Long-term Incentive Compensation Plans (Tables)

12 Months Ended

Dec. 31, 2022

Compensation Related Costs [Abstract]

Summary of Option Awards Activity

The option-related activity in our equity compensation plans during 2022 is as follows:

	Options to Buy AB Holding Units		Weighted Average Exercise Price Per Option			Weighted Average Remaining Contractual Term (Years)		Aggregate Intrinsic Value (in thousands)
Outstanding as of December 31, 2021		5,774		$	20.12		0.33
Granted		—		—
Exercised		(5,774)		20.12
Forfeited		—		—
Expired		—		—
Outstanding as of December 31, 2022		—		$	—		—		$	—
Exercisable as of December 31, 2022		—		$	—		—		$	—
Vested or expected to vest as of December 31, 2022		—		$	—		—		$	—

Summary of Activity of Unvested Restricted Holding Units

Grant details related to these awards is as follows:

	2022			2021			2020
Restricted Units Awarded		30,870			35,358			50,232
Weighted Average Grant Date Fair Value		$	38.55		$	44.29		$	23.69
Compensation Expense (in millions)		$	1.2		$	1.6		$	1.2

Grant details related to these awards is as follows:

	2022			2021			2020
	(in millions excluding share prices)
Restricted Units Awarded		0.5			3.4			0.4
Grant Date Fair Value Range	$34.86 - $49.90			$29.06 - $53.86			$18.80 - $35.42
Compensation Expense		$	35.0		$	40.9		$	32.1

Changes in unvested restricted AB Holding Units during 2022 are as follows:

	AB Holding Units	Weighted Average Grant Date Fair Value per AB Holding Unit
Unvested as of December 31, 2021	18,130,740		$	33.98
Granted	4,709,600		40.31
Vested	(7,671,109)		32.10
Forfeited	(396,995)		36.15
Unvested as of December 31, 2022	14,772,236		$	36.92