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Share-Based Compensation
 12 Months Ended
Dec. 31, 2023
Share-Based Payment Arrangement [Abstract]  
Share-Based Compensation
Long Term Incentive and Share Award Plans
The Company utilizes share-based compensation plans for officers, other employees and directors of Arch Capital and its subsidiaries to provide competitive compensation opportunities, to encourage long-term service, to recognize individual contributions and reward achievement of performance goals and to promote the creation of long-term value for shareholders by aligning the interests of such persons with those of shareholders.
The 2022 Long-Term Incentive and Share Award Plan (“the 2022 Plan”) became effective as of May 4, 2022 following approval by shareholders of the Company. The 2022 Plan provides for the issuance of stock options, stock appreciation rights, restricted shares, restricted share units payable in common shares or cash, dividend equivalents, performance shares and performance units and other share-based awards to Arch Capital’s eligible employees and directors. The number of common shares reserved for grants under the 2022 Plan, subject to anti-dilution adjustments in the event of certain changes in Arch Capital’s capital structure, is 9.0 million; provided that no more than 6.0 million common
shares may be issued as incentive stock options under Section 422 of the Code. The 2022 Plan will terminate as to future awards on February 25, 2032. At December 31, 2023, 7.8 million shares are available for future issuance.
The 2018 Long-Term Incentive and Share Award Plan (the “2018 Plan”) became effective as of May 9, 2018 following approval by shareholders of the Company. The 2018 Plan provides for the issuance of restricted stock units, performance units, restricted shares, performance shares, stock options and stock appreciation rights and other equity-based awards to our employees and directors. The 2018 Plan authorizes the issuance of 34.5 million common shares and will terminate as to future awards on February 28, 2028. At December 31, 2023, 5.8 million shares are available for future issuance.
Upon shareholder approval on May 4, 2023, the Amended and Restated Arch Capital Group Ltd. 2007 Employee Share Purchase Plan (the “ESPP”) became effective. The total common shares that may be purchased under the ESPP was increased by 3.0 million shares for a total of 12.8 million shares authorized. The purpose of the ESPP is to give employees of the Company an opportunity to purchase common shares through payroll deductions, thereby encouraging employees to share in the economic growth and success of the Company. The ESPP is designed to qualify as an “employee share purchase plan” under Section 423 of the Internal Revenue Code of 1986, as amended. At December 31, 2023, 3.6 million shares remain available for issuance.
Stock Options and Stock Appreciation Rights
The Company generally issues stock options and SARs to eligible employees, with exercise prices equal to the fair market values of the Company’s Common Shares on the grant dates. Such grants generally vest over a three year period with one-third vesting on the first, second and third anniversaries of the grant date.
The grant date fair value is determined using the Black-Scholes option valuation model. The expected life assumption is based on an expected term analysis, which incorporates the Company’s historical exercise experience. Expected volatility is based on the Company’s daily historical trading data of its common shares. The table below summarizes the assumptions used.
Year Ended December 31,
202320222021
Dividend yield— %— %— %
Expected volatility25.1 %24.0 %24.2 %
Risk free interest rate4.1 %2.0 %1.0 %
Expected option life6.0 years6.0 years6.0 years
A summary of stock option and SAR activity under the Company’s Long Term Incentive and Share Award Plans during 2023 is presented below:
Year Ended December 31, 2023
Number of
Options / SARs		Weighted Average Exercise PriceWeighted Average Contractual TermAggregate Intrinsic Value
Outstanding, beginning of year14,420,901 $28.17 
Granted479,760 $69.24 
Exercised(2,355,729)$20.66 
Forfeited or expired(8,339)$48.38 
Outstanding, end of year12,536,593 $31.14 4.10$541 
Exercisable, end of year11,205,102 $28.68 3.61$511 
The aggregate intrinsic value of stock options and SARs exercised represents the difference between the exercise price of the stock options and SARs and the closing market price of the Company’s common shares on the exercise dates. During 2023, the Company received proceeds of $20 million from the exercise of stock options and recognized a tax benefit of $9 million from the exercise of stock options and SARs.
Year Ended December 31,
202320222021
Weighted average grant date fair value$23.50 $13.26 $9.22 
Aggregate intrinsic value of Options/SARs exercised (in millions)$116 $113 $47 
Restricted Common Shares and Restricted Units
The Company also issues restricted share and unit awards to eligible employees and directors, for which the fair value is equal to the fair market values of the Company’s Common Shares on the grant dates. Restricted share and unit awards generally vest over a three year period with one-third vesting on the first, second and third anniversaries of the grant date.
