Share-based Compensation

The fair value method of accounting is used for share-based compensation plans. Under the fair value method, compensation cost is measured based on the fair value of the award at the measurement date and recognized over the requisite service period. We use the Black-Scholes model to estimate the fair values on the measurement date for share options and share appreciation rights (“SARs”). The Black-Scholes model uses several assumptions to value a share award. The risk-free rate of return assumption is based on the five-year U.S. Treasury constant maturity rate on the measurement date. The expected dividend yield is based on our history and expected dividend payouts. The expected award life is based upon the average holding period over the history of the incentive plan. The expected volatility assumption is based on the historical change in our stock price over the previous five years preceding the measurement date.

The following table summarizes the assumptions we used for the nine months ended September 30, 2018 and 2017:



	For the Nine Months Ended September 30,
	2018	2017
Risk-free rate of return	2.96%	1.85%
Expected dividend yields	1.84%	1.71%
Expected award life (years)	4.49	4.48
Expected volatility	17.82%	18.13%

All outstanding awards were adjusted to reflect the 15% stock dividend, resulting in a 15% increase to the number of awards outstanding and a 13.04% reduction in the exercise price.

Argo Group’s Long-Term Incentive Plan

In November 2007, our shareholders approved the 2007 Long-Term Incentive Plan (the “2007 Plan”), which provides for an aggregate of 4.5 million shares of our common stock that may be issued to executives, non-employee directors, and other key employees. As of May 2014, 1.46 million shares remained available for grant under the 2007 Plan. In May 2014, our shareholders approved the 2014 Long-Term Incentive Plan (the “2014 Plan”), which provides for an additional 2.8 million shares of our common stock to be available for issuance to executives, non-employee directors and other key employees. The share awards may be in the form of share options, SARs, restricted shares, restricted share awards, restricted share unit awards, performance awards, other share-based awards and other cash-based awards. Shares issued under this plan may be shares that are authorized and unissued or shares that we reacquired, including shares purchased on the open market. Share options and SARs will count as one share for the purposes of the limits under the incentive plans; restricted shares, restricted share units, performance units, performance shares or other share-based incentive awards which settle in common shares will count as 2.75 shares for purpose of the limits under the 2014 Plan.

Share options may be in the form of incentive share options, non-qualified share options and restorative options. Share options are required to have an exercise price that is not less than the market value on the date of grant. We are prohibited from repricing the options, except for the impact of stock dividend declarations. The term of the share options cannot exceed seven years from the grant date.

Restricted Shares

A summary of restricted share activity as of September 30, 2018 and changes during the nine months ended is as follows:



	Shares		Weighted-Average Grant Date Fair Value
Outstanding at January 1, 2018	767,140		$	42.91
Granted	339,515		$	48.54
Vested and issued	(202,809	)	$	43.18
Expired or forfeited	(87,435	)	$	45.00
Outstanding at September 30, 2018	816,411		$	44.96

The restricted shares vest over one to eight years. Expense recognized under this plan for the restricted shares was $2.6 million and $10.9 million for the three and nine months ended September 30, 2018, respectively, as compared to $2.5 million and $7.5 million for the three and nine months ended September 30, 2017. Compensation expense for all share-based compensation awards is included in “Underwriting, acquisition and insurance expenses” in the accompanying Consolidated Statements of Income. As of September 30, 2018, there was $26.6 million of total unrecognized compensation cost related to restricted share compensation arrangements granted by Argo Group.

Stock-Settled SARs

A summary of stock-settled SARs activity as of September 30, 2018 and changes during the nine months ended is as follows:



	Shares		Weighted-Average Exercise Price
Outstanding at January 1, 2018	1,494,458		$	30.85
Exercised	(540,233	)	$	26.64
Expired or forfeited	(16,204	)	$	36.38
Outstanding at September 30, 2018	938,021		$	33.17

The stock-settled SARs vest over a one to four-year period. Upon exercise of the stock-settled SARs, the employee is entitled to receive shares of our common stock equal to the appreciation of the stock as compared to the exercise price. Expense recognized for the stock-settled SARs was $0.4 million and $1.8 million for the three and nine months ended September 30, 2018, respectively, as compared to $0.7 million and $3.5 million for the three and nine months ended September 30, 2017. As of September 30, 2018, there was $0.7 million of total unrecognized compensation cost related to stock-settled SARs outstanding.

Cash-Settled SARs

A summary of cash-settled SARs activity as of September 30, 2018 and changes during the nine months ended is as follows:



	Shares		Weighted-Average Exercise Price
Outstanding at January 1, 2018	189,568		$	28.95
Exercised	(87,665	)	$	27.88
Expired or forfeited	(2,568	)	$	21.23
Outstanding at September 30, 2018	99,335		$	30.10

As of September 30, 2018, all the cash-settled SARs are fully vested. Upon exercise of the cash-settled SARs, the employee is entitled to receive cash payment for the appreciation in the value of our common stock over the exercise price. We account for the cash-settled SARs as liability awards, which require the awards to be revalued at each reporting period. Expense recognized for the cash-settle SARs was $0.5 million and $1.2 million for the three and nine months ended September 30, 2018, respectively. Expense recognized for the cash-settled SARs for the three months ended September 30, 2017 was $0.3 million. Due to a decrease in the fair market value of our stock, we recouped $0.6 million of expense for nine months ended September 30, 2017. As of September 30, 2018, there was no unrecognized compensation cost related to cash-settled SARs outstanding.