(9) Equity‑Based Compensation

Antero is authorized to grant up to 16,906,500 shares of common stock to employees and directors of the Company under the Antero Resources Corporation Long‑Term Incentive Plan (the “Plan”). The Plan allows equity‑based compensation awards to be granted in a variety of forms, including stock options, stock appreciation rights, restricted stock awards, restricted stock unit awards, dividend equivalent awards, and other types of awards. The terms and conditions of the awards granted are established by the Compensation Committee of Antero’s Board of Directors. A total of 8,351,638 shares were available for future grant under the Plan as of December 31, 2018.

Antero Midstream’s general partner is authorized to grant up to 10,000,000 common units representing limited partner interests in Antero Midstream under the Antero Midstream Partners LP Long-Term Incentive Plan (the “Midstream Plan”) to non-employee directors of its general partner and certain officers, employees, and consultants of Antero Midstream and its affiliates (which include Antero). A total of 7,932,261 common units were available for future grant under the Midstream Plan as of December 31, 2018.

The Company’s equity‑based compensation expense, by type of award, was as follows for the years ended December 31, 2016, 2017, and 2018 (in thousands):


	Year Ended December 31,
	2016		2017		2018
Restricted stock unit awards	$	73,081		70,866		41,505
Stock options		2,578		2,375		1,799
Performance share unit awards		8,685		10,797		9,659
Antero Midstream phantom unit awards		16,095		17,461		15,351
Equity awards issued to directors		1,982		1,946		2,100
Total expense	$	102,421		103,445		70,414

Restricted Stock Unit Awards

Restricted stock unit awards vest subject to the satisfaction of service requirements. Expense related to each restricted stock unit award is recognized on a straight-line basis over the requisite service period of the entire award. Forfeitures are accounted for as they occur by reversing the expense previously recognized for awards that were forfeited during the period. The grant date fair values of these awards are determined based on the closing price of the Company’s common stock on the date of the grant.

A summary of restricted stock unit award activity for the year ended December 31, 2018 is as follows:


		Weighted average		Aggregate
	Number of shares	grant date fair value		intrinsic value (in thousands)
Total awarded and unvested—December 31, 2017	3,424,084	$	28.51	$	65,058
Granted	687,626	$	20.69
Vested	(1,933,130)	$	29.90
Forfeited	(466,095)	$	25.65
Total awarded and unvested—December 31, 2018	1,712,485	$	24.57	$	16,080

Intrinsic values are based on the closing price of the Company’s stock on the referenced dates. As of December 31, 2018, there was $27 million of unamortized equity-based compensation expense related to unvested restricted stock units. That expense is expected to be recognized over a weighted average period of approximately 2.3 years.

Stock Options

Stock options granted under the Plan have a maximum contractual life of 10 years. Expense related to stock options is recognized on a straight‑line basis over the requisite service period of the entire award. Forfeitures are accounted for as they occur by reversing the expense previously recognized for awards that were forfeited during the period. Stock options were granted with an exercise price equal to or greater than the market price of the Company’s common stock on the dates of grant.

A summary of stock option activity for the year ended December 31, 2018 is as follows:


				Weighted
		Weighted average		average remaining	Intrinsic
	Stock options	exercise price		contractual life	value (in thousands)
Outstanding at December 31, 2017	660,512	$	50.48	7.06	$	—
Granted	—	$	—
Exercised	—	$	—
Forfeited	(80,895)	$	50.00
Expired	—	$	—
Outstanding at December 31, 2018	579,617	$	50.55	5.81	$	—
Vested or expected to vest as of December 31, 2018	579,617	$	50.55	5.81	$	—
Exercisable at December 31, 2018	462,217	$	50.69	5.69	$	—

Intrinsic values are based on the exercise price of the options and the closing price of the Company’s stock on the referenced dates.

A Black‑Scholes option‑pricing model is used to determine the grant-date fair value of stock options. Expected volatility was derived from the volatility of the historical stock prices of a peer group of similar publicly traded companies’ stock prices as the Company’s common stock had traded for a relatively short period of time at the dates the options were granted. The risk‑free interest rate was determined using the implied yield available for zero‑coupon U.S. government issues with a remaining term approximating the expected life of the options. A dividend yield of zero was assumed.

No stock options were granted during the years ended December 31, 2016, 2017 and 2018.

As of December 31, 2018, there was $0.5 million of unamortized equity‑based compensation expense related to unvested stock options. That expense is expected to be recognized over a weighted average period of approximately 0.3 years.

Performance Share Unit Awards

Performance Share Unit Awards Based on Price Targets

In 2016, the Company granted performance share unit awards (“PSUs”) to certain of its executive officers that are based on price targets. The vesting of these PSUs is conditioned on the closing price of the Company’s common stock achieving specific price thresholds over 10-day periods, subject to the following vesting restrictions: no PSUs may vest before the first anniversary of the grant date; no more than one-third of the PSUs may vest before the second anniversary of the grant date; and no more than two-thirds of the PSUs may vest before the third anniversary of the grant date. Any PSUs which have not vested by the fifth anniversary of the grant date will expire. Expense related to these PSUs is recognized on a graded basis over three years.

