574) |  |  | — |  |  | — |  |  | — |  |  | (438,719) |
Other underwriting expenses | (243,502) |  |  | (13,187) |  |  | — |  |  | — |  |  | (2,479) |  |  | (259,168) |
Underwriting profit (loss) | 134,651 |  |  | 15,184 |  |  | — |  |  | — |  |  | (4,455) |  |  | 145,380 |
Net investment income | — |  |  | — |  |  | 168,927 |  |  | 766 |  |  | — |  |  | 169,693 |
Net investment gains | — |  |  | — |  |  | 484,527 |  |  | — |  |  | — |  |  | 484,527 |
Products revenues | — |  |  | — |  |  | — |  |  | 784,882 |  |  | — |  |  | 784,882 |
Services and other revenues | — |  |  | — |  |  | (6,378) |  |  | 600,931 |  |  | 77,738 |  |  | 672,291 |
Products expenses | — |  |  | — |  |  | — |  |  | (651,469) |  |  | — |  |  | (651,469) |
Services and other expenses | — |  |  | — |  |  | — |  |  | (565,060) |  |  | (25,757) |  |  | (590,817) |
Amortization of intangible assets (2) | — |  |  | — |  |  | — |  |  | (19,859) |  |  | (24,564) |  |  | (44,423) |
Segment profit | $ | 134,651 |  |  | $ | 15,184 |  |  | $ | 647,076 |  |  | $ | 150,191 |  |  | $ | 22,962 |  |  | $ | 970,064 |
Interest expense |  |  |  |  |  |  |  |  |  |  | (47,221) |
Net foreign exchange losses |  |  |  |  |  |  |  |  |  |  | (14,976) |
Income before income taxes |  |  |  |  |  |  |  |  |  |  | $ | 907,867 |

(1) Other represents the total profit (loss) attributable to the Company's operations that are not included in a reportable segment, as well as amortization of intangible assets attributable to underwriting segments, which is not allocated between the Insurance and Reinsurance segments.
(2) Segment profit for the Markel Ventures segment includes amortization of intangible assets attributable to Markel Ventures. Amortization of intangible assets attributable to the Company's underwriting segments, included in Other, was $9.3 million for the quarter ended June 30, 2023.
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| Quarter Ended June 30, 2022
(dollars in thousands) | Insurance |  | Reinsurance |  | Investing |  | Markel Ventures |  | Other (1) |  | Consolidated
Gross premium volume | $ | 2,237,158 |  |  | $ | 289,056 |  |  | $ | — |  |  | $ | — |  |  | $ | 753,835 |  |  | $ | 3,280,049 |
Net written premiums | 1,828,162 |  |  | 273,838 |  |  | — |  |  | — |  |  | (2,205) |  |  | 2,099,795 |
Earned premiums | 1,570,001 |  |  | 264,154 |  |  | — |  |  | — |  |  | (1,051) |  |  | 1,833,104 |
Losses and loss adjustment expenses: |  |  |  |  |  |  |  |  |  |  |
Current accident year | (919,283) |  |  | (165,932) |  |  | — |  |  | — |  |  | — |  |  | (1,085,215) |
Prior accident years | 43,693 |  |  | (13,577) |  |  | — |  |  | — |  |  | (3,711) |  |  | 26,405 |
Underwriting, acquisition and insurance expenses: |  |  |  |  |  |  |  |  |  |  |
Amortization of policy acquisition costs | (323,826) |  |  | (69,125) |  |  | — |  |  | — |  |  | (32) |  |  | (392,983) |
Other underwriting expenses | (204,171) |  |  | (11,681) |  |  | — |  |  | — |  |  | (634) |  |  | (216,486) |
Underwriting profit (loss) | 166,414 |  |  | 3,839 |  |  | — |  |  | — |  |  | (5,428) |  |  | 164,825 |
Net investment income | — |  |  | — |  |  | 96,695 |  |  | 100 |  |  | — |  |  | 96,795 |
Net investment losses | — |  |  | — |  |  | (1,554,643) |  |  | — |  |  | — |  |  | (1,554,643) |
Products revenues | — |  |  | — |  |  | — |  |  | 776,959 |  |  | — |  |  | 776,959 |
Services and other revenues | — |  |  | — |  |  | (3,137) |  |  | 584,339 |  |  | 58,790 |  |  | 639,992 |
Products expenses | — |  |  | — |  |  | — |  |  | (697,718) |  |  | — |  |  | (697,718) |
Services and other expenses | — |  |  | — |  |  | — |  |  | (536,057) |  |  | (21,424) |  |  | (557,481) |
Amortization of intangible assets (2) | — |  |  | — |  |  | — |  |  | (20,577) |  |  | (24,946) |  |  | (45,523) |
Segment profit (loss) | $ | 166,414 |  |  | $ | 3,839 |  |  | $ | (1,461,085) |  |  | $ | 107,046 |  |  | $ | 6,992 |  |  | $ | (1,176,794) |
Interest expense |  |  |  |  |  |  |  |  |  |  | (50,050) |
Net foreign exchange gains |  |  |  |  |  |  |  |  |  |  | 105,067 |
Loss before income taxes |  |  |  |  |  |  |  |  |  |  | $ | (1,121,777) |

(1) Other represents the total profit (loss) attributable to the Company's operations that are not included in a reportable segment, as well as amortization of intangible assets attributable to underwriting segments, which is not allocated between the Insurance and Reinsurance segments.
(2) Segment profit for the Markel Ventures segment includes amortization of intangible assets attributable to Markel Ventures. Amortization of intangible assets attributable to the Company's underwriting segments, included in Other, was $9.6 million for the quarter ended June 30, 2022.
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| Six Months Ended June 30, 2023
(dollars in thousands) | Insurance |  | Reinsurance |  | Investing |  | Markel Ventures |  | Other (1) |  | Consolidated
Gross premium volume | $ | 4,553,341 |  |  | $ | 833,161 |  |  | $ | — |  |  | $ | — |  |  | $ | 1,837,695 |  |  | $ | 7,224,197 |
Net written premiums | 3,648,669 |  |  | 777,587 |  |  | — |  |  | — |  |  | (785) |  |  | 4,425,471 |
Earned premiums | 3,474,110 |  |  | 525,522 |  |  | — |  |  | — |  |  | (785) |  |  | 3,998,847 |
Losses and loss adjustment expenses: |  |  |  |  |  |  |  |  |  |  |
Current accident year | (2,156,996) |  |  | (343,102) |  |  | — |  |  | — |  |  | — |  |  | (2,500,098) |
Prior accident years | 124,190 |  |  | 16,678 |  |  | — |  |  | — |  |  | (1,660) |  |  | 139,208 |
Underwriting, acquisition and insurance expenses: |  |  |  |  |  |  |  |  |  |  |
Amortization of policy acquisition costs | (727,499) |  |  | (133,352) |  |  | — |  |  | — |  |  | — |  |  | (860,851) |
Other underwriting expenses | (482,650) |  |  | (26,328) |  |  | — |  |  | — |  |  | (3,763) |  |  | (512,741) |
Underwriting profit (loss) | 231,155 |  |  | 39,418 |  |  | — |  |  | — |  |  | (6,208) |  |  | 264,365 |
Net investment income | — |  |  | — |  |  | 327,521 |  |  | 1,507 |  |  | — |  |  | 329,028 |
Net investment gains | — |  |  | — |  |  | 857,090 |  |  | — |  |  | — |  |  | 857,090 |
Products revenues | — |  |  | — |  |  | — |  |  | 1,362,808 |  |  | — |  |  | 1,362,808 |
Services and other revenues | — |  |  | — |  |  | (8,758) |  |  | 1,126,944 |  |  | 119,966 |  |  | 1,238,152 |
Products expenses | — |  |  | — |  |  | — |  |  | (1,167,225) |  |  | — |  |  | (1,167,225) |
Services and other expenses | — |  |  | — |  |  | — |  |  | (1,061,806) |  |  | (9,630) |  |  | (1,071,436) |
Amortization of intangible assets (2) | — |  |  | — |  |  | — |  |  | (39,410) |  |  | (49,412) |  |  | (88,822) |
Segment profit | $ | 231,155 |  |  | $ | 39,418 |  |  | $ | 1,175,853 |  |  | $ | 222,818 |  |  | $ | 54,716 |  |  | $ | 1,723,960 |
Interest expense |  |  |  |  |  |  |  |  |  |  | (96,659) |
Net foreign exchange losses |  |  |  |  |  |  |  |  |  |  | (47,904) |
Income before income taxes |  |  |  |  |  |  |  |  |  |  | $ | 1,579,397 |

(1) Other represents the total profit (loss) attributable to the Company's operations that are not included in a reportable segment, as well as amortization of intangible assets attributable to underwriting segments, which is not allocated between the Insurance and Reinsurance segments.
(2) Segment profit for the Markel Ventures segment includes amortization of intangible assets attributable to Markel Ventures. Amortization of intangible assets attributable to the Company's underwriting segments, included in Other, was $18.8 million for the six months ended June 30, 2023.
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| Six Months Ended June 30, 2022
(dollars in thousands) | Insurance |  | Reinsurance |  | Investing |  | Markel Ventures |  | Other (1) |  | Consolidated
Gross premium volume | $ | 4,180,464 |  |  | $ | 865,372 |  |  | $ | — |  |  | $ | — |  |  | $ | 1,632,500 |  |  | $ | 6,678,336 |
Net written premiums | 3,439,182 |  |  | 829,058 |  |  | — |  |  | — |  |  | (3,711) |  |  | 4,264,529 |
Earned premiums | 3,047,149 |  |  | 548,121 |  |  | — |  |  | — |  |  | (2,396) |  |  | 3,592,874 |
Losses and loss adjustment expenses: |  |  |  |  |  |  |  |  |  |  |
Current accident year | (1,805,520) |  |  | (348,390) |  |  | — |  |  | — |  |  | — |  |  | (2,153,910) |
Prior accident years | 142,333 |  |  | (15,660) |  |  | — |  |  | — |  |  | (3,945) |  |  | 122,728 |
Underwriting, acquisition and insurance expenses: |  |  |  |  |  |  |  |  |  |  |
Amortization of policy acquisition costs | (634,232) |  |  | (140,879) |  |  | — |  |  | — |  |  | (32) |  |  | (775,143) |
Other underwriting expenses | (395,822) |  |  | (26,070) |  |  | — |  |  | — |  |  | (2,799) |  |  | (424,691) |
Underwriting profit (loss) | 353,908 |  |  | 17,122 |  |  | — |  |  | — |  |  | (9,172) |  |  | 361,858 |
Net investment income | — |  |  | — |  |  | 188,992 |  |  | 107 |  |  | — |  |  | 189,099 |
Net investment losses | — |  |  | — |  |  | (1,913,042) |  |  | — |  |  | — |  |  | (1,913,042) |
Products revenues | — |  |  | — |  |  | — |  |  | 1,258,580 |  |  | — |  |  | 1,258,580 |
Services and other revenues | — |  |  | — |  |  | (22,707) |  |  | 1,053,103 |  |  | 240,536 |  |  | 1,270,932 |
Products expenses | — |  |  | — |  |  | — |  |  | (1,145,537) |  |  | — |  |  | (1,145,537) |
Services and other expenses | — |  |  | — |  |  | — |  |  | (967,960) |  |  | (179,412) |  |  | (1,147,372) |
Amortization of intangible assets (2) | — |  |  | — |  |  | — |  |  | (41,510) |  |  | (50,062) |  |  | (91,572) |
Segment profit (loss) | $ | 353,908 |  |  | $ | 17,122 |  |  | $ | (1,746,757) |  |  | $ | 156,783 |  |  | $ | 1,890 |  |  | $ | (1,217,054) |
Interest expense |  |  |  |  |  |  |  |  |  |  | (99,742) |
Net foreign exchange gains |  |  |  |  |  |  |  |  |  |  | 128,071 |
Loss before income taxes |  |  |  |  |  |  |  |  |  |  | $ | (1,188,725) |

(1) Other represents the total profit (loss) attributable to the Company's operations that are not included in a reportable segment, as well as amortization of intangible assets attributable to underwriting segments, which is not allocated between the Insurance and Reinsurance segments.
(2) Segment profit for the Markel Ventures segment includes amortization of intangible assets attributable to Markel Ventures. Amortization of intangible assets attributable to the Company's underwriting segments, included in Other, was $19.4 million for the six months ended June 30, 2022.
b) The following amounts attributable to the Markel Ventures segment are also reviewed, or included in measures reviewed, by the Company's chief operating decision maker.

| Quarter Ended June 30, |  | Six Months Ended June 30,
(dollars in thousands) | 2023 |  | 2022 |  | 2023 |  | 2022
Depreciation expense | $ | 27,419 |  |  | $ | 26,531 |  |  | $ | 54,782 |  |  | $ | 51,566 |
Interest expense (1) | $ | 12,899 |  |  | $ | 11,025 |  |  | $ | 25,822 |  |  | $ | 22,203 |
Income tax expense | $ | 30,583 |  |  | $ | 22,419 |  |  | $ | 43,769 |  |  | $ | 31,079 |
Capital expenditures | $ | 38,045 |  |  | $ | 50,667 |  |  | $ | 69,543 |  |  | $ | 96,680 |

(1) Interest expense for the quarter and six months ended June 30, 2023 included intercompany interest expense of $6.6 million and $13.3 million, respectively. Interest expense for the quarter and six months ended June 30, 2022 included intercompany interest expense of $7.0 million and $14.1 million. Intercompany interest expense was eliminated in consolidation.
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c) The following table reconciles segment assets to the Company's consolidated balance sheets.

(dollars in thousands) | June 30, 2023 |  | December 31, 2022
Segment assets: |  |  |
Investing | $ | 28,332,303 |  |  | $ | 26,982,280 |
Underwriting | 9,865,674 |  |  | 8,853,559 |
Markel Ventures | 5,416,860 |  |  | 5,315,677 |
Total segment assets | 43,614,837 |  |  | 41,151,516 |
Other operations | 8,569,296 |  |  | 8,639,743 |
Total assets | $ | 52,184,133 |  |  | $ | 49,791,259 |

3. Investments
a) The following tables summarize the Company's available-for-sale investments. Commercial and residential mortgage-backed securities include securities issued by U.S. government-sponsored enterprises and U.S. government agencies. The net unrealized holding gains (losses) in the tables below are presented before taxes.

| June 30, 2023
(dollars in thousands) | Amortized Cost |  | Gross Unrealized Holding Gains |  | Gross Unrealized Holding Losses |  |  |  | Estimated Fair Value
Fixed maturity securities: |  |  |  |  |  |  |  |  |
U.S. Treasury securities | $ | 3,262,114 |  |  | $ | 280 |  |  | $ | (133,542) |  |  |  |  | $ | 3,128,852 |
U.S. government-sponsored enterprises | 1,044,843 |  |  | 104 |  |  | (106,212) |  |  |  |  | 938,735 |
Obligations of states, municipalities and political subdivisions | 4,093,715 |  |  | 2,728 |  |  | (220,108) |  |  |  |  | 3,876,335 |
Foreign governments | 1,691,459 |  |  | 3,717 |  |  | (151,550) |  |  |  |  | 1,543,626 |
Commercial mortgage-backed securities | 2,251,522 |  |  | 291 |  |  | (178,257) |  |  |  |  | 2,073,556 |
Residential mortgage-backed securities | 508,692 |  |  | 3 |  |  | (28,773) |  |  |  |  | 479,922 |
Asset-backed securities | 1,241 |  |  | — |  |  | (37) |  |  |  |  | 1,204 |
Corporate bonds | 799,971 |  |  | 811 |  |  | (97,320) |  |  |  |  | 703,462 |
Total fixed maturity securities | 13,653,557 |  |  | 7,934 |  |  | (915,799) |  |  |  |  | 12,745,692 |
Short-term investments | 2,036,747 |  |  | 3,840 |  |  | (1,526) |  |  |  |  | 2,039,061 |
Investments, available-for-sale | $ | 15,690,304 |  |  | $ | 11,774 |  |  | $ | (917,325) |  |  |  |  | $ | 14,784,753 |

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| December 31, 2022
(dollars in thousands) | Amortized Cost |  | Gross Unrealized Holding Gains |  | Gross Unrealized Holding Losses |  | Estimated Fair Value
Fixed maturity securities: |  |  |  |  |  |  |
U.S. Treasury securities | $ | 3,050,089 |  |  | $ | 2,363 |  |  | $ | (138,493) |  |  | $ | 2,913,959 |
U.S. government-sponsored enterprises | 871,463 |  |  | 154 |  |  | (106,079) |  |  | 765,538 |
Obligations of states, municipalities and political subdivisions | 3,973,911 |  |  | 6,503 |  |  | (247,231) |  |  | 3,733,183 |
Foreign governments | 1,473,658 |  |  | 2,843 |  |  | (169,723) |  |  | 1,306,778 |
Commercial mortgage-backed securities | 2,109,721 |  |  | 395 |  |  | (169,668) |  |  | 1,940,448 |
Residential mortgage-backed securities | 553,591 |  |  | 6 |  |  | (26,804) |  |  | 526,793 |
Asset-backed securities | 1,693 |  |  | — |  |  | (53) |  |  | 1,640 |
Corporate bonds | 771,761 |  |  | 836 |  |  | (104,101) |  |  | 668,496 |
Total fixed maturity securities | 12,805,887 |  |  | 13,100 |  |  | (962,152) |  |  | 11,856,835 |
Short-term investments | 2,663,560 |  |  | 5,760 |  |  | (58) |  |  | 2,669,262 |
Investments, available-for-sale | $ | 15,469,447 |  |  | $ | 18,860 |  |  | $ | (962,210) |  |  | $ | 14,526,097 |

b) The following tables summarize gross unrealized investment losses on available-for-sale investments by the length of time that securities have continuously been in an unrealized loss position.

| June 30, 2023
| Less than 12 months |  | 12 months or longer |  | Total
(dollars in thousands) | Estimated Fair Value |  | Gross Unrealized Holding Losses |  | Estimated Fair Value |  | Gross Unrealized Holding Losses |  | Estimated Fair Value |  | Gross Unrealized Holding Losses
Fixed maturity securities: |  |  |  |  |  |  |  |  |  |  |
U.S. Treasury securities | $ | 1,072,516 |  |  | $ | (17,213) |  |  | $ | 1,956,782 |  |  | $ | (116,329) |  |  | $ | 3,029,298 |  |  | $ | (133,542) |
U.S. government-sponsored enterprises | 301,249 |  |  | (6,205) |  |  | 628,588 |  |  | (100,007) |  |  | 929,837 |  |  | (106,212) |
Obligations of states, municipalities and political subdivisions | 1,434,351 |  |  | (18,517) |  |  | 1,929,349 |  |  | (201,591) |  |  | 3,363,700 |  |  | (220,108) |
Foreign governments | 359,569 |  |  | (12,927) |  |  | 1,005,886 |  |  | (138,623) |  |  | 1,365,455 |  |  | (151,550) |
Commercial mortgage-backed securities | 419,295 |  |  | (12,357) |  |  | 1,634,450 |  |  | (165,900) |  |  | 2,053,745 |  |  | (178,257) |
Residential mortgage-backed securities | 115,044 |  |  | (2,216) |  |  | 364,356 |  |  | (26,557) |  |  | 479,400 |  |  | (28,773) |
Asset-backed securities | — |  |  | — |  |  | 1,204 |  |  | (37) |  |  | 1,204 |  |  | (37) |
Corporate bonds | 90,952 |  |  | (1,540) |  |  | 591,258 |  |  | (95,780) |  |  | 682,210 |  |  | (97,320) |
Total fixed maturity securities | 3,792,976 |  |  | (70,975) |  |  | 8,111,873 |  |  | (844,824) |  |  | 11,904,849 |  |  | (915,799) |
Short-term investments | 1,324,927 |  |  | (1,526) |  |  | — |  |  | — |  |  | 1,324,927 |  |  | (1,526) |
Total | $ | 5,117,903 |  |  | $ | (72,501) |  |  | $ | 8,111,873 |  |  | $ | (844,824) |  |  | $ | 13,229,776 |  |  | $ | (917,325) |

