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Share Transactions
6 Months Ended
Jun. 30, 2017
Stockholders' Equity Note [Abstract]  
Share Transactions
Share Transactions

Share-Based Compensation
During the 2017 second quarter, the Company granted 492,466 stock options and 511,636 restricted shares and units to certain employees and directors with weighted average grant-date fair values of $24.66 and $96.28, respectively. During the 2016 second quarter, the Company granted 427,379 stock options and 456,217 restricted shares and units to certain employees and directors with weighted average grant-date fair values of $17.46 and $71.61, respectively. The stock options were valued at the grant date using the Black-Scholes option pricing model. Such values are being amortized over the respective substantive vesting period. For awards granted to retirement-eligible employees where no service is required for the employee to retain the award, the grant date fair value is immediately recognized as compensation expense at the grant date because the employee is able to retain the award without continuing to provide service. For employees near retirement eligibility, attribution of compensation cost is recognized over the period from the grant date to the retirement eligibility date.
Share Repurchases 
The board of directors of ACGL has authorized the investment in ACGL’s common shares through a share repurchase program. Since the inception of the share repurchase program, ACGL has repurchased approximately 125.2 million common shares for an aggregate purchase price of $3.68 billion. For the six months ended June 30, 2017, the Company did not repurchase any shares under the share repurchase program, compared to 1.1 million common shares repurchased for the six months ended June 30, 2016 with an aggregate purchase price of $75.3 million (no repurchases in the 2016 second quarter). At June 30, 2017, $446.5 million of share repurchases were available under the program, which may be effected from time to time in open market or privately negotiated transactions through December 31, 2019. The timing and amount of the repurchase transactions under this program will depend on a variety of factors, including market conditions and corporate and regulatory considerations.
Conversion of Convertible Non-Voting Common Equivalent Preferred Shares  
On June 8, 2017, ACGL and AIG entered into Amendment No. 1 (the “Amendment”) to the Investor Rights Agreement (the “Investor Rights Agreement”) dated as of December 31, 2016 to amend the restrictions on transfers of the 1,276,282 shares of ACGL’s convertible non-voting common-equivalent preference shares owned by AIG (the “Convertible Preferred Shares”). The Convertible Preferred Shares were issued to AIG as part of the consideration in UGC acquisition. Pursuant to the certificate of designations for the Convertible Preferred Shares and in accordance with the terms and conditions set forth therein, each Convertible Preferred Share is convertible into ten common shares of ACGL.
Pursuant to the Amendment, ACGL permitted AIG to transfer: (i) 638,141 Convertible Preferred Shares from and after June 8, 2017, and up to an additional 95,721 of the Convertible Preferred Shares to the extent that the several underwriters exercise the option to purchase additional securities expected to be granted pursuant to an underwritten secondary offering of AGCL common shares issuable upon conversion of the Convertible Preferred Shares by AIG and (ii) any and all of the Convertible Preferred Shares from and after January 15, 2018, subject to certain exceptions, and in each case subject to the terms and conditions of the Investor Rights Agreement. All other terms of the Investor Rights Agreement remain in effect.
In June 2017, ACGL completed an underwritten public secondary offering of 7,088,620 common shares by AIG following transfer of 708,862 Convertible Preferred Shares. Proceeds from the sale of common shares pursuant to the public offering were received by AIG. At June 30, 2017, 567,420 Convertible Preferred Shares were outstanding.