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Goodwill and Acquired Client Relationships - Additional Information (Details) - USD ($) | 3 Months Ended | 9 Months Ended | 12 Months Ended
--- | --- | --- | ---
Sep. 30, 2020 | Jun. 30, 2020 | Sep. 30, 2021 | Dec. 31, 2021 | Dec. 31, 2020 | Dec. 31, 2019
Intangible assets |  |  |  |  |  |
Goodwill impairment |  |  | $ 0 |  |  |
Acquired Client Relationships |  |  |  |  |  |
Estimated Future Amortization Expense of Finite-Lived Intangibles |  |  |  |  |  |
Indefinite-lived acquired client relationships |  | $ 0 |  |  |  |
Closure of Certain Retail Investment Products | Acquired Client Relationships |  |  |  |  |  |
Estimated Future Amortization Expense of Finite-Lived Intangibles |  |  |  |  |  |
Indefinite-lived acquired client relationships | $ 0 |  |  |  |  |
Acquired Client Relationships |  |  |  |  |  |
Intangible assets |  |  |  |  |  |
Amortization and impairment expenses of intangible assets |  |  |  | $ 35,700,000 | $ 69,800,000 |
Estimated Future Amortization Expense of Finite-Lived Intangibles |  |  |  |  |  |
Intangible future amortization expense in 2022 |  |  |  | 50,000,000 |  |
Intangible future amortization expense in 2023 |  |  |  | 50,000,000 |  |
Intangible future amortization expense in 2024 |  |  |  | 35,000,000 |  |
Intangible future amortization expense in 2025 |  |  |  | 30,000,000 |  |
Intangible future amortization expense in 2026 |  |  |  | 30,000,000 |  |
Impairment of definite-lived intangible assets |  |  |  | 0 |  |
Intangible impairments | $ 14,000,000 | 60,300,000 |  | 0 | 70,700,000 |
Indefinite-lived acquired client relationships |  |  |  | 1,630,300,000 | 909,000,000.0 | $ 972,200,000
Average projected growth rate | (14.00%) |  |  |  |  |
Discount rate for assets based fees | 15.00% |  |  |  |  |
Market participant tax rate | 25.00% |  |  |  |  |
Acquired Client Relationships | Closure of Certain Retail Investment Products |  |  |  |  |  |
Estimated Future Amortization Expense of Finite-Lived Intangibles |  |  |  |  |  |
Intangible impairments | $ 10,900,000 |  |  |  |  |
Acquired Client Relationships | Controlling Interest |  |  |  |  |  |
Estimated Future Amortization Expense of Finite-Lived Intangibles |  |  |  |  |  |
Intangible impairments | 12,500,000 | $ 32,800,000 |  |  |  |
Acquired Client Relationships | Controlling Interest | Closure of Certain Retail Investment Products |  |  |  |  |  |
Estimated Future Amortization Expense of Finite-Lived Intangibles |  |  |  |  |  |
Intangible impairments | $ 7,400,000 |  |  |  |  |
Acquired Client Relationships | Intangible Amortization and Impairments |  |  |  |  |  |
Intangible assets |  |  |  |  |  |
Amortization and impairment expenses of intangible assets |  |  |  | $ 35,700,000 | $ 55,300,000 | $ 93,400,000

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