At June 30, 2023, the Company held 1,603 available-for-sale securities in an unrealized loss position with a total estimated fair value of $13.2 billion and gross unrealized losses of $917.3 million. Of these 1,603 securities, 991 securities had been in a continuous unrealized loss position for one year or longer and had a total estimated fair value of $8.1 billion and gross unrealized losses of $844.8 million.
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| December 31, 2022
| Less than 12 months |  | 12 months or longer |  | Total
(dollars in thousands) | Estimated Fair Value |  | Gross Unrealized Holding Losses |  | Estimated Fair Value |  | Gross Unrealized Holding Losses |  | Estimated Fair Value |  | Gross Unrealized Holding Losses
Fixed maturity securities: |  |  |  |  |  |  |  |  |  |  |
U.S. Treasury securities | $ | 735,605 |  |  | $ | (30,583) |  |  | $ | 1,907,922 |  |  | $ | (107,910) |  |  | $ | 2,643,527 |  |  | $ | (138,493) |
U.S. government-sponsored enterprises | 413,495 |  |  | (40,488) |  |  | 331,391 |  |  | (65,591) |  |  | 744,886 |  |  | (106,079) |
Obligations of states, municipalities and political subdivisions | 2,474,289 |  |  | (164,537) |  |  | 348,943 |  |  | (82,694) |  |  | 2,823,232 |  |  | (247,231) |
Foreign governments | 900,322 |  |  | (115,324) |  |  | 300,423 |  |  | (54,399) |  |  | 1,200,745 |  |  | (169,723) |
Commercial mortgage-backed securities | 1,611,603 |  |  | (117,482) |  |  | 305,217 |  |  | (52,186) |  |  | 1,916,820 |  |  | (169,668) |
Residential mortgage-backed securities | 516,423 |  |  | (25,232) |  |  | 9,342 |  |  | (1,572) |  |  | 525,765 |  |  | (26,804) |
Asset-backed securities | 1,640 |  |  | (53) |  |  | — |  |  | — |  |  | 1,640 |  |  | (53) |
Corporate bonds | 496,766 |  |  | (74,542) |  |  | 153,035 |  |  | (29,559) |  |  | 649,801 |  |  | (104,101) |
Total fixed maturity securities | 7,150,143 |  |  | (568,241) |  |  | 3,356,273 |  |  | (393,911) |  |  | 10,506,416 |  |  | (962,152) |
Short-term investments | 774,480 |  |  | (58) |  |  | — |  |  | — |  |  | 774,480 |  |  | (58) |
Total | $ | 7,924,623 |  |  | $ | (568,299) |  |  | $ | 3,356,273 |  |  | $ | (393,911) |  |  | $ | 11,280,896 |  |  | $ | (962,210) |

At December 31, 2022, the Company held 1,400 available-for-sale securities in an unrealized loss position with a total estimated fair value of $11.3 billion and gross unrealized losses of $962.2 million. Of these 1,400 securities, 246 securities had been in a continuous unrealized loss position for one year or longer and had a total estimated fair value of $3.4 billion and gross unrealized losses of $393.9 million.
The Company completes a detailed analysis each quarter to assess whether the decline in the fair value of any investment below its cost basis is the result of a credit loss. All available-for-sale securities with unrealized losses are reviewed. The Company considers many factors in completing its quarterly review of securities with unrealized losses for credit-related impairment to determine whether a credit loss exists, including the extent to which fair value is below cost, the implied yield to maturity, rating downgrades of the security and whether or not the issuer has failed to make scheduled principal or interest payments. The Company also takes into consideration information about the financial condition of the issuer and industry factors that could negatively impact the issuer.
If the decline in fair value of an available-for-sale security below its amortized cost is considered to be the result of a credit loss, the Company compares the estimated present value of the cash flows expected to be collected to the amortized cost of the security. The extent to which the estimated present value of the cash flows expected to be collected is less than the amortized cost of the security represents the credit loss, which is recorded as an allowance and recognized in net income. The allowance is limited to the difference between the fair value and the amortized cost of the security. Any remaining decline in fair value represents the non-credit portion of the impairment, which is recognized in other comprehensive income. The Company did not have an allowance for credit losses as of June 30, 2023 or December 31, 2022.
Quarterly, the Company also considers whether it intends to sell an available-for-sale security or if it is more likely than not that it will be required to sell a security before recovery of its amortized cost. In these instances, a decline in fair value is recognized in net income based on the fair value of the security at the time of assessment, resulting in a new cost basis for the security. As of June 30, 2023, t he Company did not intend to sell or believe it would be required to sell any available-for-sale securities in an unrealized loss position before recovery of their amortized cost.
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c) The amortized cost and estimated fair value of fixed maturity securities at June 30, 2023 are shown below by contractual maturity.

(dollars in thousands) | Amortized Cost |  | Estimated Fair Value
Due in one year or less | $ | 1,193,540 |  |  | $ | 1,170,094 |
Due after one year through five years | 4,544,954 |  |  | 4,325,414 |
Due after five years through ten years | 3,382,145 |  |  | 3,077,695 |
Due after ten years | 1,771,463 |  |  | 1,617,807 |
| 10,892,102 |  |  | 10,191,010 |
Commercial mortgage-backed securities | 2,251,522 |  |  | 2,073,556 |
Residential mortgage-backed securities | 508,692 |  |  | 479,922 |
Asset-backed securities | 1,241 |  |  | 1,204 |
Total fixed maturity securities | $ | 13,653,557 |  |  | $ | 12,745,692 |

d) The following table presents the components of net investment income.

| Quarter Ended June 30, |  | Six Months Ended June 30,
(dollars in thousands) | 2023 |  | 2022 |  | 2023 |  | 2022
Interest: |  |  |  |  |  |  |
Fixed maturity securities | $ | 88,419 |  |  | $ | 71,920 |  |  | $ | 170,547 |  |  | $ | 143,064 |
Short-term investments | 23,712 |  |  | 3,354 |  |  | 50,331 |  |  | 4,328 |
Cash and cash equivalents | 35,491 |  |  | 2,023 |  |  | 63,092 |  |  | 1,825 |
Dividends on equity securities | 26,352 |  |  | 23,590 |  |  | 53,834 |  |  | 48,327 |
| 173,974 |  |  | 100,887 |  |  | 337,804 |  |  | 197,544 |
Investment expenses | (4,281) |  |  | (4,092) |  |  | (8,776) |  |  | (8,445) |
Net investment income | $ | 169,693 |  |  | $ | 96,795 |  |  | $ | 329,028 |  |  | $ | 189,099 |

e) The following table presents the components of net investment gains (losses) included in net income (loss) and the change in net unrealized gains (losses) included in other comprehensive income (loss). Gross realized investment gains and losses on fixed maturity securities, short-term investments and other investments were not material to the consolidated financial statements and are presented on a net basis in the following table.

| Quarter Ended June 30, |  | Six Months Ended June 30,
(dollars in thousands) | 2023 |  | 2022 |  | 2023 |  | 2022
Fixed maturity securities, short-term investments and other investments: |  |  |  |  |  |  |
Net realized investment gains (losses) | $ | 1,155 |  |  | $ | (2,259) |  |  | $ | (2,066) |  |  | $ | 3,969 |
Equity securities: |  |  |  |  |  |  |
Change in fair value of securities sold during the period | 2,434 |  |  | (2,113) |  |  | 13,487 |  |  | (19,231) |
Change in fair value of securities held at the end of the period | 480,938 |  |  | (1,550,271) |  |  | 845,669 |  |  | (1,897,780) |
Total change in fair value | 483,372 |  |  | (1,552,384) |  |  | 859,156 |  |  | (1,917,011) |
Net investment gains (losses) | $ | 484,527 |  |  | $ | (1,554,643) |  |  | $ | 857,090 |  |  | $ | (1,913,042) |
Change in net unrealized gains (losses) on available-for-sale investments included in other comprehensive income (loss): |  |  |  |  |  |  |
Fixed maturity securities | $ | (167,992) |  |  | $ | (449,089) |  |  | $ | 41,187 |  |  | $ | (1,114,899) |
Short-term investments | (2,578) |  |  | (9,239) |  |  | (3,388) |  |  | (3,377) |
Net increase (decrease) | $ | (170,570) |  |  | $ | (458,328) |  |  | $ | 37,799 |  |  | $ | (1,118,276) |

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4. Fair Value Measurements
FASB ASC 820, Fair Value Measurements and Disclosures, establishes a three-level hierarchy that prioritizes the inputs to valuation techniques used to measure fair value. The fair value hierarchy gives the highest priority to quoted prices in active markets for identical assets or liabilities (Level 1) and the lowest priority to unobservable inputs (Level 3). If the inputs used to measure the assets or liabilities fall within different levels of the hierarchy, the classification is based on the lowest level input that is significant to the fair value measurement of the asset or liability.
Classification of assets and liabilities within the hierarchy considers the markets in which the assets and liabilities are traded and the reliability and transparency of the assumptions used to determine fair value. The hierarchy requires the use of observable market data when available. The levels of the hierarchy are defined as follows:
•Level 1 – Inputs to the valuation methodology are quoted prices (unadjusted) for identical assets or liabilities traded in active markets.
•Level 2 – Inputs to the valuation methodology include quoted prices for similar assets or liabilities in active markets, quoted prices for identical or similar assets or liabilities in markets that are not active, inputs other than quoted prices that are observable for the asset or liability and market-corroborated inputs.
•Level 3 – Inputs to the valuation methodology are unobservable for the asset or liability and are significant to the fair value measurement.
In accordance with ASC 820, the Company determines fair value based on the price that would be received to sell an asset or paid to transfer a liability in an orderly transaction between market participants at the measurement date. In determining fair value, the Company uses various methods, including the market, income and cost approaches. The Company uses valuation techniques that maximize the use of observable inputs and minimize the use of unobservable inputs. The following section describes the valuation methodologies used by the Company to measure assets and liabilities at fair value, including an indication of the level within the fair value hierarchy in which each asset or liability is generally classified.
Available-for-sale investments and equity securities. Available-for-sale investments and equity securities are recorded at fair value on a recurring basis. Available-for-sale investments include fixed maturity securities and short-term investments. Fair value is determined by the Company after considering various sources of information, including information provided by a third-party pricing service. The pricing service provides prices for substantially all of the Company's fixed maturity securities and equity securities. In determining fair value, the Company generally does not adjust the prices obtained from the pricing service. The Company obtains an understanding of the pricing service's valuation methodologies and related inputs, which include, but are not limited to, reported trades, benchmark yields, issuer spreads, bids, offers, duration, credit ratings, estimated cash flows and prepayment speeds. The Company validates prices provided by the pricing service by reviewing prices from other pricing sources and analyzing pricing data in certain instances.
The Company has evaluated the various types of securities in its investment portfolio to determine an appropriate fair value hierarchy level based upon trading activity and the observability of market inputs. Level 1 investments include those traded on an active exchange, such as the New York Stock Exchange. Level 2 investments include U.S. Treasury securities, U.S. government-sponsored enterprises, municipal bonds, foreign government bonds, commercial mortgage-backed securities, residential mortgage-backed securities, asset-backed securities and corporate debt securities. Level 3 investments include the Company's investments in insurance-linked securities funds that are in run-off, which are not traded on an active exchange and are valued using unobservable inputs.
Fair value for available-for-sale investments and equity securities is measured based upon quoted prices in active markets, if available. Due to variations in trading volumes and the lack of quoted market prices, fixed maturity securities are classified as Level 2 investments. The fair value of fixed maturity securities is normally derived through recent reported trades for identical or similar securities, making adjustments through the reporting date based upon available market observable data previously described. If there are no recent reported trades, the fair value of fixed maturity securities may be derived through the use of matrix pricing or model processes, where future cash flow expectations are developed based upon collateral performance and discounted at an estimated market rate. Significant inputs used to determine the fair value of obligations of states, municipalities and political subdivisions, corporate bonds and obligations of foreign governments include reported trades, benchmark yields, issuer spreads, bids, offers, credit information and estimated cash flows. Significant inputs used to determine the fair value of commercial mortgage-backed securities, residential mortgage-backed securities and asset-backed securities include the type of underlying assets, benchmark yields, prepayment speeds, collateral information, tranche type and volatility, estimated cash flows, credit information, default rates, recovery rates, issuer spreads and the year of issue.
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Senior long-term debt and other debt. Senior long-term debt and other debt is carried at amortized cost with the estimated fair value disclosed on the consolidated balance sheets. Senior long-term debt and other debt is classified as Level 2 within the fair value hierarchy due to variations in trading volumes and the lack of quoted market prices. Fair value is generally derived through recent reported trades, making adjustments through the reporting date, if necessary, based upon available market observable data including U.S. Treasury securities and implied credit spreads. Significant inputs used to determine the fair value of senior long-term debt and other debt include reported trades, benchmark yields, issuer spreads, bids and offers.
The following tables present the balances of assets measured at fair value on a recurring basis by level within the fair value hierarchy.

| June 30, 2023
(dollars in thousands) | Level 1 |  | Level 2 |  | Level 3 |  | Total
Assets: |  |  |  |  |  |  |
Investments: |  |  |  |  |  |  |
Fixed maturity securities, available-for-sale: |  |  |  |  |  |  |
U.S. Treasury securities | $ | — |  |  | $ | 3,128,852 |  |  | $ | — |  |  | $ | 3,128,852 |
U.S. government-sponsored enterprises | — |  |  | 938,735 |  |  | — |  |  | 938,735 |
Obligations of states, municipalities and political subdivisions | — |  |  | 3,876,335 |  |  | — |  |  | 3,876,335 |
Foreign governments | — |  |  | 1,543,626 |  |  | — |  |  | 1,543,626 |
Commercial mortgage-backed securities | — |  |  | 2,073,556 |  |  | — |  |  | 2,073,556 |
Residential mortgage-backed securities | — |  |  | 479,922 |  |  | — |  |  | 479,922 |
Asset-backed securities | — |  |  | 1,204 |  |  | — |  |  | 1,204 |
Corporate bonds | — |  |  | 703,462 |  |  | — |  |  | 703,462 |
Total fixed maturity securities, available-for-sale | — |  |  | 12,745,692 |  |  | — |  |  | 12,745,692 |
Equity securities: |  |  |  |  |  |  |
Insurance, banks and other financial institutions | 3,223,393 |  |  | — |  |  | 936 |  |  | 3,224,329 |
Industrial, consumer and all other | 5,464,531 |  |  | — |  |  | — |  |  | 5,464,531 |
Total equity securities | 8,687,924 |  |  | — |  |  | 936 |  |  | 8,688,860 |
Short-term investments, available-for-sale | 1,872,751 |  |  | 166,310 |  |  | — |  |  | 2,039,061 |
Total investments | $ | 10,560,675 |  |  | $ | 12,912,002 |  |  | $ | 936 |  |  | $ | 23,473,613 |

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| December 31, 2022
(dollars in thousands) | Level 1 |  | Level 2 |  | Level 3 |  | Total
Assets: |  |  |  |  |  |  |
Investments: |  |  |  |  |  |  |
Fixed maturity securities, available-for-sale: |  |  |  |  |  |  |
U.S. Treasury securities | $ | — |  |  | $ | 2,913,959 |  |  | $ | — |  |  | $ | 2,913,959 |
U.S. government-sponsored enterprises | — |  |  | 765,538 |  |  | — |  |  | 765,538 |
Obligations of states, municipalities and political subdivisions | — |  |  | 3,733,183 |  |  | — |  |  | 3,733,183 |
Foreign governments | — |  |  | 1,306,778 |  |  | — |  |  | 1,306,778 |
Commercial mortgage-backed securities | — |  |  | 1,940,448 |  |  | — |  |  | 1,940,448 |
Residential mortgage-backed securities | — |  |  | 526,793 |  |  | — |  |  | 526,793 |
Asset-backed securities | — |  |  | 1,640 |  |  | — |  |  | 1,640 |
Corporate bonds | — |  |  | 668,496 |  |  | — |  |  | 668,496 |
Total fixed maturity securities, available-for-sale | — |  |  | 11,856,835 |  |  | — |  |  | 11,856,835 |
Equity securities: |  |  |  |  |  |  |
Insurance, banks and other financial institutions | 2,952,689 |  |  | — |  |  | 899 |  |  | 2,953,588 |
Industrial, consumer and all other | 4,718,324 |  |  | — |  |  | — |  |  | 4,718,324 |
Total equity securities | 7,671,013 |  |  | — |  |  | 899 |  |  | 7,671,912 |
Short-term investments, available-for-sale | 2,510,164 |  |  | 159,098 |  |  | — |  |  | 2,669,262 |
Total investments | $ | 10,181,177 |  |  | $ | 12,015,933 |  |  | $ | 899 |  |  | $ | 22,198,009 |

The following table summarizes changes in Level 3 investments measured at fair value on a recurring basis.

| Quarter Ended June 30, |  | Six Months Ended June 30,
(dollars in thousands) | 2023 |  | 2022 |  | 2023 |  | 2022
Equity securities, beginning of period | $ | 853 |  |  | $ | 8,468 |  |  | $ | 899 |  |  | $ | 56,472 |
Purchases | — |  |  | — |  |  | — |  |  | — |
Sales | — |  |  | (4,027) |  |  | — |  |  | (52,807) |
Net investment gains (losses) | 83 |  |  | (61) |  |  | 37 |  |  | 715 |
Equity securities, end of period | $ | 936 |  |  | $ | 4,380 |  |  | $ | 936 |  |  | $ | 4,380 |

Previously, Level 3 investments included the Company's investment in an insurance-linked securities fund managed by Markel CATCo Investment Management Ltd. (MCIM). During the first quarter of 2022, the Company's remaining investment was redeemed ($41.3 million) in conjunction with a buy-out transaction that provided for an accelerated return of all remaining capital to investors. See note 11 for further details about the Company's Markel CATCo operations and the buy-out transaction.
The Company did not have any assets or liabilities measured at fair value on a non-recurring basis during the six months ended June 30, 2023 and 2022.
5. Equity Method Investments
The Company holds certain investments that are accounted for under the equity method of accounting. The Company's equity method investments, which are included in other assets on the consolidated balance sheets, totaled $489.7 million and $494.0 million as of June 30, 2023 and December 31, 2022, respectively. The Company's proportionate share of earnings in its equity method investments were losses of $7.1 million and $8.7 million for the quarter and six months ended June 30, 2023, respectively, and losses of $4.2 million and $27.4 million for the quarter and six months ended June 30, 2022, respectively.
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The Company's most significant equity method investment is an investment in Hagerty, Inc. (Hagerty), which is accounted for on a quarter lag. Hagerty is an automotive enthusiast brand offering integrated membership products and programs as well as a specialty insurance provider focused on the global automobile enthusiast market. The Company's ownership interest in Hagerty's common stock was 23% as of June 30, 2023 and December 31, 2022. The Company's investment is comprised of Class A common shares, which are listed for trading on the New York Stock Exchange, as well as Class V common shares, associated with the Company's original investment, that have special voting rights and can be converted on a one-for-one basis into Class A common shares. The Company accounts for its investment under the equity method as it is deemed to have the ability to exercise significant influence over Hagerty's operating and financial policies through a combination of its voting interest, its right to designate a board member and business it conducts with Hagerty. As of June 30, 2023 and December 31, 2022, the carrying value of the Company's investment in Hagerty was $232.1 million and $245.1 million, respectively.
As of June 30, 2023 and December 31, 2022, the estimated value of the Company's investment, based on the closing stock price of Hagerty's Class A common shares, was $730.1 million and $656.0 million, respectively. See note 12 for further details regarding related party transactions with Hagerty.
6. Products, Services, and Other Revenues
The following tables present revenues from contracts with customers by type, all of which are included in products revenues and services and other revenues in the consolidated statements of income (loss) and comprehensive income (loss), along with a reconciliation to total products revenues and services and other revenues.

