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Share-Based Compensation
 12 Months Ended
Dec. 31, 2024
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, 2024, 6.7 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 eligible employees and directors. The 2018 Plan authorizes the issuance of 34.5 million common shares; provided that no more than 6.0 million common shares may be issued as incentive stock options under Section 422 of the Code. The 2018 Plan will terminate as to future awards on February 28, 2028. At December 31, 2024, 2.7 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 12.75 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, 2024, 3.2 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 (adjusted for special dividends). Such grants generally vest over a three year period with one-third vesting on the first, second and third anniversaries of the grant date. In connection with the Company’s recent leadership transition in November 2024, the Compensation and Human Capital Committee approved the grant of equity awards, which consist of 1.75 million premium-priced stock options to eligible employees. The premium-priced stock options have an exercise price equal to 1.685 times the closing price of the Company's common shares on the grant date (or $161.24 per share) and will vest in full on the third anniversary 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,
202420232022
Dividend yield— %— %— %
Expected volatility (1)26.5 %25.1 %24.0 %
Risk free interest rate (1)4.4 %4.1 %2.0 %
Expected option life (1)9.0 years6.0 years6.0 years
(1) The 2024 period includes an expected volatility, risk free interest rate and expected option life of 26.65%, 4.39% and 10 years, respectively, related to the grant of 1.75 million premium-priced stock options.
A summary of stock option and SAR activity under the Company’s Long Term Incentive and Share Award Plans during 2024 is presented below:
Year Ended December 31, 2024
Number of
Options / SARs		Weighted Average Exercise PriceWeighted Average Contractual TermAggregate Intrinsic Value
Outstanding, beginning of year12,536,593 $31.14 
Granted (1)2,172,916 $145.88 
Exercised(2,270,334)$22.82 
Forfeited or expired(10,141)$46.47 
Outstanding, end of year12,429,034 $48.54 4.69$665 
Exercisable, end of year9,710,426 $26.55 3.40$639 
(1) Includes 1.75 million premium-priced stock options with a weighted average exercise price of $161.24 per share.
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 2024, the Company received proceeds of $19 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,
202420232022
Weighted average grant date fair value$29.03 $23.50 $13.26 
Aggregate intrinsic value of Options/SARs exercised (in millions)$153 $116 $113 
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 2024 is presented below:
Number of Restricted
Common
Shares
Number of Restricted
Unit
Awards
Unvested Shares:
Unvested balance, beginning of year1,524,605 305,928 
Granted835,843 146,496 
Vested(809,174)(154,710)
Forfeited(22,733)(16,621)
Unvested balance, end of year1,528,541 281,093 
Weighted Average Grant Date Fair Value:
Unvested balance, beginning of year$54.57 $55.63 
Granted$90.32 $87.21 
Vested$49.88 $50.57 
Forfeited$72.05 $77.53 
Unvested balance, end of year$76.34 $73.58 
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,
202420232022
Number of restricted shares and restricted unit awards granted 982,339 825,191 1,089,393 
Weighted average grant date fair value$89.86 $69.42 $47.45 
Aggregate fair value of vested restricted share and unit awards (in millions)$85 $122 $51 
The aggregate intrinsic value of restricted units outstanding at December 31, 2024 was $26 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,
202420232022
Expected volatility25.3 %30.4 %38.1 %
Risk free interest rate4.5 %4.6 %1.7 %
Number of Performance
Shares
Number of Performance
Units
Unvested Shares:
Unvested balance, beginning of year1,880,696 49,594 
Granted476,906 15,728 
Performance adjustment (1) (2)— 10,698 
Vested(674,406)(21,396)
Forfeited(3,820)(1,687)
Unvested balance, end of year1,679,376 52,937 
Weighted Average Grant Date Fair Value:
Unvested balance, beginning of year$52.47 $56.15 
Granted$93.28 $93.24 
Performance adjustment (1) (2)$0.00 $37.38 
Vested$37.38 $37.38 
Forfeited$75.41 $68.61 
Unvested balance, end of year$70.07 $70.57 
(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,
202420232022
Number of performance awards492,634 568,576 690,772 
Weighted average grant date fair value$93.28 $74.09 $49.91 
Aggregate fair value of vested performance share and unit awards (in millions)$61 $14 $27 
The aggregate intrinsic value of performance units outstanding at December 31, 2024 was $5 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,
202420232022
Pre-Tax
Stock options and SARs$15 $11 $12 
Restricted share and unit awards57 54 50 
Performance awards55 23 22 
ESPP6 4 4 
Total$133 $92 $88 
After-Tax
Stock options and SARs$13 $10 $11 
Restricted share and unit awards48 45 42 
Performance awards50 21 20 
ESPP5 4 4 
Total$116 $80 $77 

December 31, 2024
Stock Options and SARs (1)Restricted Common
Shares and Units (1)		Performance Common Shares and Units
Unrecognized compensation cost related to unvested awards$55 $70 $12 
Weighted average recognition period (years)2.081.210.38
(1) Includes awards granted in connection with 1.75 million premium-priced stock options and 0.3 million time-vested restricted shares granted in November 2024.