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Share-Based Compensation | 12 Months Ended
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Dec. 31, 2022
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 9,000,000; provided that no more than 6,000,000 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, 2022, 9,000,000 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 34,500,000 common shares and will terminate as to future awards on February 28, 2028. At December 31, 2022, 4,577,991 shares are available for future issuance. The 2015 Long Term Incentive and Share Award Plan (the (“2015 Plan”) authorizes the issuance of 12,900,000 common shares and became effective as of May 7, 2015 following approval by shareholders of the Company. The 2015 Plan provides for the issuance of share-based awards to our employees and directors and will terminate as to future awards on February 26, 2025. At December 31, 2022, 504,872 shares are available for future issuance. Upon shareholder approval on May 6, 2016, the Amended and Restated Arch Capital Group Ltd. 2007 Employee Share Purchase Plan (the “ESPP”) became effective and a total of 4,689,777 common shares were reserved for issuance. The purpose of the ESPP is to give employees of Arch Capital and its subsidiaries an opportunity to purchase common shares through payroll deductions, thereby encouraging employees to share in the economic growth and success of Arch Capital and its subsidiaries. The ESPP is designed to qualify as an “employee share purchase plan” under Section 423 of the Code. At December 31, 2022, 1,041,837 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,
| 2022 |  | 2021 |  | 2020
Dividend yield | — | % |  | — | % |  | — | %
Expected volatility | 24.0 | % |  | 24.2 | % |  | 16.6 | %
Risk free interest rate | 2.0 | % |  | 1.0 | % |  | 1.2 | %
Expected option life | 6.0 years |  | 6.0 years |  | 6.0 years
A summary of stock option and SAR activity under the Company’s Long Term Incentive and Share Award Plans during 2022 is presented below:
| Year Ended December 31, 2022
| Number of Options / SARs |  | Weighted Average Exercise Price |  | Weighted Average Contractual Term |  | Aggregate Intrinsic Value
Outstanding, beginning of year | 17,083,160 |  |  | $ | 25.06 |  |  |  |  |
Granted | 784,963 |  |  | $ | 47.46 |  |  |  |  |
Exercised | (3,412,371) |  |  | $ | 16.91 |  |  |  |  |
Forfeited or expired | (34,851) |  |  | $ | 39.96 |  |  |  |  |
Outstanding, end of year | 14,420,901 |  |  | $ | 28.17 |  |  | 4.37 |  | $ | 499,051 |
Exercisable, end of year | 12,433,470 |  |  | $ | 26.20 |  |  | 3.77 |  | $ | 454,769 |
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 2022, the Company received proceeds of $17.2 million from the exercise of stock options and recognized a tax benefit of $8.7 million from the exercise of stock options and SARs.
| Year Ended December 31,
| 2022 |  | 2021 |  | 2020
Weighted average grant date fair value | $ | 13.26 |  |  | $ | 9.22 |  |  | $ | 8.14 |
Aggregate intrinsic value of Options/SARs exercised | $ | 113,409 |  |  | $ | 47,074 |  |  | $ | 59,723 |
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 2022 is presented below:
| Restricted Common Shares |  | Restricted Unit Awards
Unvested Shares: |  |  |
Unvested balance, beginning of year | 2,070,837 |  |  | 699,866 |
Granted | 914,694 |  |  | 174,699 |
Vested | (744,096) |  |  | (330,144) |
Forfeited | (75,881) |  |  | (27,128) |
Unvested balance, end of year | 2,165,554 |  |  | 517,293 |
Weighted Average Grant Date Fair Value: |  |  |
Unvested balance, beginning of year | $ | 36.35 |  |  | $ | 33.29 |
Granted | $ | 47.45 |  |  | $ | 47.50 |
Vested | $ | 38.21 |  |  | $ | 34.38 |
Forfeited | $ | 41.13 |  |  | $ | 37.51 |
Unvested balance, end of year | $ | 40.23 |  |  | $ | 37.17 |
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,
| 2022 |  | 2021 |  | 2020
Restricted shares and restricted unit awards granted | 1,089,393 |  |  | 1,261,773 |  |  | 1,535,330 |
Weighted average grant date fair value | $ | 47.45 |  |  | $ | 36.12 |  |  | $ | 37.55 |
Aggregate fair value of vested restricted share and unit awards | $ | 78,129 |  |  | $ | 65,477 |  |  | $ | 39,703 |
The aggregate intrinsic value of restricted units outstanding at December 31, 2022 was $32.5 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,
| 2022 |  | 2021 |  | 2020
Expected volatility | 38.1 | % |  | 37.5 | % |  | 18.1 | %
Risk free interest rate | 1.7 | % |  | 0.3 | % |  | 1.1 | %
| Performance Shares |  | Performance Units
Unvested Shares: |  |  |
Unvested balance, beginning of year | 1,861,760 |  |  | 29,770 |
Granted | 669,742 |  |  | 21,030 |
Performance adjustment (1) (2) | (54,904) |  |  | 8,921 |
Vested | (583,544) |  |  | (19,695) |
Forfeited | (10,138) |  |  | (316) |
Unvested balance, end of year | 1,882,916 |  |  | 39,710 |
Weighted Average Grant Date Fair Value: |  |  |
Unvested balance, beginning of year | $ | 38.93 |  |  | $ | 38.71 |
Granted | $ | 49.91 |  |  | $ | 49.91 |
Performance adjustment (1) (2) | $ | 36.07 |  |  | $ | 35.83 |
Vested | $ | 36.07 |  |  | $ | 35.83 |
Forfeited | $ | 49.91 |  |  | $ | 49.91 |
Unvested balance, end of year | $ | 43.75 |  |  | $ | 45.33 |
(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,
| 2022 |  | 2021 |  | 2020
Performance awards | 690,772 |  |  | 685,104 |  |  | 557,204 |
Weighted average grant date fair value | $ | 49.91 |  |  | $ | 37.38 |  |  | $ | 44.17 |
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,
| 2022 |  | 2021 |  | 2020
Pre-Tax |  |  |  |  |
Stock options and SARs | $ | 11,891 |  |  | $ | 12,316 |  |  | $ | 11,744 |
Restricted share and unit awards | 50,278 |  |  | 46,817 |  |  | 41,284 |
Performance awards | 21,510 |  |  | 23,696 |  |  | 14,729 |
ESPP | 3,993 |  |  | 3,751 |  |  | 2,135 |
Total | $ | 87,672 |  |  | $ | 86,580 |  |  | $ | 69,892 |
After-Tax |  |  |  |  |
Stock options and SARs | $ | 10,726 |  |  | $ | 10,927 |  |  | $ | 10,388 |
Restricted share and unit awards | 42,346 |  |  | 39,349 |  |  | 34,599 |
Performance awards | 19,794 |  |  | 21,920 |  |  | 13,380 |
ESPP | 3,660 |  |  | 3,471 |  |  | 1,978 |
Total | $ | 76,526 |  |  | $ | 75,667 |  |  | $ | 60,345 |
| December 31, 2022
| Stock Options and SARs |  | Restricted Common Shares and Units |  | Performance Common Shares and Units
Unrecognized compensation cost related to unvested awards | $ | 6,357 |  |  | $ | 42,096 |  |  | $ | 7,520 |
Weighted average recognition period (years) | 0.75 |  | 1.00 |  | 0.48

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