| Quarter Ended June 30,
| 2023 |  | 2022
(dollars in thousands) | Markel Ventures |  | Other |  | Total |  | Markel Ventures |  | Other |  | Total
Products | $ | 770,171 |  |  | $ | — |  |  | $ | 770,171 |  |  | $ | 764,543 |  |  | $ | — |  |  | $ | 764,543 |
Services | 569,013 |  |  | 1,784 |  |  | 570,797 |  |  | 561,596 |  |  | 8,450 |  |  | 570,046 |
Investment management | — |  |  | 21,445 |  |  | 21,445 |  |  | — |  |  | 20,328 |  |  | 20,328 |
Total revenues from contracts with customers | 1,339,184 |  |  | 23,229 |  |  | 1,362,413 |  |  | 1,326,139 |  |  | 28,778 |  |  | 1,354,917 |
Program services and other fronting | — |  |  | 37,563 |  |  | 37,563 |  |  | — |  |  | 29,731 |  |  | 29,731 |
Disposition gain | — |  |  | 16,923 |  |  | 16,923 |  |  | — |  |  | — |  |  | — |
Equity method investments loss | (387) |  |  | (6,762) |  |  | (7,149) |  |  | (975) |  |  | (3,247) |  |  | (4,222) |
Other | 47,016 |  |  | 407 |  |  | 47,423 |  |  | 36,134 |  |  | 391 |  |  | 36,525 |
Total | $ | 1,385,813 |  |  | $ | 71,360 |  |  | $ | 1,457,173 |  |  | $ | 1,361,298 |  |  | $ | 55,653 |  |  | $ | 1,416,951 |

| Six Months Ended June 30,
| 2023 |  | 2022
(dollars in thousands) | Markel Ventures |  | Other |  | Total |  | Markel Ventures |  | Other |  | Total
Products | $ | 1,336,066 |  |  | $ | — |  |  | $ | 1,336,066 |  |  | $ | 1,233,999 |  |  | $ | — |  |  | $ | 1,233,999 |
Services | 1,054,675 |  |  | 4,638 |  |  | 1,059,313 |  |  | 999,229 |  |  | 30,018 |  |  | 1,029,247 |
Investment management | — |  |  | 31,904 |  |  | 31,904 |  |  | — |  |  | 39,556 |  |  | 39,556 |
Total revenues from contracts with customers | 2,390,741 |  |  | 36,542 |  |  | 2,427,283 |  |  | 2,233,228 |  |  | 69,574 |  |  | 2,302,802 |
Program services and other fronting | — |  |  | 66,453 |  |  | 66,453 |  |  | — |  |  | 63,063 |  |  | 63,063 |
Disposition gain | — |  |  | 16,923 |  |  | 16,923 |  |  | — |  |  | 107,293 |  |  | 107,293 |
Equity method investments income (loss) | 1,108 |  |  | (9,775) |  |  | (8,667) |  |  | 2,083 |  |  | (29,493) |  |  | (27,410) |
Other | 97,903 |  |  | 1,065 |  |  | 98,968 |  |  | 76,372 |  |  | 7,392 |  |  | 83,764 |
Total | $ | 2,489,752 |  |  | $ | 111,208 |  |  | $ | 2,600,960 |  |  | $ | 2,311,683 |  |  | $ | 217,829 |  |  | $ | 2,529,512 |

In February 2022, the Company sold the majority of its controlling interest in its Velocity managing general agent companies, which resulted in a gain of $107.3 million. In June 2023, the Company sold one of its licensed insurance subsidiaries to Velocity, which resulted in a gain of $16.9 million. Both gains were included in services and other revenues.
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Receivables from contracts with customers were $663.7 million and $624.1 million as of June 30, 2023 and December 31, 2022, respectively.
7. Unpaid Losses and Loss Adjustment Expenses
The following table presents a reconciliation of consolidated beginning and ending reserves for losses and loss adjustment expenses.

| Six Months Ended June 30,
(dollars in thousands) | 2023 |  | 2022
Gross reserves for losses and loss adjustment expenses, beginning of year | $ | 20,947,898 |  |  | $ | 18,178,894 |
Reinsurance recoverables on unpaid losses, beginning of year | 7,994,884 |  |  | 6,876,317 |
Net reserves for losses and loss adjustment expenses, beginning of year | 12,953,014 |  |  | 11,302,577 |
Effect of foreign currency rate changes on beginning of year balance | 46,000 |  |  | (149,383) |
Adjusted net reserves for losses and loss adjustment expenses, beginning of year | 12,999,014 |  |  | 11,153,194 |
Incurred losses and loss adjustment expenses: |  |  |
Current accident year | 2,500,098 |  |  | 2,153,910 |
Prior accident years | (139,208) |  |  | (122,728) |
Total incurred losses and loss adjustment expenses | 2,360,890 |  |  | 2,031,182 |
Payments: |  |  |
Current accident year | 164,713 |  |  | 167,262 |
Prior accident years | 1,461,051 |  |  | 1,291,318 |
Total payments | 1,625,764 |  |  | 1,458,580 |
Effect of foreign currency rate changes on current year activity | (2,949) |  |  | 221 |
Change in net reserves for losses and loss adjustment expenses of Markel CATCo Re (see note 11) | (131,874) |  |  | 465,196 |
Reinsurance recoverable for retroactive reinsurance transaction | (125,067) |  |  | — |
Net reserves for losses and loss adjustment expenses, end of period | 13,474,250 |  |  | 12,191,213 |
Reinsurance recoverables on unpaid losses | 7,900,563 |  |  | 6,871,547 |
Gross reserves for losses and loss adjustment expenses, end of period | $ | 21,374,813 |  |  | $ | 19,062,760 |

For the six months ended June 30, 2023, prior accident years losses and loss adjustment expenses included $139.2 million of favorable development on prior years loss reserves, which included $169.6 million of favorable development on the Company's professional liability, property, marine and energy and workers' compensation product lines within its Insurance segment and $20.9 million of favorable development on the Company's professional liability and property product lines within its Reinsurance segment. Favorable development on prior years loss reserves for the six months ended June 30, 2023 was partially offset by $53.0 million of adverse development on the Company's general liability product lines within its Insurance segment.
For the six months ended June 30, 2022, prior accident years losses and loss adjustment expenses included $122.7 million of favorable development on prior years loss reserves, which included $123.3 million of favorable development on the Company's property, marine and energy, workers' compensation and programs product lines within the Insurance segment.
In March 2023, the Company completed a retroactive reinsurance transaction to cede its portfolio of policies comprised of liabilities for its run-off book of United Kingdom motor casualty business in exchange for payments totaling $125.1 million, which approximated the carrying value of the Company's reserves for losses and loss adjustment expenses on the ceded policies.
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8. Reinsurance
The following tables summarize the effect of reinsurance and retrocessional reinsurance on premiums written and earned.

| Quarter Ended June 30,
| 2023 |  | 2022
(dollars in thousands) | Direct |  | Assumed |  | Ceded |  | Net Premiums |  | Direct |  | Assumed |  | Ceded |  | Net Premiums
Underwriting: |  |  |  |  |  |  |  |  |  |  |  |  |  |  |
Written | $ | 2,285,739 |  |  | $ | 448,837 |  |  | $ | (526,562) |  |  | $ | 2,208,014 |  |  | $ | 2,108,859 |  |  | $ | 420,026 |  |  | $ | (427,959) |  |  | $ | 2,100,926 |
Earned | 2,025,324 |  |  | 424,404 |  |  | (418,264) |  |  | 2,031,464 |  |  | 1,772,695 |  |  | 382,876 |  |  | (321,438) |  |  | 1,834,133 |
Program services and other fronting: |  |  |  |  |  |  |  |  |  |  |  |  |  |  |
Written | 824,171 |  |  | 229,438 |  |  | (1,053,930) |  |  | (321) |  |  | 664,590 |  |  | 86,574 |  |  | (752,295) |  |  | (1,131) |
Earned | 649,562 |  |  | 159,075 |  |  | (808,958) |  |  | (321) |  |  | 607,099 |  |  | 65,116 |  |  | (673,244) |  |  | (1,029) |
Consolidated: |  |  |  |  |  |  |  |  |  |  |  |  |  |  |
Written | 3,109,910 |  |  | 678,275 |  |  | (1,580,492) |  |  | 2,207,693 |  |  | 2,773,449 |  |  | 506,600 |  |  | (1,180,254) |  |  | 2,099,795 |
Earned | $ | 2,674,886 |  |  | $ | 583,479 |  |  | $ | (1,227,222) |  |  | $ | 2,031,143 |  |  | $ | 2,379,794 |  |  | $ | 447,992 |  |  | $ | (994,682) |  |  | $ | 1,833,104 |

| Six Months Ended June 30,
| 2023 |  | 2022
(dollars in thousands) | Direct |  | Assumed |  | Ceded |  | Net Premiums |  | Direct |  | Assumed |  | Ceded |  | Net Premiums
Underwriting: |  |  |  |  |  |  |  |  |  |  |  |  |  |  |
Written | $ | 4,255,102 |  |  | $ | 1,137,732 |  |  | $ | (966,591) |  |  | $ | 4,426,243 |  |  | $ | 3,932,114 |  |  | $ | 1,116,386 |  |  | $ | (781,341) |  |  | $ | 4,267,159 |
Earned | 3,997,200 |  |  | 823,123 |  |  | (820,704) |  |  | 3,999,619 |  |  | 3,470,665 |  |  | 785,943 |  |  | (661,367) |  |  | 3,595,241 |
Program services and other fronting: |  |  |  |  |  |  |  |  |  |  |  |  |  |  |
Written | 1,397,382 |  |  | 433,981 |  |  | (1,832,135) |  |  | (772) |  |  | 1,361,564 |  |  | 268,272 |  |  | (1,632,466) |  |  | (2,630) |
Earned | 1,290,675 |  |  | 233,792 |  |  | (1,525,239) |  |  | (772) |  |  | 1,306,704 |  |  | 113,976 |  |  | (1,423,047) |  |  | (2,367) |
Consolidated: |  |  |  |  |  |  |  |  |  |  |  |  |  |  |
Written | 5,652,484 |  |  | 1,571,713 |  |  | (2,798,726) |  |  | 4,425,471 |  |  | 5,293,678 |  |  | 1,384,658 |  |  | (2,413,807) |  |  | 4,264,529 |
Earned | $ | 5,287,875 |  |  | $ | 1,056,915 |  |  | $ | (2,345,943) |  |  | $ | 3,998,847 |  |  | $ | 4,777,369 |  |  | $ | 899,919 |  |  | $ | (2,084,414) |  |  | $ | 3,592,874 |

Substantially all of the premiums written and earned in the Company's program services and other fronting operations for the six months ended June 30, 2023 and 2022 were ceded. The percentage of consolidated ceded earned premiums to gross earned premiums was 38% and 37% and for the quarter and six months ended June 30, 2023, respectively, and 35% and 37% for the quarter and six months ended June 30, 2022, respectively. The percentage of consolidated assumed earned premiums to net earned premiums was 29% and 26% for the quarter and six months ended June 30, 2023 and 2022, respectively, 24% and 25% for the quarter and six months ended June 30, 2022, respectively.
Substantially all of the incurred losses and loss adjustment expenses in the Company's program services and other fronting operations were ceded. These gross losses totaled $594.7 million and $1.1 billion for the quarter and six months ended June 30, 2023, respectively, and $574.8 million and $990.5 million for the quarter and six months ended June 30, 2022, respectively.
The following table summarizes the effect of reinsurance and retrocessional reinsurance on losses and loss adjustment expenses in the Company's underwriting operations.

| Quarter Ended June 30, |  | Six Months Ended June 30,
(dollars in thousands) | 2023 |  | 2022 |  | 2023 |  | 2022
Gross losses and loss adjustment expenses | $ | 1,476,189 |  |  | $ | 1,186,691 |  |  | $ | 2,868,537 |  |  | $ | 2,337,040 |
Ceded losses and loss adjustment expenses | (288,676) |  |  | (127,895) |  |  | (507,931) |  |  | (305,889) |
Net losses and loss adjustment expenses | $ | 1,187,513 |  |  | $ | 1,058,796 |  |  | $ | 2,360,606 |  |  | $ | 2,031,151 |

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9. Life and Annuity Benefits
The Company's run-off block of life and annuity reinsurance contracts consists primarily of Euro and U.S. Dollar denominated life-contingent payout annuities and traditional and universal life contracts. The following table presents the components of the Company's liabilities for life and annuity benefits.

(dollars in thousands) | June 30, 2023 |  | December 31, 2022
Liability for future policyholder benefits | $ | 549,601 |  |  | $ | 554,366 |
Deferred profit liability | 47,122 |  |  | 48,569 |
Other | 46,849 |  |  | 47,786 |
Total | $ | 643,572 |  |  | $ | 650,721 |

The primary component of the Company's liabilities for life and annuity benefits is the liability for future policyholder benefits. Life and annuity benefit reserves are calculated for aggregated cohorts of contracts, which are determined based on the attributes of the underlying contracts, and are discounted using standard actuarial techniques and cash flow models. Since the development of the life and annuity reinsurance reserves is based upon cash flow projection models, the Company makes estimates and assumptions based on cedent experience and industry mortality tables. The cash flow assumptions used to determine the Company's life and annuity benefit reserves are updated at least annually. The discount rate assumptions are updated at each reporting date. The following table presents a rollforward of the present value of the liability for future policyholder benefits.

| Six Months Ended June 30,
(dollars in thousands) | 2023 |  | 2022
Liability for future policyholder benefits, beginning of year | $ | 554,366 |  |  | $ | 821,632 |
Liability for future policyholder benefits at original discount rate, beginning of year | 667,761 |  |  | 745,313 |
Effect of changes in cash flow assumptions | — |  |  | — |
Effect of actual variances from expected experience | — |  |  | — |
Adjusted liability for future policyholder benefits, beginning of year | 667,761 |  |  | 745,313 |
Interest accretion | 7,594 |  |  | 8,178 |
Benefit payments | (26,661) |  |  | (27,801) |
Effect of foreign currency rate changes | 6,926 |  |  | (48,509) |
Liability for future policyholder benefits at original discount rate, end of period | 655,620 |  |  | 677,181 |
Cumulative effect of changes in discount rate assumptions | (106,019) |  |  | (80,505) |
Liability for future policyholder benefits, end of period (1) | $ | 549,601 |  |  | $ | 596,676 |

(1) The undiscounted liability for future policyholder benefits was $843.3 million and $874.2 million as of June 30, 2023 and 2022, respectively.
The following table summarizes additional details for the Company's liability for future policyholder benefits.

| June 30, 2023 |  | December 31, 2022
Weighted-average interest rate: |  |  |
Interest accretion rate | 2.3 | % |  | 2.3 | %
Current discount rate | 4.2 | % |  | 4.3 | %
Weighted-average liability duration | 8.7 years |  | 8.6 years

10. Senior Long-Term Debt and Other Debt
In March 2023, the Company retired its 3.625% unsecured senior notes due March 30, 2023 ($250.0 million aggregate principal outstanding at December 31, 2022).
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In June 2023, the Company entered into an amended and restated credit agreement for its corporate revolving credit facility, which provides up to $300 million of capacity for future acquisitions, investments and stock repurchases, and for other working capital and general corporate purposes. At the Company's discretion, up to $200 million of the total capacity may be used for letters of credit. The Company may increase the capacity of the facility by up to $200 million subject to obtaining commitments for the increase and certain other terms and conditions. The Company pays interest on balances outstanding under the facility and fees for letters of credit issued under the facility. The Company also pays a commitment fee on the unused portion of the facility based on the Company's leverage ratio as calculated under the credit agreement. The credit agreement includes financial covenants that require that the Company not exceed a maximum debt to capitalization (leverage) ratio and maintain a minimum amount of consolidated net worth, as well as other customary covenants and events of default. Markel Group guaranteed the obligations under the facility of certain subsidiaries that are also parties to the credit agreement. This facility expires in June 2028. The credit agreement for this revolving credit facility amended and restated the credit agreement for the Company's previous $300 million revolving credit facility. At June 30, 2023 and December 31, 2022, the Company had no borrowings outstanding under either revolving credit facility. As of June 30, 2023, the Company was in compliance with all covenants contained in its corporate revolving credit facility.
Various of the Company's Markel Ventures subsidiaries maintain revolving credit facilities or lines of credit, which provide up to $715 million of aggregate capacity for working capital and other general operational purposes. A portion of the capacity on certain of these credit facilities may be used as security for letters of credit and other obligations. At June 30, 2023 and December 31, 2022, the Company had $209.0 million and $238.1 million, respectively, of borrowings outstanding under these credit facilities. As of June 30, 2023, all of the Company's subsidiaries were in compliance with all covenants contained in their respective credit facilities.
11. Variable Interest Entities
MCIM, a wholly-owned consolidated subsidiary of the Company, is an insurance-linked securities investment fund manager and reinsurance manager headquartered in Bermuda. Results attributable to MCIM are not included in a reportable segment.
MCIM serves as the insurance manager for Markel CATCo Re Ltd. (Markel CATCo Re), a Bermuda Class 3 reinsurance company, and as the investment manager for Markel CATCo Reinsurance Fund Ltd., a Bermuda exempted mutual fund company comprised of multiple segregated accounts (Markel CATCo Funds). Voting shares in Markel CATCo Reinsurance Fund Ltd. and Markel CATCo Re are held by MCIM, which has the power to direct the activities that most significantly impact the economic performance of these entities. The Markel CATCo Funds issued multiple classes of nonvoting, redeemable preference shares to investors, and the Markel CATCo Funds are primarily invested in nonvoting preference shares of Markel CATCo Re. The underwriting results of Markel CATCo Re are attributed to investors through its nonvoting preference shares. Both Markel CATCo Re and the Markel CATCo Funds were placed into run-off in July 2019.
In March 2022, the Company completed a buy-out transaction with Markel CATCo Re and the Markel CATCo Funds that provided for an accelerated return of all remaining capital to investors in the Markel CATCo Funds. Under the terms of the transaction, the Company provided cash funding of $45.1 million to purchase substantially all of the Markel CATCo Funds' interests in Markel CATCo Re and substantially all of the preference shares held by investors in the Markel CATCo Funds were redeemed, including preference shares previously held by the Company. See note 4 for details regarding the Company's investment in the Markel CATCo Funds. In order to complete the transaction, the Company also made $101.9 million in additional payments, net of insurance proceeds, to or for the benefit of investors, which were recognized as an expense to the Company and included in services and other expenses for the first quarter of 2022.
In June 2022, the Company received a return of $24.9 million of the capital it provided in March 2022 and the related preference shares were redeemed. As of June 30, 2023 and December 31, 2022, the Company's investment in the remaining preference shares of Markel CATCo Re totaled $20.1 million, which comprised 25% and 23% of the equity of Markel CATCo Re, respectively. Through that investment, the Company has exposure to adverse loss development on reinsurance contracts previously written by Markel CATCo Re for loss events that occurred from 2014 to 2020. If loss reserves held by Markel CATCo Re are sufficient to settle claims on the remaining open contracts, the Company will receive a full return of the remaining $20.1 million in capital provided in March 2022. Favorable development on loss reserves held by Markel CATCo Re, less operating expenses, will be distributed to the Markel CATCo Funds, and ultimately to investors in the Markel CATCo Funds.
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Markel CATCo Re is considered a VIE, as the equity at risk does not have the right to receive residual returns that exceed the capital provided by the Company in the buy-out transaction. As a result of the preference shares acquired by the Company in the buy-out transaction, and the voting shares held by its consolidated subsidiary, MCIM, the Company consolidates Markel CATCo Re as its primary beneficiary. Results attributed to the run-off of Markel CATCo Re are reported with the Company's other ILS operations, within services and other revenues and expenses, and are not included in a reportable segment. Favorable loss reserve development on the run-off of reinsurance contracts written by Markel CATCo Re was $8.7 million and $53.5 million for the quarter and six months ended June 30, 2023, respectively, and $28.2 million for both the quarter and six months ended June 30, 2022. For all periods, the favorable development was included in services and other expenses and attributable to noncontrolling interests. During the six months ended June 30, 2023 and 2022, $62.6 million and $22.3 million, respectively, of preference shares of Markel CATCo Re held by noncontrolling interests were redeemed.
The Company's consolidated balance sheets include the following amounts attributable to Markel CATCo Re.