Performance Share Unit Awards Based on Total Shareholder Return (“TSR”)

In 2016 and 2017, the Company granted PSUs to certain of its employees and executive officers that vest based on the TSR of the Company’s common stock relative to the TSR of a peer group of companies over a three-year performance period. The number of common shares which may ultimately be earned ranges from zero to 200% of the PSUs granted. Expense related to these PSUs is recognized on a straight-line basis over three years.

Performance Share Unit Awards Based on TSR and Return on Capital Employed (“ROCE”)

In 2018, the Company granted PSUs to certain of its employees and executive officers, a portion of which vest based on the Company’s common stock reaching a target price per share equal to 125% of the beginning price (as defined in the award agreement) at the end of a three-year performance period (“TSR PSUs”). The number of awards actually earned with respect to the TSR PSUs will be subject to further adjustment based on the TSR of the Company’s common stock relative to the TSR of a peer group of companies over the same period. The number of shares of common stock that may ultimately be earned with respect to the TSR PSUs ranges from zero to 200% of the target number of TSR PSUs originally granted. Expense related to the TSR PSUs is recognized on a straight-line basis over three years.

The other portion of the PSUs granted in 2018 vest based on the Company’s actual ROCE (as defined in the award agreement) over a three-year period as compared to a targeted ROCE (“ROCE PSUs”). The number of shares of common stock that may ultimately be earned with respect to the ROCE PSUs ranges from zero to 200% of the target number of ROCE PSUs originally granted. Expense related to the ROCE PSUs is recognized based on the number of shares of common stock that are expected to be issued at the end of the measurement period, and is reversed if the likelihood of achieving the performance condition decreases.

Summary Information for Performance Share Unit Awards

A summary of PSU activity for the year ended December 31, 2018 is as follows:


	Number of units	Weighted average grant date fair value
Total awarded and unvested—December 31, 2017	1,283,843	$	28.29
Granted	756,466	$	23.61
Vested	(41,666)	$	27.38
Forfeited	(231,344)	$	27.89
Total awarded and unvested—December 31, 2018	1,767,299	$	26.36

The grant-date fair values of market-based PSUs were determined using Monte Carlo simulations, which use a probabilistic approach for estimating the fair values of the awards. Expected volatilities were derived from the volatility of the historical stock prices of a peer group of similar publicly-traded companies. The risk-free interest rate was determined using the yield available for zero-coupon U.S. government issues with remaining terms corresponding to the service periods of the PSUs. A dividend yield of zero was assumed. The grant-date fair value for the ROCE-based PSUs is based on the closing price of the Company’s common stock on the date of the grant, assuming the achievement of the performance condition.

The following table presents information regarding the weighted average fair values for market-based PSUs granted during the years ended December 31, 2017 and 2018, and the assumptions used to determine the fair values:


	Year Ended December 31,
	2017			2018
Dividend yield		—	%		—	%
Volatility		42	%		41	%
Risk-free interest rate		1.40	%		2.49	%
Weighted average fair value of awards granted	$	26.21		$	24.85

As of December 31, 2018, there was $20 million of unamortized equity-based compensation expense related to unvested PSUs. That expense is expected to be recognized over a weighted average period of approximately 1.9 years.

Antero Midstream Partners Phantom Unit Awards

Phantom units granted by Antero Midstream vest subject to the satisfaction of service requirements, upon the completion of which common units in Antero Midstream are delivered to the holder of the phantom units. Phantom units also contain distribution equivalent rights which entitle the holder of vested common units to receive a “catch up” payment equal to common unit distributions paid by Antero Midstream during the vesting period of the phantom unit award. These phantom units are treated, for accounting purposes, as if Antero Midstream distributed the units to Antero. Antero recognizes compensation expense as the units are granted to its employees, and a portion of the expense is allocated to Antero Midstream. Expense related to each phantom unit award is recognized on a straight-line basis over the requisite service period of the entire award. Forfeitures are accounted for as they occur by reversing the expense previously recognized for awards that were forfeited during the period. The grant date fair values of these awards are determined based on the closing price of Antero Midstream’s common units on the date of grant.

A summary of phantom unit awards activity for the year ended December 31, 2018 is as follows:


	Number of units	Weighted average grant date fair value		Aggregate intrinsic value (in thousands)
Total awarded and unvested—December 31, 2017	1,042,963	$	28.69	$	30,288
Granted	260,847	$	25.84
Vested	(577,566)	$	28.63
Forfeited	(143,244)	$	28.08
Total awarded and unvested—December 31, 2018	583,000	$	27.63	$	12,470

Intrinsic values are based on the closing price of Antero Midstream’s common units on the referenced dates. As of December 31, 2018, there was $12 million of unamortized equity-based compensation expense related to unvested phantom unit awards. That expense is expected to be recognized over a weighted average period of approximately 2.5 years.