A summary of restricted share and restricted unit activity under the Company’s Long Term Incentive and Share Award Plans for 2023 is presented below:
Number of Restricted
Common
Shares
Number of Restricted
Unit
Awards
Unvested Shares:
Unvested balance, beginning of year2,165,554 517,293 
Granted678,657 146,534 
Vested(1,281,449)(352,190)
Forfeited(38,157)(5,709)
Unvested balance, end of year1,524,605 305,928 
Weighted Average Grant Date Fair Value:
Unvested balance, beginning of year$40.23 $37.17 
Granted$69.47 $69.20 
Vested$38.37 $34.16 
Forfeited$49.65 $55.55 
Unvested balance, end of year$54.57 $55.63 
The following table presents the weighted average grant date fair value of restricted shares and restricted unit awards granted and the aggregate fair value of restricted shares and unit awards vesting in each year.
Year Ended December 31,
202320222021
Number of restricted shares and restricted unit awards granted 825,191 1,089,393 1,261,773 
Weighted average grant date fair value$69.42 $47.45 $36.12 
Aggregate fair value of vested restricted share and unit awards (in millions)$122 $51 $41 
The aggregate intrinsic value of restricted units outstanding at December 31, 2023 was $23 million, and the aggregate intrinsic value of restricted units vested and deferred was $0.4 million.
Performance Awards
The Company also issues performance share and unit awards (“performance awards”) to eligible employees, which are earned based on the achievement of pre-established threshold, target and maximum goals over three-year performance periods. Final payouts depend on the level of achievement along with each employees continued service through the vest date, and can vary between 0% and 200%. The grant date fair value of the performance awards is measured using a Monte Carlo simulation model, which incorporated the assumptions summarized in the table below. Expected volatility is based on the Company’s daily historical trading data of its common shares. The cumulative compensation expense recognized and unrecognized as of any reporting period date represents the adjusted estimate of performance shares and units that will ultimately be awarded, valued at their original grant date fair values.
Year Ended December 31,
202320222021
Expected volatility30.4 %38.1 %37.5 %
Risk free interest rate4.6 %1.7 %0.3 %
Number of Performance
Shares
Number of Performance
Units
Unvested Shares:
Unvested balance, beginning of year1,882,916 39,710 
Granted550,394 18,182 
Performance adjustment (1) (2)(341,420)(2,024)
Vested(207,486)(6,274)
Forfeited(3,708)— 
Unvested balance, end of year1,880,696 49,594 
Weighted Average Grant Date Fair Value:
Unvested balance, beginning of year$43.75 $45.33 
Granted$74.08 $74.31 
Performance adjustment (1) (2)$44.17 $44.17 
Vested$44.17 $44.17 
Forfeited$59.83 $— 
Unvested balance, end of year$52.47 $56.15 
(1)    The performance adjustment represents the difference between the number of performance shares granted and earned, which vested following the end of the performance period. The performance shares were granted at the maximum level of achievement.
(2)    The performance adjustment represents the change in PSUs, which vested following the end of the performance period. The performance units were granted at the target level of achievement.

The following table presents the weighted average grant date fair values of performance awards granted.
Year Ended December 31,
202320222021
Number of performance awards568,576 690,772 685,104 
Weighted average grant date fair value$74.09 $49.91 $37.38 
Aggregate fair value of vested performance share and unit awards (in millions)$14 $27 $24 
The aggregate intrinsic value of performance units outstanding at December 31, 2023 was $4 million.
The issuance of share-based awards and amortization thereon has no effect on the Company’s consolidated shareholders’ equity.
Share-Based Compensation Expense
The following tables present pre-tax and after-tax share-based compensation expense recognized as well as the unrecognized compensation cost associated with unvested awards and the weighted average period over which it is expected to be recognized.
Year Ended December 31,
202320222021
Pre-Tax
Stock options and SARs$11 $12 $12 
Restricted share and unit awards54 50 47 
Performance awards23 22 24 
ESPP4 4 4 
Total$92 $88 $87 
After-Tax
Stock options and SARs$10 $11 $11 
Restricted share and unit awards45 42 39 
Performance awards21 20 22 
ESPP4 4 4 
Total$80 $77 $76 
December 31, 2023
Stock Options and SARsRestricted Common
Shares and Units		Performance Common Shares and Units
Unrecognized compensation cost related to unvested awards$7 $43 $11 
Weighted average recognition period (years)0.670.950.44