(dollars in thousands) | June 30, 2023 |  | December 31, 2022
Assets |  |  |
Cash and cash equivalents | $ | 69,744 |  |  | $ | 104,443 |
Restricted cash and cash equivalents | 198,938 |  |  | 317,577 |
Other assets and receivables due from cedents | 27,846 |  |  | 41,357 |
Total Assets | $ | 296,528 |  |  | $ | 463,377 |
Liabilities and Equity |  |  |
Unpaid losses and loss adjustment expenses | $ | 216,047 |  |  | $ | 347,921 |
Other liabilities | 923 |  |  | 26,717 |
Total Liabilities | 216,970 |  |  | 374,638 |
Shareholders' equity | 21,139 |  |  | 21,139 |
Noncontrolling interests | 58,419 |  |  | 67,600 |
Total Equity | 79,558 |  |  | 88,739 |
Total Liabilities and Equity | $ | 296,528 |  |  | $ | 463,377 |

In connection with the buy-out transaction, the Company also entered into a tail risk cover with Markel CATCo Re. Through this contract, the Company has $142.7 million of uncollateralized exposure to adverse development on loss reserves held by Markel CATCo Re for loss exposures in excess of limits that the Company believes are unlikely to be exceeded.
12. Related Party Transactions
The Company engages in certain related party transactions in the normal course of business at arm's length.
Insurance-Linked Securities
Within the Company's insurance-linked securities operations, the Company provides investment and insurance management services through Nephila Holdings Ltd. (together with its subsidiaries, Nephila). Nephila serves as the investment manager to several Bermuda based private funds (the Nephila Funds). To provide access for the Nephila Funds to a variety of insurance-linked securities in the property catastrophe, climate and specialty markets, Nephila also acts as an insurance manager to certain Bermuda Class 3 and 3A reinsurance companies, Lloyd's Syndicate 2357 and Lloyd's Syndicate 2358 (collectively, the Nephila Reinsurers). Nephila receives management fees for investment and insurance management services provided through its insurance-linked securities operations primarily based on the net asset value of the accounts managed, and, for certain funds, incentive fees based on their annual performance. Prior to the disposition of Velocity in February 2022, Nephila also provided managing general agent services to the Nephila Reinsurers in exchange for commissions. For the quarter and six months ended June 30, 2023, total revenues attributed to unconsolidated entities managed by Nephila were $20.8 million and $30.6 million, respectively. For the quarter and six months ended June 30, 2022, total revenues attributed to unconsolidated entities managed by Nephila were $17.5 million and $39.9 million, respectively.
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Through the Company's program services and other fronting operations, as well as its underwriting operations, the Company has programs with Nephila through which the Company writes insurance policies that are either partially or fully ceded to Nephila Reinsurers. Through these programs, Nephila utilizes certain of the Company's licensed insurance companies to write U.S. catastrophe-exposed property risk that is then ceded to Nephila Reinsurers. A portion of this business is placed by Velocity, which the Company retained a minority interest in following its disposition. Additionally, through the Company's insurance underwriting operations, the Company has a quota share agreement with Nephila through which it cedes a portion of its property business to Nephila Reinsurers. The following table summarizes the premiums ceded to Nephila Reinsurers.

| Quarter Ended June 30, |  | Six Months Ended June 30,
(dollars in thousands) | 2023 |  | 2022 |  | 2023 |  | 2022
Program services and other fronting: |  |  |  |  |  |  |
Gross and ceded written premiums attributable to Nephila programs | $ | 297,393 |  |  | $ | 175,185 |  |  | $ | 534,288 |  |  | $ | 490,772 |
Underwriting: |  |  |  |  |  |  |
Premiums ceded to Nephila Reinsurers | $ | 16,384 |  |  | $ | 13,512 |  |  | $ | 29,847 |  |  | $ | 29,619 |

As of June 30, 2023 and December 31, 2022, reinsurance recoverables on the consolidated balance sheets included $949.3 million and $1.4 billion, respectively, due from Nephila Reinsurers. Under its programs with Nephila Reinsurers, the Company bears underwriting risk for annual aggregate agreement year losses in excess of a limit the Company believes is unlikely to be exceeded. To the extent losses under these programs exceed the prescribed limits, the Company is obligated to pay such losses to the cedents without recourse to the Nephila Reinsurers. While the Company believes losses under these programs are unlikely, those losses, if incurred, could be material to the Company's consolidated results of operations and financial condition.
The Company has also entered into other assumed and ceded reinsurance transactions with the Nephila Reinsurers in the normal course of business, which are not material to the Company's consolidated financial statements.
In June 2023, the Company sold one of the licensed insurance subsidiaries within its program services operations to Velocity, which resulted in a gain of $16.9 million during the second quarter of 2023.
Hagerty
The Company holds a minority ownership interest in Hagerty, which operates primarily as a managing general agent and also includes Hagerty Reinsurance Limited (Hagerty Re), a Bermuda Class 3 reinsurance company. Through the Company's underwriting operations, the Company underwrites insurance for Hagerty, a portion of which is ceded to Hagerty Re. The amounts attributed to these arrangements are summarized in the following table.

| Quarter Ended June 30, |  | Six Months Ended June 30,
(dollars in thousands) | 2023 |  | 2022 |  | 2023 |  | 2022
Gross written premiums attributable to Hagerty | $ | 236,225 |  |  | $ | 204,392 |  |  | $ | 401,196 |  |  | $ | 343,406 |
Premiums ceded to Hagerty Re | $ | 181,841 |  |  | $ | 135,241 |  |  | $ | 306,469 |  |  | $ | 227,299 |

As of June 30, 2023 and December 31, 2022, reinsurance recoverables on the consolidated balance sheets included $178.2 million and $159.7 million, respectively, due from Hagerty Re.
13. Shareholders' Equity
a) The Company has 50,000,000 shares of no par value common stock authorized. The following table presents a rollforward of changes in common shares issued and outstanding.

| Quarter Ended June 30, |  | Six Months Ended June 30, |  |  |
(in thousands) | 2023 |  | 2022 |  | 2023 |  | 2022 |  |  |
Issued and outstanding common shares, beginning of period | 13,362 |  |  | 13,570 |  |  | 13,423 |  |  | 13,632 |  |  |  |
Issuance of common shares | 1 |  |  | 1 |  |  | 3 |  |  | 2 |  |  |  |
Repurchase of common shares | (78) |  |  | (33) |  |  | (141) |  |  | (96) |  |  |  |
Issued and outstanding common shares, end of period | 13,285 |  |  | 13,538 |  |  | 13,285 |  |  | 13,538 |  |  |  |

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b) The Company also has 10,000,000 shares of no par value preferred stock authorized, of which 600,000 shares were issued and outstanding at June 30, 2023 and December 31, 2022. The Company declared and paid dividends on preferred shares of $18.0 million, or $30 per share, in both the quarter ended June 30, 2023 and 2022.
c) Net income (loss) per common share was determined by dividing adjusted net income (loss) to common shareholders by the applicable weighted average common shares outstanding. Basic common shares outstanding include restricted stock units that are no longer subject to any contingencies for issuance, but for which corresponding shares have not been issued. Diluted net income (loss) per common share is computed by dividing adjusted net income (loss) to common shareholders by the weighted average number of common shares and dilutive potential common shares outstanding during the period. The following table presents net income (loss) per common share and diluted net income (loss) per common share.

| Quarter Ended June 30, |  | Six Months Ended June 30,
(in thousands, except per share amounts) | 2023 |  | 2022 |  | 2023 |  | 2022
Net income (loss) to common shareholders | $ | 677,511 |  |  | $ | (933,796) |  |  | $ | 1,166,163 |  |  | $ | (985,537) |
Adjustment of redeemable noncontrolling interests | (5,758) |  |  | (7,498) |  |  | 7,715 |  |  | (44,438) |
Adjusted net income (loss) to common shareholders | $ | 671,753 |  |  | $ | (941,294) |  |  | $ | 1,173,878 |  |  | $ | (1,029,975) |
Basic common shares outstanding | 13,382 |  |  | 13,612 |  |  | 13,416 |  |  | 13,632 |
Dilutive potential common shares from restricted stock units and restricted stock (1) | 29 |  |  | — |  |  | 25 |  |  | — |
Diluted common shares outstanding | 13,411 |  |  | 13,612 |  |  | 13,441 |  |  | 13,632 |
Basic net income (loss) per common share | $ | 50.20 |  |  | $ | (69.15) |  |  | $ | 87.50 |  |  | $ | (75.56) |
Diluted net income (loss) per common share (1) | $ | 50.09 |  |  | $ | (69.15) |  |  | $ | 87.34 |  |  | $ | (75.56) |

(1) The impact of 31 thousand and 29 thousand shares from restricted stock units and restricted stock was excluded from the computation of diluted net loss per common share for the quarter and six months ended June 30, 2022, respectively, because the effect would have been anti-dilutive.
14. Contingencies
Contingencies arise in the normal course of the Company's operations and are not expected to have a material impact on the Company's financial condition or results of operations.
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Item 2. Management's Discussion and Analysis of Financial Condition and Results of Operations
The following discussion and analysis should be read in conjunction with the consolidated financial statements and related notes included under Item 1 Financial Statements and our 2022 Annual Report on Form 10-K. The accompanying consolidated financial statements and related notes have been prepared in accordance with United States (U.S.) generally accepted accounting principles (GAAP) and include the accounts of Markel Group Inc., formerly Markel Corporation, and its consolidated subsidiaries, as well as any variable interest entities that meet the requirements for consolidation. Effective May 26, 2023, Markel Corporation changed its name to Markel Group Inc. (Markel Group). This section is divided into the following sections:
•Our Business
•Results of Operations
•Financial Condition
•Critical Accounting Estimates
•Safe Harbor and Cautionary Statement
Our Business
Markel Group is a holding company comprised of a diverse family of businesses and investments. The leadership teams of our businesses operate with a high degree of independence, while at the same time living the values that we call the Markel Style. Our specialty insurance business sits at the core of our company. Through decades of sound underwriting, the insurance team has provided the capital base from which we built a system of businesses and investments that collectively increase Markel Group's durability and adaptability. We aspire to build one of the world's great companies by enabling our customers, associates and shareholders to win and deploy three financial engines in pursuit of this goal.
Insurance - Our principal business markets and underwrites specialty insurance products using multiple platforms that enable us to best match risk and capital.
Investments - Our investing activities are primarily related to our underwriting operations. The majority of our investable assets come from premiums paid by policyholders and the remainder is comprised of shareholder funds.
Markel Ventures - Through our Markel Ventures operations, we own controlling interests in a diverse portfolio of businesses that operate in a variety of industries.
Our three interdependent engines form a system that provides diverse income streams, access to a wide range of investment opportunities and the ability to efficiently move capital to the best ideas across the Company. We allocate capital across the Company using a four-step process that we have consistently followed for years: invest in our existing businesses for organic growth opportunities, acquire controlling interests in businesses, build our portfolio of equity securities, and repurchase shares of our common stock. Our system is uniquely equipped for long-term growth. To mitigate effects of short-term volatility and align with the long-term perspective that we apply to operating our businesses, we generally use five-year time periods to measure our performance. We measure financial success by our ability to grow the market price per common share of our stock, or total shareholder return, at high rates of return over a long period of time. Over the five-year period ended June 30, 2023, our common share price increased at a compound annual rate of 5%. While this measure, considered independently of other factors, falls below our internal targets, we believe the operating performance at all three of our engines positions us well to achieve our targets over the long-term. We also consider the performance of book value per common share over the long-term, although we believe that as our business has evolved, this measure has become less reflective of shareholder value because a significant portion of our operations is not recorded at fair value. Over the five-year period ended June 30, 2023, the compound annual growth in book value per common share was 8%.
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Insurance
Our insurance engine is comprised of the following types of operations:
•Underwriting - Our underwriting operations are comprised of our risk-bearing insurance and reinsurance operations.
•Insurance-linked securities - Our insurance-linked securities (ILS) operations provide investment management services for a variety of investment products, including insurance-linked securities, catastrophe bonds, insurance swaps and weather derivatives.
•Program services - Our program services business serves as a fronting platform that provides other insurance entities access to the U.S. property and casualty insurance market.
Through our underwriting, ILS and program services operations, we have a suite of capabilities through which we can access capital to support our customers' risks, which includes our own capital through our underwriting operations, as well as third-party capital through our ILS and program services operations. Within each of these insurance platforms, we believe that our specialty product focus and niche market strategy enable us to develop expertise and specialized market knowledge. We seek to differentiate ourselves from competitors by our expertise, service, continuity and other value-based considerations, including the multiple platforms through which we can manage risk and deploy capital. For example, through our program services platform, we have programs through which we write insurance policies on behalf of our ILS operations that are supported by third-party capital. Additionally, we cede certain risks written through our underwriting operations to our ILS operations to the extent those risks are more aligned with the risk profile of our ILS investors than our own corporate tolerance. Our ability to access multiple insurance platforms allows us to achieve income streams from our insurance operations beyond the traditional underwriting model. We believe this multi-platform approach provides us with a unique advantage through which we have the ability to unlock additional value for our customers and business partners, which we refer to as "the power of the platform."
Underwriting
Our chief operating decision maker reviews our ongoing underwriting operations on a global basis in the following two segments: Insurance and Reinsurance. In determining how to allocate resources and assess the performance of our underwriting results, we consider many factors, including the nature of the insurance product sold, the type of account written and the type of customer served. The Insurance segment includes all direct business and facultative placements written on a risk-bearing basis within our underwriting operations. The Reinsurance segment includes all treaty reinsurance written on a risk-bearing basis within our underwriting operations.
Our Insurance segment includes both hard-to-place risks written outside of the standard market on an excess and surplus lines basis and unique and hard-to-place risks that are typically written on an admitted basis due to marketing and regulatory reasons. Risks written in our Insurance segment are written on either a direct basis or a subscription basis, the latter of which means that the loss exposures brought into the market are typically insured by more than one insurance company or Lloyd's of London (Lloyd's) syndicate. When we write business in the subscription market, we prefer to participate as lead underwriter in order to control underwriting terms, policy conditions and claims handling. The following products are included in this segment: professional liability, general liability, personal lines, marine and energy, primary and excess of loss property, workers' compensation, credit and surety coverages, specialty program insurance for well-defined niche markets and liability and other coverages tailored for unique exposures. Business in this segment is primarily written through our Markel Specialty and Markel International divisions. The Markel Specialty division writes business on both an excess and surplus lines and admitted basis, primarily through our platforms in the United States and Bermuda, as well as the United Kingdom (U.K.) and European Union. The Markel International division writes business worldwide from our London and Munich-based platforms, which include branch offices around the world. The Insurance segment also includes collateral protection insurance written on an admitted basis through our State National division.
Our Reinsurance segment includes casualty and specialty treaty reinsurance products offered to other insurance and reinsurance companies globally through the broker market. Our treaty reinsurance offerings include both quota share and excess of loss reinsurance and are typically written on a participation basis, which means each reinsurer shares proportionally in the business ceded under the reinsurance treaty written. Business in this segment is primarily written by our Global Reinsurance division. Principal lines of business include: professional liability, general liability, credit and surety, marine and energy and workers' compensation.
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Insurance-Linked Securities
Our insurance-linked securities operations are primarily comprised of our Nephila operations and are not included in a reportable segment. Nephila Holdings Ltd. (together with its subsidiaries, Nephila) provides investment and insurance management services through which we offer alternative capital to the reinsurance market while providing investors with investment strategies that typically are uncorrelated with traditional asset classes. We receive management fees for investment and insurance management services provided through these operations primarily based on the net asset value of the accounts managed, and for certain funds, incentive fees based on their annual performance.
Nephila serves as the investment manager to several Bermuda-based private funds (the Nephila Funds). To provide access for the Nephila Funds to a variety of insurance-linked securities in the property catastrophe, climate and specialty markets, Nephila acts as an insurance manager to certain Bermuda Class 3 and 3A reinsurance companies, Lloyd's Syndicate 2357 and Lloyd's Syndicate 2358 (collectively, the Nephila Reinsurers). The results of the Nephila Reinsurers are attributed to the Nephila Funds primarily through derivative transactions between these entities. Neither the Nephila Funds nor the Nephila Reinsurers are subsidiaries of Markel Group, and as such, these entities are not included in our consolidated financial statements. The Nephila Reinsurers subscribe to various reinsurance contracts based on their investors' risk profiles, including property reinsurance business fronted through our underwriting and program services platforms. See note 12 of the notes to consolidated financial statements for further details regarding transactions with entities managed through our Nephila operations.
Nephila also served as a managing general agent prior to the sales of our Velocity managing general agent operations in February 2022 and our Volante managing general agent operations in October 2022.
Our insurance-linked securities operations also include our run-off Markel CATCo operations, the results of which are reported separately from our ongoing insurance-linked securities operations. Our Markel CATCo operations are conducted through Markel CATCo Investment Management Ltd. (MCIM), an ILS investment fund manager headquartered in Bermuda. MCIM serves as the insurance manager for Markel CATCo Re Ltd. (Markel CATCo Re), a Bermuda Class 3 reinsurance company, and as the investment manager for Markel CATCo Reinsurance Fund Ltd., a Bermuda exempted mutual fund company comprised of multiple segregated accounts (Markel CATCo Funds). In July 2019, these operations were placed into run-off. In March 2022, we completed a buy-out transaction that provided for an accelerated return of all remaining capital to investors in the Markel CATCo Funds. Following the completion of the buy-out transaction, we consolidate Markel CATCo Re as its primary beneficiary. Results attributable to the run-off of Markel CATCo Re are included with our other Markel CATCo operations within services and other expenses, and for the six months ended June 30, 2023 and 2022, these results were entirely attributable to noncontrolling interest holders in Markel CATCo Re. In connection with the buy-out transaction, we entered into a tail risk cover with Markel CATCo Re through which we have uncollateralized exposure to adverse development on loss reserves held by Markel CATCo Re for loss exposures in excess of limits that we believe are unlikely to be exceeded. See note 11 of the notes to consolidated financial statements for further details regarding our Markel CATCo operations and the consolidation of Markel CATCo Re.
Program Services and Other Fronting
Our program services business, which is provided through our State National division, generates fee income in the form of ceding fees in exchange for fronting insurance business to other insurance carriers (capacity providers), including the Nephila Reinsurers. In general, fronting refers to business in which we write insurance on behalf of a general agent or capacity provider and then cede all, or substantially all, of the risk under these policies to the capacity provider in exchange for ceding fees. These capacity providers are domestic and foreign insurers and institutional risk investors that want to access specific lines of U.S. property and casualty insurance business but may not have the required licenses and filings to do so. The results of our program services operations are not included in a reportable segment.
In certain instances, we also leverage the strength of our underwriting platform to write business on behalf of our ILS operations, in exchange for ceding fees, to support their business plans and assist in meeting their desired return objectives. This fronting business is conducted separately from our program services business and consists of catastrophe-exposed property insurance and reinsurance business and specialty reinsurance business.
Although we reinsure substantially all of the risks inherent in our program services business and ILS fronting arrangements, we have certain programs that contain limits on our reinsurers' obligations to us that expose us to underwriting risk, including loss ratio caps, aggregate reinsurance limits or exclusion of the credit risk of producers. Under certain programs, including programs and contracts with Nephila Reinsurers, we also bear underwriting risk for annual aggregate agreement year losses in excess of a limit that we believe is unlikely to be exceeded. See note 12 of the notes to consolidated financial statements for further details regarding our programs with Nephila Reinsurers.
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Investments
The majority of our investable assets come from premiums paid by policyholders. We rely on sound underwriting practices to produce investable funds. Policyholder funds are invested predominantly in high-quality government and municipal bonds and mortgage-backed securities that generally match the duration and currency of our loss reserves. We typically hold these fixed maturity investments until maturity. As a result, unrealized holding gains and losses on these securities are generally expected to reverse as the securities mature. Premiums collected through our underwriting operations may also be held as short-term investments or cash and cash equivalents to provide short-term liquidity for projected claims payments, reinsurance costs and operating expenses. The balance of our investable assets, comprised of shareholder funds, is available to be invested in equity securities, which over the long run, have produced higher returns relative to fixed maturity and short-term investments. When purchasing equity securities, we seek to invest in profitable companies, with honest and talented management, that exhibit reinvestment opportunities and capital discipline, at reasonable prices. We intend to hold these equity investments over the long-term. Substantially all of our investment portfolio is managed by company employees.
Markel Ventures
Through our wholly owned subsidiary, Markel Ventures, Inc. (Markel Ventures), we own controlling interests in high-quality businesses that operate in a variety of different industries with shared values and the shared goal of positively contributing to the long-term financial performance of Markel Group. Management teams for each business operate autonomously and are responsible for developing strategic initiatives, managing day-to-day operations and making investment and capital allocation decisions for their respective companies.
Our corporate management team is responsible for decisions regarding allocation of capital for acquisitions and new investments. Our strategy in making these acquisitions is similar to our strategy for purchasing equity securities. We seek to invest in profitable companies, with honest and talented management, that exhibit reinvestment opportunities and capital discipline, at reasonable prices. We intend to own the businesses acquired for a long period of time. Our chief operating decision maker allocates resources to and assesses the performance of these various businesses in the aggregate as the Markel Ventures segment.
The Markel Ventures segment includes a diverse portfolio of specialized businesses from different industries that offer various types of products and services to businesses and consumers across many markets. The following types of businesses are included in this segment: construction services, consumer and building products, transportation-related products, consulting services and equipment manufacturing products. All of our businesses in this segment are headquartered in the U.S., with subsidiaries of certain businesses located outside of the U.S.
Results of Operations
The following table presents the components of operating revenues.

| Quarter Ended June 30, |  | Six Months Ended June 30,
(dollars in thousands) | 2023 |  | 2022 |  | 2023 |  | 2022
Insurance segment | $ | 1,763,186 |  |  | $ | 1,570,001 |  |  | $ | 3,474,110 |  |  | $ | 3,047,149 |
Reinsurance segment | 268,288 |  |  | 264,154 |  |  | 525,522 |  |  | 548,121 |
Insurance-linked securities, program services and other insurance | 77,407 |  |  | 57,739 |  |  | 119,181 |  |  | 238,140 |
Insurance operations | 2,108,881 |  |  | 1,891,894 |  |  | 4,118,813 |  |  | 3,833,410 |
Net investment income | 168,927 |  |  | 96,695 |  |  | 327,521 |  |  | 188,992 |
Net investment gains (losses) | 484,527 |  |  | (1,554,643) |  |  | 857,090 |  |  | (1,913,042) |
Other | (6,378) |  |  | (3,137) |  |  | (8,758) |  |  | (22,707) |
Investing segment | 647,076 |  |  | (1,461,085) |  |  | 1,175,853 |  |  | (1,746,757) |
Markel Ventures segment | 1,386,579 |  |  | 1,361,398 |  |  | 2,491,259 |  |  | 2,311,790 |
Total operating revenues | $ | 4,142,536 |  |  | $ | 1,792,207 |  |  | $ | 7,785,925 |  |  | $ | 4,398,443 |

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The following table presents the components of comprehensive income (loss) to shareholders.

| Quarter Ended June 30, |  | Six Months Ended June 30,
(dollars in thousands) | 2023 |  | 2022 |  | 2023 |  | 2022
Insurance segment profit | $ | 134,651 |  |  | $ | 166,414 |  |  | $ | 231,155 |  |  | $ | 353,908 |
Reinsurance segment profit | 15,184 |  |  | 3,839 |  |  | 39,418 |  |  | 17,122 |
Insurance-linked securities, program services and other insurance | 47,526 |  |  | 31,938 |  |  | 104,128 |  |  | 51,952 |
Amortization of intangible assets (1) | (24,564) |  |  | (24,946) |  |  | (49,412) |  |  | (50,062) |
Insurance operations | 172,797 |  |  | 177,245 |  |  | 325,289 |  |  | 372,920 |
Investing segment profit (loss) | 647,076 |  |  | (1,461,085) |  |  | 1,175,853 |  |  | (1,746,757) |
Markel Ventures segment profit (2) | 150,191 |  |  | 107,046 |  |  | 222,818 |  |  | 156,783 |
Interest expense | (47,221) |  |  | (50,050) |  |  | (96,659) |  |  | (99,742) |
Net foreign exchange gains (losses) | (14,976) |  |  | 105,067 |  |  | (47,904) |  |  | 128,071 |
Income tax (expense) benefit | (191,937) |  |  | 238,953 |  |  | (325,668) |  |  | 257,089 |
Net income attributable to noncontrolling interests | (20,419) |  |  | (32,972) |  |  | (69,566) |  |  | (35,901) |
Net income (loss) to shareholders | 695,511 |  |  | (915,796) |  |  | 1,184,163 |  |  | (967,537) |
Preferred stock dividends | (18,000) |  |  | (18,000) |  |  | (18,000) |  |  | (18,000) |
Net income (loss) to common shareholders | 677,511 |  |  | (933,796) |  |  | 1,166,163 |  |  | (985,537) |
Other comprehensive income (loss) to shareholders | (130,962) |  |  | (301,892) |  |  | 26,751 |  |  | (762,065) |
Comprehensive income (loss) to shareholders | $ | 564,549 |  |  | $ | (1,217,688) |  |  | $ | 1,210,914 |  |  | $ | (1,729,602) |

(1) Amortization of intangible assets includes all amortization attributable to our insurance operations. Amortization of intangible assets attributable to our underwriting segments was $9.3 million and $18.8 million for the quarter and six months ended June 30, 2023, respectively, and $9.6 million and $19.4 million for the quarter and six months ended June 30, 2022, respectively; however, we do not allocate amortization of intangible assets between the Insurance and Reinsurance segments. Amortization of intangible assets attributable to our insurance-linked securities, program services and other insurance operations was $15.3 million and $30.6 million for the quarter and six months ended June 30, 2023, respectively, and $15.3 million and $30.7 million for the quarter and six months ended June 30, 2022, respectively.
(2) Segment profit for the Markel Ventures segment includes amortization of intangible assets attributable to Markel Ventures.
The change in comprehensive income (loss) to shareholders for the second quarter of 2023 compared to the second quarter of 2022 was primarily due to pre-tax net investments gains on our equity securities of $483.4 million in 2023 compared to pre-tax net investment losses on our equity securities of $1.6 billion in 2022.
The change in comprehensive income (loss) to shareholders for the six months ended June 30, 2023 compared to the six months ended June 30, 2022 was primarily due to pre-tax net investment gains on our equity securities of $859.2 million in 2023 compared to pre-tax net investment losses on our equity securities of $1.9 billion in 2022, as well as pre-tax net unrealized gains on our fixed maturity securities of $41.2 million in 2023 compared to pre-tax net unrealized losses on our fixed maturity securities of $1.1 billion in 2022.
The components of net income (loss) to shareholders and comprehensive income (loss) to shareholders are discussed in further detail under "Insurance Results," "Investing Results," "Markel Ventures Results," "Interest Expense, Net Foreign Exchange Gains (Losses) and Income Taxes" and "Comprehensive Income (Loss) to Shareholders and Book Value per Common Share."
Insurance Results
Our Insurance engine includes our underwriting, insurance-linked securities, program services and other fronting operations. We have a suite of capabilities through which we can access capital to support our customers' risks, which includes our own capital through our underwriting operations and third-party capital through our ILS and program services operations. Our underwriting operations, which are primarily comprised of our Insurance and Reinsurance segments, produce revenues primarily by underwriting insurance contracts and earning premiums in the specialty insurance market. Our insurance-linked securities and program services operations produce revenues primarily through fees earned for investment management services and fronting services, respectively. Our insurance operations also include the underwriting results of run-off lines of business that were discontinued prior to, or in conjunction with, insurance acquisitions, and the results of our run-off life and annuity reinsurance business.
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The following table presents the components of our Insurance engine gross premium volume and operating revenues.

| Quarter Ended June 30, |  | Six Months Ended June 30,
(dollars in thousands) | 2023 |  | 2022 |  | % Change |  | 2023 |  | 2022 |  | % Change
Gross premium volume: |  |  |  |  |  |  |  |  |  |  |
Underwriting | $ | 2,734,576 |  |  | $ | 2,528,885 |  |  | 8 | % |  | $ | 5,392,834 |  |  | $ | 5,048,500 |  |  | 7 | %
Program services and other fronting (1) | 1,053,609 |  |  | 751,164 |  |  | 40 | % |  | 1,831,363 |  |  | 1,629,836 |  |  | 12 | %
Insurance operations | $ | 3,788,185 |  |  | $ | 3,280,049 |  |  | 15 | % |  | $ | 7,224,197 |  |  | $ | 6,678,336 |  |  | 8 | %
Operating revenues: |  |  |  |  |  |  |  |  |  |  |
Insurance segment | $ | 1,763,186 |  |  | $ | 1,570,001 |  |  | 12 | % |  | $ | 3,474,110 |  |  | $ | 3,047,149 |  |  | 14 | %
Reinsurance segment | 268,288 |  |  | 264,154 |  |  | 2 | % |  | 525,522 |  |  | 548,121 |  |  | (4) | %
Insurance-linked securities, program services and other insurance | 77,407 |  |  | 57,739 |  |  | 34 | % |  | 119,181 |  |  | 238,140 |  |  | (50) | %
Insurance operations | $ | 2,108,881 |  |  | $ | 1,891,894 |  |  | 11 | % |  | $ | 4,118,813 |  |  | $ | 3,833,410 |  |  | 7 | %

(1) Substantially all gross premiums from our program services business and other fronting arrangements were ceded to third parties for the quarter and six months ended June 30, 2023 and 2022.
Underwriting Results
Underwriting profits are a key component of our strategy to build shareholder value. We believe that the ability to achieve consistent underwriting profits demonstrates knowledge and expertise, commitment to superior customer service and the ability to manage insurance risk. The property and casualty insurance industry commonly defines underwriting profit or loss as earned premiums net of losses and loss adjustment expenses and underwriting, acquisition and insurance expenses. We use underwriting profit or loss and the combined ratio as a basis for evaluating our underwriting performance. The U.S. GAAP combined ratio is a measure of underwriting performance and represents the relationship of incurred losses, loss adjustment expenses and underwriting, acquisition and insurance expenses to earned premiums. The combined ratio is the sum of the loss ratio and the expense ratio. The loss ratio represents the relationship of incurred losses and loss adjustment expenses to earned premiums. The expense ratio represents the relationship of underwriting, acquisition and insurance expenses to earned premiums. A combined ratio less than 100% indicates an underwriting profit, while a combined ratio greater than 100% reflects an underwriting loss.
In addition to the U.S. GAAP combined ratio, loss ratio and expense ratio, we also evaluate our underwriting performance using measures that exclude the impacts of certain items on these ratios. We believe these adjusted measures, which are non-GAAP measures, provide financial statement users with a better understanding of the significant factors that comprise our underwriting results and how management evaluates underwriting performance.
When analyzing our combined ratio, we exclude current accident year losses and loss adjustment expenses attributed to natural catastrophes and certain significant, infrequent loss events, for example, the military conflict between Russia and Ukraine that began following Russia's invasion of Ukraine in February 2022. Due to the unique characteristics of a catastrophe loss and other significant, infrequent events, there is inherent variability as to the timing or loss amount, which cannot be predicted in advance. We believe measures that exclude the effects of such events are meaningful to understand the underlying trends and variability in our underwriting results that may be obscured by these items.
When analyzing our loss ratio, we evaluate losses and loss adjustment expenses attributable to the current accident year separate from losses and loss adjustment expenses attributable to prior accident years. Prior accident year reserve development, which can either be favorable or unfavorable, represents changes in our estimates of losses and loss adjustment expenses related to loss events that occurred in prior years. We believe a discussion of current accident year loss ratios, which exclude prior accident year reserve development, is helpful since it provides more insight into estimates of current underwriting performance and excludes changes in estimates related to prior year loss reserves. We also analyze our current accident year loss ratio excluding losses and loss adjustment expenses attributable to catastrophes and, in 2022, the Russia-Ukraine conflict. The current accident year loss ratio excluding the impact of catastrophes and other significant, infrequent loss events is also commonly referred to as an attritional loss ratio within the property and casualty insurance industry.
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The following table presents summary data for our consolidated underwriting operations, which are comprised predominantly of our Insurance and Reinsurance segments. Our consolidated underwriting results also include results from discontinued lines of business and the retained portion of our program services operations.

| Quarter Ended June 30, |  | Six Months Ended June 30,
(dollars in thousands) | 2023 |  | 2022 |  | % Change |  | 2023 |  | 2022 |  | % Change
Gross premium volume | $ | 2,734,255 |  | $ | 2,527,754 |  | 8 | % |  | $ | 5,392,062 |  | $ | 5,045,870 |  | 7 | %
Net written premiums | $ | 2,207,693 |  | $ | 2,099,795 |  | 5 | % |  | $ | 4,425,471 |  | $ | 4,264,529 |  | 4 | %
Earned premiums | $ | 2,031,143 |  | $ | 1,833,104 |  | 11 | % |  | $ | 3,998,847 |  | $ | 3,592,874 |  | 11 | %
Underwriting profit | $ | 145,380 |  | $ | 164,825 |  | (12) | % |  | $ | 264,365 |  | $ | 361,858 |  | (27) | %
Underwriting Ratios (1) |  |  |  |  | Point Change |  |  |  |  |  | Point Change
Loss ratio |  |  |  |  |  |  |  |  |  |  |
Current accident year loss ratio | 61.8 | % |  | 59.2 | % |  | 2.6 |  |  | 62.5 | % |  | 59.9 | % |  | 2.6 |
Prior accident years loss ratio | (3.3) | % |  | (1.4) | % |  | (1.9) |  |  | (3.5) | % |  | (3.4) | % |  | (0.1) |
Loss ratio | 58.5 | % |  | 57.8 | % |  | 0.7 |  |  | 59.0 | % |  | 56.5 | % |  | 2.5 |
Expense ratio | 34.4 | % |  | 33.2 | % |  | 1.2 |  |  | 34.3 | % |  | 33.4 | % |  | 0.9 |
Combined ratio | 92.8 | % |  | 91.0 | % |  | 1.8 |  |  | 93.4 | % |  | 89.9 | % |  | 3.5 |
Current accident year loss ratio Russia-Ukraine conflict impact (2) | — | % |  | — | % |  | — |  |  | — | % |  | 1.0 | % |  | (1.0) |
Current accident year loss ratio, excluding Russia-Ukraine conflict impact | 61.8 | % |  | 59.2 | % |  | 2.6 |  |  | 62.5 | % |  | 59.0 | % |  | 3.5 |
Combined ratio, excluding current year Russia-Ukraine conflict impact | 92.8 | % |  | 91.0 | % |  | 1.8 |  |  | 93.4 | % |  | 89.0 | % |  | 4.4 |

(1) Amounts may not reconcile due to rounding.
(2) The point impact of the Russia-Ukraine conflict is calculated as the associated net losses and loss adjustment expenses divided by total earned premiums.
Premiums
The increase in gross premium volume in our underwriting operations for the quarter and six months ended June 30, 2023 was driven by growth within our Insurance segment. Net retention of gross premium volume in our underwriting operations was 81% the quarter ended June 30, 2023 compared to 83% for the same period of 2022. Net retention of gross premium volume in our underwriting operations was 82% for the six months ended June 30, 2023 compared to 85% for the same period of 2022. The decrease in net retention for the quarter and six months ended June 30, 2023 was driven by lower retention across both of our underwriting segments. Within our underwriting operations, we purchase reinsurance and retrocessional reinsurance to manage our net retention on individual risks and overall exposure to losses and to enable us to write policies with sufficient limits to meet policyholder needs. The increase in earned premiums in our underwriting operations for the quarter and six months ended June 30, 2023 was primarily attributable to higher gross premium volume in recent periods.
After several years of significant rate increases across most of our product lines, we began to see rate increases slow on many of our product lines in the latter half of 2022. We continued to achieve rate increases across most product lines during the first half of 2023; however, the current rate environment varies by product line. In certain product lines, such as property coverages, and marine and energy, we have continued to realize significant rate increases in 2023 due to recent industry loss experience and the rising cost of reinsurance within those product lines. We continue to see low single-digit rate decreases within our workers' compensation product line and are also seeing rate pressure within our professional liability product lines, most notably on our large account directors and officers product. In most of our casualty lines, we continue to realize rate increases. As a result of our focus on rate adequacy, gross premium volume is being impacted in certain product lines where we are concerned around the level of price adequacy and are allowing business to lapse in certain instances to maintain underwriting discipline. When we believe the prevailing market price will not support our underwriting profit targets, the business is not written.
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Combined Ratio
The increase in our consolidated combined ratio for the quarter ended June 30, 2023 compared to the same period of 2022 was primarily driven by a higher current accident year loss ratio and expense ratio in 2023 compared to 2022 across both our underwriting segments, partially offset by the impact of more favorable development on prior accident years loss reserves in 2023 compared to 2022.
Underwriting results for the six months ended June 30, 2022 included $35.0 million of net losses and loss adjustment expenses attributed to the Russia-Ukraine conflict. Excluding these losses, the increase in our consolidated combined ratio for the six months ended June 30, 2023 compared to the same period of 2022 was primarily driven by a higher attritional loss ratio and expense ratio in 2023 compared to 2022 within our Insurance segment.
Insurance Segment

| Quarter Ended June 30, |  | Six Months Ended June 30,
(dollars in thousands) | 2023 |  | 2022 |  | % Change |  | 2023 |  | 2022 |  | % Change
Gross premium volume | $ | 2,455,403 |  | $ | 2,237,158 |  | 10 | % |  | $ | 4,553,341 |  | $ | 4,180,464 |  | 9 | %
Net written premiums | $ | 1,946,528 |  | $ | 1,828,162 |  | 6 | % |  | $ | 3,648,669 |  | $ | 3,439,182 |  | 6 | %
Earned premiums | $ | 1,763,186 |  | $ | 1,570,001 |  | 12 | % |  | $ | 3,474,110 |  | $ | 3,047,149 |  | 14 | %
Underwriting profit | $ | 134,651 |  | $ | 166,414 |  | (19) | % |  | $ | 231,155 |  | $ | 353,908 |  | (35) | %
Underwriting Ratios (1) |  |  |  |  | Point Change |  |  |  |  |  | Point Change
Loss ratio |  |  |  |  |  |  |  |  |  |  |
Current accident year loss ratio | 61.2 | % |  | 58.6 | % |  | 2.6 |  |  | 62.1 | % |  | 59.3 | % |  | 2.8 |
Prior accident years loss ratio | (3.5) | % |  | (2.8) | % |  | (0.7) |  |  | (3.6) | % |  | (4.7) | % |  | 1.1 |
Loss ratio | 57.7 | % |  | 55.8 | % |  | 1.9 |  |  | 58.5 | % |  | 54.6 | % |  | 3.9 |
Expense ratio | 34.6 | % |  | 33.6 | % |  | 1.0 |  |  | 34.8 | % |  | 33.8 | % |  | 1.0 |
Combined ratio | 92.4 | % |  | 89.4 | % |  | 3.0 |  |  | 93.3 | % |  | 88.4 | % |  | 4.9 |
Current accident year loss ratio Russia-Ukraine conflict impact (2) | — | % |  | — | % |  | — |  |  | — | % |  | 0.7 | % |  | (0.7) |
Current accident year loss ratio, excluding Russia-Ukraine conflict impact | 61.2 | % |  | 58.6 | % |  | 2.6 |  |  | 62.1 | % |  | 58.6 | % |  | 3.5 |
Combined ratio, excluding current year Russia-Ukraine conflict impact | 92.4 | % |  | 89.4 | % |  | 3.0 |  |  | 93.3 | % |  | 87.7 | % |  | 5.6 |

(1) Amounts may not reconcile due to rounding.
(2) The point impact of the Russia-Ukraine conflict is calculated as the associated net losses and loss adjustment expenses divided by total earned premiums.
Premiums
The increase in gross premium volume in our Insurance segment for the quarter and six months ended June 30, 2023 was driven by more favorable rates and new business growth within our personal lines, marine and energy, property and general liability product lines, partially offset by lower premium volume within our professional liability product lines, where we are adjusting our writings in response to changes in market conditions and downward pressure on rates. We continue to focus on rate adequacy, particularly within certain classes within our casualty and professional liability product lines, and will not write business that does not meet our underwriting profit targets. Net retention of gross premium volume was 79% the quarter ended June 30, 2023 compared to 82% for the same period of 2022. Net retention of gross premium volume was 80% for the six months ended June 30, 2023 compared to 82% for the same period of 2022. The decrease in net retention was primarily due to higher cession rates on our personal lines and professional liability product lines in 2023 compared to 2022. The increase in earned premiums for the quarter and six months ended June 30, 2023 was primarily due to higher gross premium volume across most product lines in recent periods.
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Combined Ratio: Quarter-to-Date
The increase in the Insurance segment's current accident year loss ratio for the quarter ended June 30, 2023 compared to the same period of 2022 was primarily attributable to higher attritional loss ratios within our professional liability and general liability product lines in 2023 compared to 2022. We have been increasing our attritional loss ratios on these lines since the latter half of 2022 due to the impacts of recent claims trend, including impacts from economic and social inflation.
The Insurance segment's combined ratio for the quarter ended June 30, 2023 included $61.6 million of favorable development on prior accident years loss reserves compared to $43.7 million for the same period of 2022. The increase in favorable development was primarily due to favorable development on our professional liability product lines in the second quarter of 2023, primarily attributable to our international business, compared to modest adverse development in 2022. This favorable change was partially offset by more adverse development on our general liability product lines in 2023 compared to 2022. Adverse development on our general liability product lines for the quarter ended June 30, 2023 was primarily attributable to an increased frequency of large claims over the past several quarters on our excess and umbrella product and was most significant on the 2017 to 2019 accident years.
For the quarter ended June 30, 2023, favorable development was most significant on our professional liability and property product lines in the more recent accident years. Despite favorable development on our professional liability product lines in the period, we continue to approach reductions of prior year loss reserves on our longer tail professional liability and general liability product lines with caution given the prevailing economic environment and recent claims trend, particularly on U.S.-based risks. The favorable development on prior years loss reserves in 2022 was most significant on our property, marine and energy, workers' compensation and programs product lines.
The increase in the Insurance segment's expense ratio for the quarter ended June 30, 2023 compared to the same period of 2022 was primarily due to a higher policy acquisition cost ratio, due to changes in mix of business, as well as higher general and administrative expenses, which were largely offset by the favorable impact of higher earned premiums.
Combined Ratio: Year-to-Date
The Insurance segment's current accident year losses and loss adjustment expenses for the six months ended June 30, 2022 included $20.0 million of net losses and loss adjustment expenses attributed to the Russia-Ukraine conflict. Excluding these losses, the increase in the current accident year loss ratio for the six months ended June 30, 2023 compared to the same period of 2022 was primarily attributable to higher attritional loss ratios within our professional liability and general liability product lines in 2023 compared to 2022, as previously discussed. We also increased our attritional loss ratios within our professional liability product lines in the first quarter of 2023 related to exposures arising from bank failures.
The Insurance segment's combined ratio for the six months ended June 30, 2023 included $124.2 million of favorable development on prior accident years loss reserves compared to $142.3 million for the same period of 2022. The decrease in favorable development was primarily due to adverse development on our general liability product lines in 2023 compared to favorable development in 2022, partially offset by more favorable development on our professional liability product lines in 2023 compared to 2022, primarily attributable to our international business. Adverse development on our general liability product lines for the six months ended June 30, 2023 was impacted by the same factors as quarter-to-date development.
For the six months ended June 30, 2023, favorable development was most significant on our professional liability, property, marine and energy and workers' compensation product lines in more recent accident years. The favorable development on prior years loss reserves in 2022 was most significant on our property, marine and energy, workers' compensation and programs product lines.
The increase in the Insurance segment's expense ratio for the six months ended June 30, 2023 compared to the same period of 2022 was primarily due to a higher policy acquisition cost ratio, due to changes in mix of business, as well as higher general and administrative expenses, which were largely offset by the favorable impact of higher earned premiums.
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Reinsurance Segment

| Quarter Ended June 30, |  | Six Months Ended June 30,
(dollars in thousands) | 2023 |  | 2022 |  | % Change |  | 2023 |  | 2022 |  | % Change
Gross premium volume | $ | 281,100 |  |  | $ | 289,056 |  |  | (3) | % |  | $ | 833,161 |  |  | $ | 865,372 |  |  | (4) | %
Net written premiums | $ | 261,496 |  |  | $ | 273,838 |  |  | (5) | % |  | $ | 777,587 |  |  | $ | 829,058 |  |  | (6) | %
Earned premiums | $ | 268,288 |  |  | $ | 264,154 |  |  | 2 | % |  | $ | 525,522 |  |  | $ | 548,121 |  |  | (4) | %
Underwriting profit | $ | 15,184 |  |  | $ | 3,839 |  |  | 296 | % |  | $ | 39,418 |  |  | $ | 17,122 |  |  | 130 | %
Underwriting Ratios (1) |  |  |  |  | Point Change |  |  |  |  |  | Point Change
Loss ratio |  |  |  |  |  |  |  |  |  |  |
Current accident year loss ratio | 65.7 | % |  | 62.8 | % |  | 2.9 |  |  | 65.3 | % |  | 63.6 | % |  | 1.7 |
Prior accident years loss ratio | (3.0) | % |  | 5.1 | % |  | (8.1) |  |  | (3.2) | % |  | 2.9 | % |  | (6.1) |
Loss ratio | 62.7 | % |  | 68.0 | % |  | (5.3) |  |  | 62.1 | % |  | 66.4 | % |  | (4.3) |
Expense ratio | 31.6 | % |  | 30.6 | % |  | 1.0 |  |  | 30.4 | % |  | 30.5 | % |  | (0.1) |
Combined ratio | 94.3 | % |  | 98.5 | % |  | (4.2) |  |  | 92.5 | % |  | 96.9 | % |  | (4.4) |
Current accident year loss ratio Russia-Ukraine conflict impact (2) | — | % |  | — | % |  | — |  |  | — | % |  | 2.7 | % |  | (2.7) |
Current accident year loss ratio, excluding Russia-Ukraine conflict impact | 65.7 | % |  | 62.8 | % |  | 2.9 |  |  | 65.3 | % |  | 60.8 | % |  | 4.5 |
Combined ratio, excluding current year Russia-Ukraine conflict impact | 94.3 | % |  | 98.5 | % |  | (4.2) |  |  | 92.5 | % |  | 94.1 | % |  | (1.6) |

(1) Amounts may not reconcile due to rounding.
(2) The point impact of the Russia-Ukraine conflict is calculated as the associated net losses and loss adjustment expenses divided by total earned premiums.
Premiums
The decrease in gross premium volume in our Reinsurance segment for the quarter and six months ended June 30, 2023 was primarily attributable to lower gross premiums with our professional liability product lines, partially offset by higher gross premiums within our marine and energy product lines. Lower gross premiums within our professional liability product lines were primarily attributable to unfavorable premium adjustments in 2023 compared to significant favorable premium adjustments in 2022 on our transaction liability product and decreases on renewals, due to decreased exposures and participation. Higher gross premiums within our marine and energy product lines were primarily attributable to increases on renewals, due to increased exposures and more favorable rates, as well as new business. Significant variability in gross premium volume can be expected in our Reinsurance segment due to individually significant contracts and multi-year contracts.
Net retention of gross premium volume for the quarter ended June 30, 2023 was 93% compared to 95% for the same period of 2022. Net retention of gross premium volume for the six months ended June 30, 2023 was 93% compared to 96% for the same period of 2022. The decrease in net retention for both periods was driven by changes in mix of business, as we are writing more marine and energy business, which carries a higher cession rate than the rest of the segment, and less of our fully retained professional liability business.
The increase in earned premiums for the quarter ended June 30, 2023 was primarily attributable to earnings on multi-year deals within our professional liability product lines, which have experienced growth in recent periods. The decrease in earned premiums for the six months ended June 30, 2023 was primarily due to less favorable premium adjustments in 2023 compared to 2022, primarily attributable to our professional liability product lines, and the non-renewal of a large treaty within our workers' compensation product line.
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Combined Ratio: Quarter-to-Date
The increase in the Reinsurance segment's current accident year loss ratio for the quarter ended June 30, 2023 compared to the same period of 2022 was primarily due to less favorable premium adjustments in 2023 compared to 2022, primarily on our professional liability product lines. The decrease in favorable prior period adjustments had an offsetting benefit in the segment prior accident years loss ratio.
The Reinsurance segment's combined ratio for the quarter ended June 30, 2023 included $8.0 million of favorable development on prior accident years loss reserves, which was primarily attributable to modest favorable development across several product lines and accident years. This favorable development was partially offset by adverse development and additional exposures recognized on prior accident years related to net favorable premium adjustments on our general liability product lines. For the quarter ended June 30, 2022, the combined ratio included a $13.6 million increase in prior accident years loss reserves, which was attributable to additional exposures recognized on prior accident years related to net favorable premium adjustments on our general liability product lines and modest adverse development on certain of our other product lines.
The increase in the Reinsurance segment's expense ratio for the quarter ended June 30, 2023 compared to the same period of 2022 was primarily due to a slightly higher policy acquisition cost ratio and a slight increase in general and administrative expenses.
Combined Ratio: Year-to-Date
The Reinsurance segment's current accident year losses and loss adjustment expenses for the six months ended June 30, 2022 included $15.0 million of net losses and loss adjustment expenses attributed to the Russia-Ukraine conflict. Excluding these losses, the increase in the current accident year loss ratio for the six months ended June 30, 2023 compared to the same period of 2022 was primarily due to less favorable premium adjustments in 2023 compared to 2022, primarily on our professional liability and credit and surety product lines. The decrease in favorable prior period adjustments had an offsetting benefit in the segment prior accident years loss ratio.
The Reinsurance segment's combined ratio for the six months ended June 30, 2023 included $16.7 million of favorable development on prior accident years loss reserves, which was primarily attributable to favorable development on our professional liability and property product lines across several accident years. This favorable development was partially offset by adverse development and additional exposures recognized on prior accident years related to net favorable premium adjustments on our general liability product lines. For the six months ended June 30, 2022, the combined ratio included a $15.7 million increase in prior accident years loss reserves, which was primarily attributable to additional exposures recognized on prior accident years related to net favorable premium adjustments on our general liability, professional liability and credit and surety product lines. This increase in prior years loss reserves for the six months ended June 30, 2022 was partially offset by favorable development on our credit and surety and property product lines.
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Insurance-linked Securities, Program Services and Other Insurance
The following table presents the components of operating revenues and operating expenses attributable to our insurance-linked securities, program services and other insurance operations, including our run-off block of life and annuity reinsurance contracts, none of which are included in a reportable segment. Underwriting results attributable to these operations include results from discontinued lines of business, which are reported separate from our Insurance and Reinsurance segments, and the retained portion of our program services operations. Investment income earned on the investments that support life and annuity policy benefit reserves are included in our Investing segment.

| Quarter Ended June 30,
| 2023 |  | 2022
(dollars in thousands) | Operating revenues |  | Operating expenses |  | Net |  | Operating revenues |  | Operating expenses |  | Net
Services and other: |  |  |  |  |  |  |  |  |  |  |
Program services and other fronting | $ | 37,680 |  |  | $ | 7,084 |  |  | $ | 30,596 |  |  | $ | 29,762 |  |  | $ | 6,731 |  |  | $ | 23,031 |
Program services - disposition gain | 16,923 |  |  | — |  |  | 16,923 |  |  | — |  |  | — |  |  | — |
Insurance-linked securities | 20,803 |  |  | 19,041 |  |  | 1,762 |  |  | 23,201 |  |  | 34,849 |  |  | (11,648) |
Life and annuity | 23 |  |  | 3,740 |  |  | (3,717) |  |  | 281 |  |  | 2,827 |  |  | (2,546) |
Markel CATCo Re | — |  |  | (8,673) |  |  | 8,673 |  |  | — |  |  | (28,199) |  |  | 28,199 |
Other | 2,309 |  |  | 4,565 |  |  | (2,256) |  |  | 5,546 |  |  | 5,216 |  |  | 330 |
| 77,738 |  |  | 25,757 |  |  | 51,981 |  |  | 58,790 |  |  | 21,424 |  |  | 37,366 |
Underwriting | (331) |  |  | 4,124 |  |  | (4,455) |  |  | (1,051) |  |  | 4,377 |  |  | (5,428) |
| 77,407 |  |  | 29,881 |  |  | 47,526 |  |  | 57,739 |  |  | 25,801 |  |  | 31,938 |
Amortization of intangible assets |  |  | 15,294 |  |  | (15,294) |  |  |  |  | 15,302 |  |  | (15,302) |
| $ | 77,407 |  |  | $ | 45,175 |  |  | $ | 32,232 |  |  | $ | 57,739 |  |  | $ | 41,103 |  |  | $ | 16,636 |

| Six Months Ended June 30,
| 2023 |  | 2022
(dollars in thousands) | Operating revenues |  | Operating expenses |  | Net |  | Operating revenues |  | Operating expenses |  | Net
Services and other: |  |  |  |  |  |  |  |  |  |  |
Program services and other fronting | $ | 66,870 |  |  | $ | 14,371 |  |  | $ | 52,499 |  |  | $ | 63,833 |  |  | $ | 14,114 |  |  | $ | 49,719 |
Program services - disposition gain | 16,923 |  |  | — |  |  | 16,923 |  |  | — |  |  | — |  |  | — |
Insurance-linked securities | 30,581 |  |  | 33,442 |  |  | (2,861) |  |  | 60,210 |  |  | 72,595 |  |  | (12,385) |
Insurance-linked securities - disposition gain | — |  |  | — |  |  | — |  |  | 107,293 |  |  | — |  |  | 107,293 |
Life and annuity | 48 |  |  | 6,946 |  |  | (6,898) |  |  | 606 |  |  | 6,223 |  |  | (5,617) |
Markel CATCo buy-out | — |  |  | — |  |  | — |  |  | — |  |  | 101,904 |  |  | (101,904) |
Markel CATCo Re | — |  |  | (53,465) |  |  | 53,465 |  |  | — |  |  | (28,199) |  |  | 28,199 |
Other | 5,544 |  |  | 8,336 |  |  | (2,792) |  |  | 8,594 |  |  | 12,775 |  |  | (4,181) |
| 119,966 |  |  | 9,630 |  |  | 110,336 |  |  | 240,536 |  |  | 179,412 |  |  | 61,124 |
Underwriting | (785) |  |  | 5,423 |  |  | (6,208) |  |  | (2,396) |  |  | 6,776 |  |  | (9,172) |
| 119,181 |  |  | 15,053 |  |  | 104,128 |  |  | 238,140 |  |  | 186,188 |  |  | 51,952 |
Amortization of intangible assets |  |  | 30,575 |  |  | (30,575) |  |  |  |  | 30,667 |  |  | (30,667) |
| $ | 119,181 |  |  | $ | 45,628 |  |  | $ | 73,553 |  |  | $ | 238,140 |  |  | $ | 216,855 |  |  | $ | 21,285 |

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Program Services and Other Fronting
For both the quarter and the six months ended June 30, 2023, the increase in operating revenues in our program services and other fronting operations was primarily due to higher gross premium volume within our program services operations driven by the expansion of existing programs and growth from new programs. Gross written premiums in our program services operations were $883.4 million and $1.5 billion for the quarter and six months ended June 30, 2023, respectively, compared to $709.8 million and $1.4 billion for the quarter and six months ended June 30, 2022, respectively.
In June 2023, we sold Independent Specialty Insurance Company (ISIC), a subsidiary within our program services operations, to Velocity Holdco, LLC (Velocity). ISIC is a licensed insurance carrier, the value of which is attributed to its insurance licenses. Through its managing general agent operations, Velocity has an existing program with our program services operations, through which it places business on behalf of our Nephila ILS operations. Following the sale, Velocity intends to use ISIC to start writing a portion of the business it places directly. The sale resulted in a gain of $16.9 million during the second quarter of 2023.
Gross written premiums from our other fronting operations, which consist of business written by our underwriting platform on behalf of our ILS operations, were $170.2 million and $328.6 million for the quarter and six months ended June 30, 2023, respectively, compared to $41.4 million and $214.5 million for the quarter and six months ended June 30, 2022, respectively.
Insurance-Linked Securities
For both the quarter and six months ended June 30, 2023, the decrease in operating revenues and operating expenses in our Nephila ILS operations was primarily due to the disposition of our Volante managing general agent operations in October 2022. For the six months ended June 30, 2023, the decrease in operating revenues was also partially attributable to lower revenues in our fund management operations and the disposition of our Velocity managing general agent operations in February 2022. The sale of the majority of our controlling interest in our Velocity managing general agent operations resulted in a gain of $107.3 million during the first quarter of 2022. Our Nephila ILS operations in 2023 are solely comprised of our fund management operations. As of June 30, 2023, Nephila's net assets under management were $7.2 billion.
Markel CATCo
In March 2022, we completed a buy-out transaction with Markel CATCo Re and the Markel CATCo Funds that provided for an accelerated return of all remaining capital to investors in the Markel CATCo Funds and resulted in the consolidation of Markel CATCo Re upon completion of the transaction. In order to complete the transaction, we made $101.9 million in payments, net of insurance proceeds, to or for the benefit of investors that were recognized as an expense during the first quarter of 2022. For the quarter and six months ended June 30, 2023 and 2022, results attributable to Markel CATCo Re were primarily related to favorable loss reserve development on the run-off of reinsurance contracts, all of which were attributable to noncontrolling interest holders in Markel CATCo Re. See note 11 of the notes to consolidated financial statements for further details regarding our Markel CATCo operations, the buy-out transaction and the consolidation of Markel CATCo Re.
Investing Results
Our business strategy recognizes the importance of both consistent underwriting and operating profits and superior investment returns to build shareholder value. We rely on sound underwriting practices to produce investable funds. We measure our investment performance by analyzing net investment income earned on our investment portfolio, as well as through net investment gains, which include unrealized gains on our equity portfolio, and the change in net unrealized gains on available-for-sale investments. Our investment performance measures also include investment yield and taxable equivalent total investment return. Other income or losses within our investing operations primarily relate to equity method investments in our investing segment, which are managed separately from the rest of our investment portfolio.
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The following table summarizes our consolidated investment performance, which consists predominantly of our Investing segment.

| Quarter Ended June 30, |  | Six Months Ended June 30,
(dollars in thousands) | 2023 |  | 2022 |  | Change |  | 2023 |  | 2022 |  | Change
Net investment income | $ | 169,693 |  | $ | 96,795 |  | 75 | % |  | $ | 329,028 |  | $ | 189,099 |  | 74 | %
Net investment gains (losses) | $ | 484,527 |  | $ | (1,554,643) |  | $ | 2,039,170 |  |  | $ | 857,090 |  | $ | (1,913,042) |  | $ | 2,770,132 |
Change in net unrealized gains (losses) on available-for-sale investments | $ | (170,570) |  | $ | (458,328) |  | $ | 287,758 |  |  | $ | 37,799 |  | $ | (1,118,276) |  | $ | 1,156,075 |
Other | $ | (6,378) |  | $ | (3,137) |  | $ | (3,241) |  |  | $ | (8,758) |  | $ | (22,707) |  | $ | 13,949 |
Investment Ratios |  |  |  |  |  |  |  |  |  |  |
Investment yield (1) | 0.8 | % |  | 0.5 | % |  | 0.3 |  |  | 1.5 | % |  | 1.0 | % |  | 0.5 |
Taxable equivalent total investment return |  |  |  |  |  |  | 5.1 | % |  | (10.7) | % |  | 15.8 |

(1) Investment yield reflects net investment income as a percentage of monthly average invested assets at amortized cost.
The increase in net investment income for the quarter and six months ended June 30, 2023 compared to the same periods of 2022 was primarily attributable to higher interest income on short-term investments and cash equivalents due to higher short-term interest rates in 2023 compared to 2022. Additionally, interest income on our fixed maturity securities increased, primarily attributable to a higher yield and higher average holdings of fixed maturity securities during the quarter and six months ended June 30, 2023 compared to the same periods of 2022. See note 3(d) of the notes to consolidated financial statements for details regarding the components of net investment income.
Net investment gains for the both the quarter and six months ended June 30, 2023 were primarily attributable to an increase in the fair value of our equity portfolio driven by favorable market value movements. Net investment losses for both the quarter and the six months ended June 30, 2022 were primarily attributable to a decrease in the fair value of our equity portfolio driven by unfavorable market value movements. See note 3(e) of the notes to consolidated financial statements for further details on the components of net investment gains (losses).
The change in net unrealized losses on available-for-sale investments for the quarter ended June 30, 2023 was primarily attributable to a decrease in the fair value of our fixed maturity investment portfolio as a result of increases in interest rates during the period. For the six months ended June 30, 2023, the impact of increases in interest rates on our fixed maturity investment portfolio during the second quarter of 2023 largely offset the impact of decreases in interest rates during the first quarter of 2023. The change in net unrealized losses on available-for-sale investments for the six months ended June 30, 2023 was primarily attributable to net foreign exchange gains on our fixed maturity investment portfolio. The change in net unrealized gains (losses) on available-for-sale investments for both the quarter and six months ended June 30, 2022 was primarily attributable to a decrease in the fair value of our fixed maturity investment portfolio as a result of increases in interest rates during the first half of 2022. As of June 30, 2023, our fixed maturity portfolio had an average rating of "AAA," with 99% rated "A" or better by at least one nationally recognized rating organization.
Taxable equivalent total investment return is a non-GAAP financial measure. Taxable equivalent total investment return includes items that impact net income, such as coupon interest on fixed maturity securities, changes in fair value of equity securities, dividends on equity securities and realized investment gains or losses on available-for-sale securities, as well as changes in unrealized gains or losses on available-for-sale securities, which do not impact net income. Certain items that are included in net investment income have been excluded from the calculation of taxable equivalent total investment return, such as amortization and accretion of premiums and discounts on our fixed maturity portfolio, to provide a comparable basis for measuring our investment return against industry investment returns. The calculation of taxable equivalent total investment return also includes the current tax benefit associated with income on certain investments that is either taxed at a lower rate than the statutory income tax rate or is not fully included in U.S. taxable income. We believe the taxable equivalent total investment return is a better reflection of the economics of our decision to invest in certain asset classes. We focus on our long-term investment return, understanding that the level of investment gains or losses may vary from one period to the next.
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The following table reconciles investment yield to taxable equivalent total investment return.

| Six Months Ended June 30,
| 2023 |  | 2022
Investment yield (1) | 1.5 | % |  | 1.0 | %
Adjustment of investment yield from amortized cost to fair value | (0.3) | % |  | (0.3) | %
Net amortization of net premium on fixed maturity securities | 0.1 | % |  | 0.2 | %
Net investment gains (losses) and change in net unrealized investment gains (losses) on available-for-sale securities | 3.4 | % |  | (12.2) | %
Taxable equivalent effect for interest and dividends (2) | — | % |  | — | %
Other (3) | 0.4 | % |  | 0.6 | %
Taxable equivalent total investment return | 5.1 | % |  | (10.7) | %

(1) Investment yield reflects net investment income as a percentage of monthly average invested assets at amortized cost.
(2) Adjustment to tax-exempt interest and dividend income to reflect a taxable equivalent basis.
(3) Adjustment to reflect the impact of time-weighting the inputs to the calculation of taxable equivalent total investment return.
Markel Ventures Results
Our Markel Ventures segment includes a diverse portfolio of businesses from different industries that offer various types of products and services to businesses and consumers, predominantly in the United States. Our strategy in acquiring these businesses is to invest in profitable companies, with honest and talented management, that exhibit reinvestment opportunities and capital discipline, at reasonable prices. We measure Markel Ventures' results by its operating income and net income, as well as earnings before interest, income taxes, depreciation and amortization (EBITDA). We consolidate the results of our Markel Ventures subsidiaries on a one-month lag, with the exception of significant transactions or events that occur during the intervening period.
The following table summarizes the operating revenues, operating income, EBITDA and net income to shareholders from our Markel Ventures segment.

| Quarter Ended June 30, |  | Six Months Ended June 30,
(dollars in thousands) | 2023 |  | 2022 |  | % Change |  | 2023 |  | 2022 |  | % Change
Operating revenues | $ | 1,386,579 |  |  | $ | 1,361,398 |  |  | 2 | % |  | $ | 2,491,259 |  |  | $ | 2,311,790 |  |  | 8 | %
Operating income | $ | 150,191 |  |  | $ | 107,046 |  |  | 40 | % |  | $ | 222,818 |  |  | $ | 156,783 |  |  | 42 | %
EBITDA | $ | 197,469 |  |  | $ | 154,154 |  |  | 28 | % |  | $ | 317,010 |  |  | $ | 249,859 |  |  | 27 | %
Net income to shareholders | $ | 93,804 |  |  | $ | 68,205 |  |  | 38 | % |  | $ | 133,227 |  |  | $ | 93,985 |  |  | 42 | %

The increases in operating revenues for the quarter and six months ended June 30, 2023 compared to the same periods of 2022 were driven by higher revenues at our construction services businesses and one of our equipment manufacturing businesses, primarily due to increased demand and higher prices. For the quarter ended June 30, 2023, operating revenues at one of our construction services businesses decreased compared to the same period of 2022, primarily due to lower demand. For the six months ended June 30, 2023, the increase in operating revenues also reflected a full six-month contribution from Metromont in 2023, compared to a partial contribution in 2022 following its acquisition. For both the quarter and six months ended June 30, 2023, these increases were partially offset by the impact of decreased demand at our other consumer and building products businesses and our consulting services businesses.
The increases in operating income, EBITDA and net income to shareholders for the quarter and six months ended June 30, 2023 compared to the same periods of 2022 were driven by our products businesses, particularly our consumer and building products businesses, which had higher margins in 2023 compared to 2022. In 2022, the operating margins at many of these businesses were impacted by increased costs of materials, freight and labor, which reflected the impact of broader economic conditions. As conditions stabilized in 2023, particularly in regards to materials and freight costs, our operating margins improved. The increases in operating income, EBITDA and net income to shareholders for the quarter and six months ended June 30, 2023 at many of our businesses were partially offset by the impact of lower operating margins at one of our construction services businesses and lower revenues at our consulting services businesses.
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Markel Ventures EBITDA is a non-GAAP financial measure. We use Markel Ventures EBITDA as an operating performance measure in conjunction with U.S. GAAP measures, including operating revenues, operating income and net income to shareholders, to monitor and evaluate the performance of our Markel Ventures segment. Because EBITDA excludes interest, income taxes, depreciation and amortization, it provides an indicator of economic performance that is useful to both management and investors in evaluating our Markel Ventures businesses as it is not affected by levels of debt, interest rates, effective tax rates or levels of depreciation or amortization resulting from purchase accounting. The following table reconciles Markel Ventures operating income to Markel Ventures EBITDA.

| Quarter Ended June 30, |  | Six Months Ended June 30,
(dollars in thousands) | 2023 |  | 2022 |  | 2023 |  | 2022
Markel Ventures operating income | $ | 150,191 |  |  | $ | 107,046 |  |  | $ | 222,818 |  |  | $ | 156,783 |
Depreciation expense | 27,419 |  |  | 26,531 |  |  | 54,782 |  |  | 51,566 |
Amortization of intangible assets | 19,859 |  |  | 20,577 |  |  | 39,410 |  |  | 41,510 |
Markel Ventures EBITDA | $ | 197,469 |  |  | $ | 154,154 |  |  | $ | 317,010 |  |  | $ | 249,859 |

Interest Expense, Net Foreign Exchange Gains (Losses) and Income Taxes
Interest Expense
Interest expense was $47.2 million and $96.7 million for the quarter and six months ended June 30, 2023, respectively, compared to $50.1 million and $99.7 million for the same periods of 2022. The decrease in interest expense for the quarter and six months ended June 30, 2023 was attributable to the impact of the retirement of our 4.9% unsecured senior notes in July 2022 and our 3.625% unsecured senior notes in March 2023. See note 10 of the notes to consolidated financial statements for further details regarding the retirement of our senior long-term debt.
Net Foreign Exchange Gains (Losses)
Net foreign exchange losses included in net income were $15.0 million and $47.9 million for the quarter and six months ended June 30, 2023, respectively, compared to net foreign exchange gains of $105.1 million and $128.1 million for the same periods of 2022. Net foreign exchange gains (losses) are primarily due to the remeasurement of our foreign currency denominated insurance reserves to the U.S. Dollar. During the first half of 2023, the U.S. Dollar weakened against the Euro and British Pound, the predominant foreign currencies within our insurance operations, while it strengthened during the first half of 2022. Pre-tax net foreign exchange gains and losses attributed to changes in exchange rates on available-for-sale securities supporting our insurance reserves, which are included in the changes in net unrealized gains (losses) on available-for-sale investments in other comprehensive income (losses), were gains of $1.2 million and $35.2 million for the quarter and six months ended June 30, 2023, respectively, compared to losses of $92.3 million and $108.3 million for the same periods of 2022.
Income Taxes
The effective tax rate was 21% and 22% for the six months ended June 30, 2023 and 2022, respectively.
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Comprehensive Income (Loss) to Shareholders and Book Value per Common Share
The following table summarizes the components of comprehensive income (loss) to shareholders.

| Quarter Ended June 30, |  | Six Months Ended June 30,
(dollars in thousands) | 2023 |  | 2022 |  | 2023 |  | 2022
Net income (loss) to shareholders | $ | 695,511 |  |  | $ | (915,796) |  |  | $ | 1,184,163 |  |  | $ | (967,537) |
Other comprehensive income (loss): |  |  |  |  |  |  |
Change in net unrealized gains (losses) on available-for-sale investments, net of taxes | (134,586) |  |  | (361,131) |  |  | 29,614 |  |  | (881,894) |
Change in discount rate for life and annuity benefits, net of taxes | 3,224 |  |  | 63,198 |  |  | (5,828) |  |  | 123,891 |
Other, net of taxes | 379 |  |  | (3,902) |  |  | 2,976 |  |  | (4,018) |
Other comprehensive (income) loss attributable to noncontrolling interest | 21 |  |  | (57) |  |  | (11) |  |  | (44) |
Other comprehensive income (loss) to shareholders | (130,962) |  |  | (301,892) |  |  | 26,751 |  |  | (762,065) |
Comprehensive income (loss) to shareholders | $ | 564,549 |  |  | $ | (1,217,688) |  |  | $ | 1,210,914 |  |  | $ | (1,729,602) |

Book value per common share was $1,023.23 as of June 30, 2023 compared to $935.65 at December 31, 2022.
Financial Condition
Liquidity and Capital Resources
We seek to maintain prudent levels of liquidity and financial leverage for the protection of our policyholders, creditors and shareholders. Our consolidated debt to capital ratio was 21% at June 30, 2023 and 24% at December 31, 2022. The decrease reflects a decrease in senior long-term debt, primarily attributable to the retirement of our 3.625% unsecured senior notes due March 30, 2023, as well as an increase in shareholders' equity.
Investments, cash and cash equivalents and restricted cash and cash equivalents (invested assets) were $28.7 billion and $27.4 billion at June 30, 2023 and December 31, 2022, respectively. The following table presents the composition of our invested assets.

| June 30, 2023 |  | December 31, 2022
Fixed maturity securities | 45 | % |  | 43 | %
Equity securities | 30 | % |  | 28 | %
Short-term investments, cash and cash equivalents and restricted cash and cash equivalents | 25 | % |  | 29 | %
Total | 100 | % |  | 100 | %

Our holding company had $3.2 billion and $3.7 billion of invested assets at June 30, 2023 and December 31, 2022, respectively. The decrease was due in part to the retirement of our 3.625% unsecured senior notes due March 30, 2023. The following table presents the composition of our holding company's invested assets.

| June 30, 2023 |  | December 31, 2022
Fixed maturity securities | 4 | % |  | 4 | %
Equity securities | 50 | % |  | 40 | %
Short-term investments, cash and cash equivalents and restricted cash and cash equivalents | 46 | % |  | 56 | %
Total | 100 | % |  | 100 | %

We have a share repurchase program, authorized by our Board of Directors, that provides for the repurchase of up to $750 million of common stock. As of June 30, 2023, $323.8 million remained available for repurchases under the program. This share repurchase program has no expiration date but may be terminated by the Board of Directors at any time.
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We may from time to time seek to prepay, retire or repurchase our outstanding senior notes or preferred shares, through open market purchases, privately negotiated transactions or otherwise. Those prepayments, retirements or repurchases, if any, will depend on prevailing market conditions, our liquidity requirements, contractual restrictions and other factors.
In June 2023, we entered into an amended and restated credit agreement for our corporate revolving credit facility, which provides up to $300 million of capacity for future acquisitions, investments and stock repurchases, and for other working capital and general corporate purposes. At our discretion, up to $200 million of the total capacity may be used for letters of credit. We may increase the capacity of the facility by up to $200 million subject to obtaining commitments for the increase and certain other terms and conditions. This facility expires in June 2028. The credit agreement for this revolving credit facility amended and restated the credit agreement for our previous $300 million revolving credit facility. At June 30, 2023 and December 31, 2022, there were no borrowings outstanding under either revolving credit facility. As of June 30, 2023, we were in compliance with all covenants contained in our corporate revolving credit facility. To the extent that we are not in compliance with our covenants, access to the revolving credit facility could be restricted. While we believe this to be unlikely, the inability to access the revolving credit facility could adversely affect our liquidity.
We have access to various capital sources, including dividends from certain of our subsidiaries, holding company invested assets, undrawn capacity under our revolving credit facility and access to the debt and equity capital markets. We believe we have adequate liquidity to meet our capital and operating needs, including that which may be required to support the operating needs of our subsidiaries. However, the availability of these sources of capital and the availability and terms of future financings will depend on a variety of factors.
Various of our Markel Ventures subsidiaries maintain revolving credit facilities or lines of credit, which provide up to $715 million of aggregate capacity for working capital and other general operational purposes. A portion of the capacity on certain of these credit facilities may be used as security for letters of credit and other obligations. At June 30, 2023 and December 31, 2022, we had $209.0 million and $238.1 million, respectively, of borrowings outstanding under these credit facilities. As of June 30, 2023, all of our subsidiaries were in compliance with all covenants contained in their respective credit facilities. To the extent our subsidiaries are not in compliance with their respective covenants, access to their credit facilities could be restricted, which could adversely affect their operations.
Cash Flows
Net cash provided by operating activities was $1.0 billion for the six months ended June 30, 2023 compared to $921.0 million for the same period of 2022. The increase in net cash flows from operating activities for the six months ended June 30, 2023 was primarily due to an increase in operating cash flows from Markel Ventures, partially offset by a $125.1 million payment made to complete a retroactive reinsurance transaction to cede our portfolio of policies comprised of liabilities related to our run-off book of U.K. motor casualty business.
Net cash used by investing activities was $373.6 million for the six months ended June 30, 2023 compared to $403.4 million for the same period of 2022. During the six months ended June 30, 2023, net cash used by investing activities included net purchases of fixed maturity securities and equity securities of $778.2 million and $154.6 million, respectively, and a net decrease in short-term investments of $675.3 million. During the six months ended June 30, 2022, net cash used by investing activities included net purchases of fixed maturity securities, short-term investments and equity securities of $519.9 million, $256.7 million and $63.5 million, respectively. Net cash used by investing activities for the six months ended June 30, 2022 was net of $630.0 million of net cash and restricted cash acquired as part of our consolidation of Markel CATCo Re, of which $169.4 million was subsequently distributed to Markel CATCo investors for shares that were redeemed in conjunction with the buy-out transaction. Cash flows from investing activities is affected by various factors such as anticipated payment of claims, financing activity, acquisition opportunities and individual buy and sell decisions made in the normal course of our investment portfolio management.
Net cash used by financing activities was $629.9 million for the six months ended June 30, 2023 compared to $386.7 million for the same period of 2022. During the six months ended June 30, 2023, net cash used by financing activities included $250.0 million to retire our 3.625% unsecured senior notes due March 30, 2023. In June 2022, we made a cash payment of $350.0 million to a third-party trust account to pre-fund the retirement our 4.90% unsecured senior notes, which were retired on July 1, 2022. During the six months ended June 30, 2022, we had net increases in borrowings, primarily on revolving lines of credit at two of our Markel Ventures businesses. Cash of $187.2 million and $126.3 million was used to repurchase shares of our common stock during the first six months of 2023 and 2022, respectively.
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Critical Accounting Estimates
Critical accounting estimates are those estimates that both are important to the portrayal of our financial condition and results of operations and require us to exercise significant judgment. The preparation of financial statements in accordance with U.S. GAAP requires us to make estimates and assumptions that affect the reported amounts of assets, liabilities, revenues and expenses and the disclosure of material contingent assets and liabilities. These estimates, by necessity, are based on assumptions about numerous factors.
Our critical accounting estimates consist of estimates and assumptions used in determining the reserves for unpaid losses and loss adjustment expenses as well as estimates and assumptions used in the valuation of goodwill and intangible assets. We review the adequacy of reserves for unpaid losses and loss adjustment expenses quarterly. Estimates and assumptions for goodwill and intangible assets are reviewed in conjunction with acquisitions and impairment assessments. Goodwill and indefinite-lived intangible assets are reassessed for impairment at least annually. All intangible assets, including goodwill, are also reviewed for impairment when events or circumstances indicate that their carrying value may not be recoverable. Actual results may differ materially from the estimates and assumptions used in preparing the consolidated financial statements.
Readers are urged to review our 2022 Annual Report on Form 10-K for a more complete description of our critical accounting estimates.
Safe Harbor and Cautionary Statement
This report contains statements concerning or incorporating our expectations, assumptions, plans, objectives, future financial or operating performance and other statements that are not historical facts. These statements are "forward-looking statements" within the meaning of the Private Securities Litigation Reform Act of 1995. Such statements may use words such as "anticipate," "believe," "estimate," "expect," "intend," "predict," "project" and similar expressions as they relate to us or our management.
There are risks and uncertainties that may cause actual results to differ materially from predicted results in forward-looking statements. Factors that may cause actual results to differ are often presented with the forward-looking statements themselves. Additional factors that could cause actual results to differ from those predicted are set forth under "Business," "Risk Factors," "Management's Discussion and Analysis of Financial Condition and Results of Operations" and "Quantitative and Qualitative Disclosures About Market Risk" in our 2022 Annual Report on Form 10-K, or are included in the items listed below:
•the effect of cyclical trends or changes in market conditions on our underwriting, investing, Markel Ventures and other operations, including demand and pricing in the insurance, reinsurance and other markets in which we operate;
•actions by competitors, including the use of technology and innovation to simplify the customer experience, increase efficiencies, redesign products, alter models and effect other potentially disruptive changes in the insurance industry, and the effect of competition on market trends and pricing;
•our efforts to develop new products, expand in targeted markets or improve business processes and workflows may not be successful and may increase or create new risks (e.g., insufficient demand, change to risk exposures, distribution channel conflicts, execution risk, increased expenditures);
•the frequency and severity of man-made and natural catastrophes (including earthquakes, wildfires and weather-related catastrophes) may exceed expectations, are unpredictable and, in the case of wildfires and weather-related catastrophes, may be exacerbated if, as many forecast, changing conditions in the climate, oceans and atmosphere result in increased hurricane, flood, drought or other adverse weather-related activity;
•we offer insurance and reinsurance coverage against terrorist acts in connection with some of our programs, and in other instances we are legally required to offer terrorism insurance; in both circumstances, we actively manage our exposure, but if there is a covered terrorist attack, we could sustain material losses;
•emerging claim and coverage issues, changing industry practices and evolving legal, judicial, social and other claims and coverage trends or conditions, can increase the scope of coverage, the frequency and severity of claims and the period over which claims may be reported; these factors, as well as uncertainties in the loss estimation process, can adversely impact the adequacy of our loss reserves and our allowance for reinsurance recoverables;
•reinsurance reserves are subject to greater uncertainty than insurance reserves, primarily because of reliance upon the original underwriting decisions made by ceding companies and the longer lapse of time from the occurrence of loss events to their reporting to the reinsurer for ultimate resolution;
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•inaccuracies (whether due to data error, human error or otherwise) in the various modeling techniques and data analytics (e.g., scenarios, predictive and stochastic modeling, and forecasting) we use to analyze and estimate exposures, loss trends and other risks associated with our insurance and insurance-linked securities businesses could cause us to misprice our products or fail to appropriately estimate the risks to which we are exposed;
•changes in the assumptions and estimates used in establishing reserves for our life and annuity reinsurance book (which is in runoff), for example, changes in assumptions and estimates of mortality, longevity, morbidity and interest rates, could result in material changes in our estimated loss reserves for such business;
•adverse developments in insurance coverage litigation or other legal or administrative proceedings could result in material increases in our estimates of loss reserves;
•initial estimates for catastrophe losses and other significant, infrequent events (such as the COVID-19 pandemic and the Russia-Ukraine conflict), are often based on limited information, are dependent on broad assumptions about the nature and extent of losses, coverage, liability and reinsurance, and those losses may ultimately differ materially from our expectations;
•changes in the availability, costs, quality and providers of reinsurance coverage, which may impact our ability to write or continue to write certain lines of business or to mitigate the volatility of losses on our results of operations and financial condition;
•the ability or willingness of reinsurers to pay balances due may be adversely affected by industry and economic conditions, deterioration in reinsurer credit quality and coverage disputes, and collateral we hold, if any, may not be sufficient to cover a reinsurer's obligation to us;
•after the commutation of ceded reinsurance contracts, any subsequent adverse development in the re-assumed loss reserves will result in a charge to earnings;
•regulatory actions can impede our ability to charge adequate rates and efficiently allocate capital;
•general economic and market conditions and industry specific conditions, including extended economic recessions or expansions; prolonged periods of slow economic growth; inflation or deflation; fluctuations in foreign currency exchange rates, commodity and energy prices and interest rates; volatility in the credit and capital markets; and other factors;
•economic conditions, actual or potential defaults in corporate bonds, municipal bonds, mortgage-backed securities or sovereign debt obligations, volatility in interest and foreign currency exchange rates and changes in market value of concentrated investments can have a significant impact on the fair value of our fixed maturity securities and equity securities, as well as the carrying value of our other assets and liabilities, and this impact may be heightened by market volatility and our ability to mitigate our sensitivity to these changing conditions;
•economic conditions may adversely affect our access to capital and credit markets;
•the effects of government intervention, including material changes in the monetary policies of central banks, to address financial downturns, inflation and other economic and currency concerns;
•the impacts that political and civil unrest and regional conflicts, such as the conflict between Russia and Ukraine, may have on our businesses and the markets they serve or that any disruptions in regional or worldwide economic conditions generally arising from these situations may have on our businesses, industries or investments;
•the significant volatility, uncertainty and disruption caused by health epidemics and pandemics, including the COVID-19 pandemic and its variants, as well as governmental, legislative, judicial or regulatory actions or developments in response thereto;
•changes in U.S. tax laws, regulations or interpretations, or in the tax laws, regulations or interpretations of other jurisdictions in which we operate, and adjustments we may make in our operations or tax strategies in response to those changes;
•a failure or security breach of, or cyberattack on, enterprise information technology systems that we use or a failure to comply with data protection or privacy regulations;
•third-party providers may perform poorly, breach their obligations to us or expose us to enhanced risks;
•our acquisitions may increase our operational and internal control risks for a period of time;
•we may not realize the contemplated benefits, including cost savings and synergies, of our acquisitions;
•any determination requiring the write-off of a significant portion of our goodwill and intangible assets;
•the failure or inadequacy of any methods we employ to manage our loss exposures;
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•the loss of services of any senior executive or other key personnel of our businesses could adversely impact one or more of our operations;
•the manner in which we manage our global operations through a network of business entities could result in inconsistent management, governance and oversight practices and make it difficult for us to implement strategic decisions and coordinate procedures;
•our substantial international operations and investments expose us to increased political, civil, operational and economic risks, including foreign currency exchange rate and credit risk;
•our ability to obtain additional capital for our operations on terms favorable to us;
•our compliance, or failure to comply, with covenants and other requirements under our credit facilities, senior debt and other indebtedness and our preferred shares;
•our ability to maintain or raise third-party capital for existing or new investment vehicles and risks related to our management of third-party capital;
•the effectiveness of our procedures for compliance with existing and future guidelines, policies and legal and regulatory standards, rules, laws and regulations;
•the impact of economic and trade sanctions and embargo programs on our businesses, including instances in which the requirements and limitations applicable to the global operations of U.S. companies and their affiliates are more restrictive than, or conflict with, those applicable to non-U.S. companies and their affiliates;
•regulatory changes, or challenges by regulators, regarding the use of certain issuing carrier or fronting arrangements;
•our dependence on a limited number of brokers for a large portion of our revenues and third-party capital;
•adverse changes in our assigned financial strength, debt or preferred share ratings or outlook could adversely impact us, including our ability to attract and retain business, the amount of capital our insurance subsidiaries must hold and the availability and cost of capital;
•changes in the amount of statutory capital our insurance subsidiaries are required to hold, which can vary significantly and is based on many factors, some of which are outside our control;
•losses from litigation and regulatory investigations and actions;
•investor litigation or disputes, as well as regulatory inquiries, investigations or proceedings related to our Markel CATCo operations; delays or disruptions in the run-off of those operations; or the failure to realize the benefits of the transaction that permitted the accelerated return of capital to our Markel CATCo investors; and
•a number of additional factors may adversely affect our Markel Ventures operations, and the markets they serve, and negatively impact their revenues and profitability, including, among others: adverse weather conditions, plant disease and other contaminants; changes in government support for education, healthcare and infrastructure projects; changes in capital spending levels; changes in the housing, commercial and industrial construction markets; liability for environmental matters; supply chain and shipping issues, including increases in freight costs; volatility in the market prices for their products; and volatility in commodity, wholesale and raw materials prices and interest and foreign currency exchange rates.
Results from our underwriting, investing, Markel Ventures and other operations have been and will continue to be potentially materially affected by these factors.
By making forward-looking statements, we do not intend to become obligated to publicly update or revise any such statements whether as a result of new information, future events or other changes. Readers are cautioned not to place undue reliance on any forward-looking statements, which are based on our current knowledge and speak only as at their dates.
Item 3. Quantitative and Qualitative Disclosures About Market Risk
Market risk is the risk of economic losses due to adverse changes in the estimated fair value of a financial instrument as the result of changes in equity prices, interest rates, foreign currency exchange rates and commodity prices. Our consolidated balance sheets include assets and liabilities with estimated fair values that are subject to market risk. Our primary market risks are equity price risk associated with investments in equity securities, interest rate risk associated with investments in fixed maturity securities and foreign currency exchange rate risk associated with our international operations. During the six months ended June 30, 2023, there were no material changes in our market risk exposures from those described in our 2022 Annual Report on Form 10-K.
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Credit Risk
Credit risk, which is not considered a market risk, is the risk that an entity becomes unable or unwilling to fulfill their obligations to us. Our primary credit risks are the credit risk within our fixed maturity portfolio and the credit risk related to our reinsurance recoverables within our underwriting, program services and other fronting operations. During the six months ended June 30, 2023, there were no material changes in our credit risk exposures from those described in our 2022 Annual Report on Form 10-K.
Item 4. Controls and Procedures
Evaluation of Disclosure Controls and Procedures
As of the end of the period covered by this quarterly report, we evaluated the effectiveness of the design and operation of our disclosure controls and procedures (Disclosure Controls), as defined under Rules 13a-15(e) and 15d-15(e) of the Securities Exchange Act of 1934 (Exchange Act). This evaluation was conducted under the supervision and with the participation of our management, including the Principal Executive Officer (PEO) and the Principal Financial Officer (PFO).
Based upon this evaluation, the PEO and PFO concluded that effective Disclosure Controls were in place to ensure that the information required to be disclosed in reports we file or submit under the Exchange Act is recorded, processed, summarized and reported within the time periods specified in the Securities and Exchange Commission's rules and forms.
Changes in Internal Control over Financial Reporting
There were no changes in our internal control over financial reporting during the second quarter of 2023 that materially affected, or are reasonably likely to materially affect, our internal control over financial reporting.
PART II. OTHER INFORMATION
Item 1. Legal Proceedings
Thomas Yeransian v. Markel Corporation
We previously reported that Thomas Yeransian, in his capacity as the representative of holders of certain contingent value rights, has filed three suits against the Company:
•Thomas Yeransian v. Markel Corporation (U.S. District Court for the District of Delaware), filed September 15, 2016;
•Thomas Yeransian v. Markel Corporation (U.S. District Court for the District of Delaware), filed November 13, 2018; and
•Thomas Yeransian v. Markel Corporation (U.S. District Court for the District of Delaware), filed June 5, 2020.
The three suits have been consolidated. On June 8, 2023, the court ruled in favor of the Company and against Mr. Yeransian on all counts. Mr. Yeransian has appealed the court's decision. For additional information regarding these three suits, see Item 3 Legal Proceedings in our 2022 Annual Report on Form 10-K. We believe Mr. Yeransian's suits to be without merit. We further believe that any material loss resulting from the suits to be remote.
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Item 2. Unregistered Sales of Equity Securities and Use of Proceeds
The following table summarizes our common share repurchases for the quarter ended June 30, 2023.

Issuer Purchases of Equity Securities
| (a) |  | (b) |  | (c) |  | (d)
Period | Total Number of Shares Purchased |  | Average Price Paid per Share |  | Total Number of Shares Purchased as Part of Publicly Announced Plans or Programs(1) |  | Approximate Dollar Value of Shares that May Yet Be Purchased Under the Plans or Programs (in thousands)
April 1, 2023 through April 30, 2023 | 23,900 |  |  | $ | 1,326.43 |  |  | 23,900 |  |  | $ | 396,736 |
May 1, 2023 through May 31, 2023 | 27,686 |  |  | $ | 1,351.15 |  |  | 27,686 |  |  | $ | 359,328 |
June 1, 2023 through June 30, 2023 | 26,431 |  |  | $ | 1,345.46 |  |  | 26,431 |  |  | $ | 323,766 |
Total | 78,017 |  |  | $ | 1,341.65 |  |  | 78,017 |  |  | $ | 323,766 |

(1) The Board of Directors approved the repurchase of up to $750 million of our common shares pursuant to a share repurchase program publicly announced in February 2022. Under our share repurchase program, we may repurchase outstanding common shares of our stock from time to time in privately negotiated or open market transactions, including under plans complying with Rule 10b5-1 and Rule 10b-18 under the Securities Exchange Act of 1934. The share repurchase program has no expiration date but may be terminated by the Board at any time.
Item 5. Other Information
Adoption or Termination of Trading Arrangements by Directors or Officers
On May 31, 2023, Steven A. Markel, Chair of the Board and a Director of the Company, adopted a Rule 10b5-1 trading arrangement that is intended to satisfy the affirmative defense of Rule 10b5-1(c) for the sale of up to 1,398 of the Company's common shares until May 17, 2024 (or the date on which all shares have been sold).
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Item 6. Exhibits

Exhibit No. | Document Description
3.1(a) | Amended and Restated Articles of Incorporation (incorporated by reference from Exhibit 3.1 in the Registrant's report on Form 8-K filed with the Commission May 13, 2011)
3.1(b) | Articles of Amendment to the Amended and Restated Articles of Incorporation (incorporated by reference from Exhibit 3.1 in the Registrant's report on Form 8-K filed with the Commission May 27, 2020)
3.1(c) | Articles of Amendment to the Amended and Restated Articles of Incorporation (incorporated by reference from Exhibit 3.1 in the Registrant's report on Form 8-K filed with the Commission May 16, 2023)
3.2 | Bylaws, as amended and restated May 26, 2023**
4.1(a) | Indenture dated as of June 5, 2001, between Markel Corporation and The Chase Manhattan Bank, as Trustee (incorporated by reference from Exhibit 4.1 in the Registrant's report on Form 8-K filed with the Commission June 5, 2001)
4.1(b) | Form of Third Supplemental Indenture dated as of August 13, 2004 between Markel Corporation and JPMorgan Chase Bank (formerly known as The Chase Manhattan Bank), as Trustee, including form of the securities as Exhibit A (incorporated by reference from Exhibit 4.2 in the Registrant's report on Form 8-K filed with the Commission August 11, 2004)
4.1(c) | Form of Ninth Supplemental Indenture dated as of March 8, 2013 between Markel Corporation and The Bank of New York Mellon (as successor to The Chase Manhattan Bank), as Trustee, including form of the securities as Exhibit A (incorporated by reference from Exhibit 4.3 in the Registrant's report on Form 8-K filed with the Commission March 7, 2013)
4.1(d) | Form of Tenth Supplemental Indenture dated as of April 5, 2016 between Markel Corporation and The Bank of New York Mellon (as successor to The Chase Manhattan Bank), as Trustee, including form of the securities as Exhibit A (incorporated by reference from Exhibit 4.2 in the Registrant's report on Form 8-K filed with the Commission March 31, 2016)
4.1(e) | Eleventh Supplemental Indenture dated as of November 2, 2017 between Markel Corporation and The Bank of New York Mellon (as successor to The Chase Manhattan Bank), as Trustee, including form of the securities as Exhibit A (incorporated by reference from Exhibit 4.2 in the Registrant's report on Form 8-K filed with the Commission November 2, 2017)
4.1(f) | Twelfth Supplemental Indenture dated as of November 2, 2017 between Markel Corporation and The Bank of New York Mellon (as successor to The Chase Manhattan Bank), as Trustee, including form of the securities as Exhibit A (incorporated by reference from Exhibit 4.3 in the Registrant's report on Form 8-K filed with the Commission November 2, 2017)
4.1(g) | Thirteenth Supplemental Indenture, dated as of May 20, 2019, between Markel Corporation and The Bank of New York Mellon (as successor to The Chase Manhattan Bank), as Trustee, including form of the securities as Exhibit A (incorporated by reference from Exhibit 4.2 in the Registrant's report on Form 8-K filed with the Commission May 20, 2019)
4.1(h) | Fourteenth Supplemental Indenture, dated as of September 17, 2019, between Markel Corporation and The Bank of New York Mellon (as successor to The Chase Manhattan Bank), as Trustee, including form of the securities as Exhibit A (incorporated by reference from Exhibit 4.2 in the Registrant's report on Form 8-K filed with the Commission September 17, 2019)
4.1(i) | Fifteenth Supplemental Indenture, dated as of September 17, 2019, between Markel Corporation and The Bank of New York Mellon (as successor to The Chase Manhattan Bank), as Trustee, including form of the securities as Exhibit A (incorporated by reference from Exhibit 4.3 in the Registrant's report on Form 8-K filed with the Commission September 17, 2019)
4.1(j) | Sixteenth Supplemental Indenture, dated as of May 7, 2021, between Markel Corporation and The Bank of New York Mellon (as successor to The Chase Manhattan Bank), as Trustee, including form of the securities as Exhibit A (incorporated by reference from Exhibit 4.2 in the Registrant's report on Form 8-K filed with the Commission May 7, 2021)
The registrant hereby agrees to furnish to the Securities and Exchange Commission, upon request, a copy of all other instruments defining the rights of holders of long-term debt of the registrant and its subsidiaries.
10.1 | Amended and Restated Credit Agreement, dated as of June 23, 2023, among Markel Group Inc., Markel Bermuda Limited, Markel Global Reinsurance Company, the lenders from time to time party thereto, and Wells Fargo Bank, National Association, as the administrative agent (incorporated by reference from Exhibit 10.1 in the Registrant's report on Form 8-K filed with the Commission June 23, 2023)

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10.2 | Form of Amended and Restated Executive Employment Agreement with Robert C. Cox, Andrew G. Crowley, Thomas S. Gayner, Teresa S. Gendron, Richard R. Grinnan, Michael R. Heaton, and Jeremy A. Noble* **
31.1 | Certification of Principal Executive Officer Pursuant to Rule 13a-14(a)/15d-14(a)**
31.2 | Certification of Principal Financial Officer Pursuant to Rule 13a-14(a)/15d-14(a)**
32.1 | Certification furnished Pursuant to 18 U.S.C. Section 1350**
101 | The following consolidated financial statements from Markel Group's Quarterly Report on Form 10-Q for the quarter ended June 30, 2023, filed on August 2, 2023, formatted in Inline XBRL: (i) Consolidated Balance Sheets, (ii) Consolidated Statements of Income (Loss) and Comprehensive Income (Loss), (iii) Consolidated Statements of Changes in Equity, (iv) Condensed Consolidated Statements of Cash Flows and (v) Notes to Consolidated Financial Statements.**
104 | Cover Page Interactive Data File (embedded within the Inline XBRL document)

* Indicates management contract or compensatory plan or arrangement
** Filed with this report
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Signatures
Pursuant to the requirements of the Securities Exchange Act of 1934, the registrant has duly caused this report to be signed on its behalf by the undersigned, thereunto duly authorized, this 2 nd day of August 2023.

| Markel Group Inc.
| By: | /s/ Thomas S. Gayner
|  | Thomas S. Gayner
|  | Chief Executive Officer
|  | (Principal Executive Officer)
| By: | /s/ Teresa S. Gendron
|  | Teresa S. Gendron
|  | Chief Financial Officer
|  | (Principal Financial Officer)

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