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Fair Value Measurements - Schedule of Assets and Liabilities Measured at Fair Value on a Recurring Basis (Details) - USD ($) $ in Millions | Jun. 30, 2025 | Sep. 30, 2024
--- | --- | ---
Liability [Abstract] |  |  |
Equity Securities without Readily Determinable Fair Value, Amount | [1] | $ 16.1 |
Sponsored funds and separate accounts [Member] |  |  |
Assets [Abstract] |  |  |
Investments, at fair value |  | 752.9 | $ 509.1
Investments related to long-term incentive plans [Member] |  |  |
Assets [Abstract] |  |  |
Investments, at fair value |  | 261.1 | 271.6
Other equity and debt investments [Member] |  |  |
Assets [Abstract] |  |  |
Investments, at fair value |  | 66.6 | 57.3
Fair Value, Recurring [Member] |  |  |
Assets [Abstract] |  |  |
Total Assets Measured at Fair Value |  | 1,064.5 | 838.0
Liability [Abstract] |  |  |
Securities sold short |  | 261.7 | 178.1
Contingent consideration liabilities |  | 21.5 | 28.2
Total Liabilities Measured at Fair Value |  | 283.2 | 206.3
Fair Value, Recurring [Member] | Level 1 [Member] |  |  |
Assets [Abstract] |  |  |
Total Assets Measured at Fair Value |  | 736.3 | 552.9
Liability [Abstract] |  |  |
Securities sold short |  | 261.7 | 178.1
Contingent consideration liabilities |  | 0.0 | 0.0
Total Liabilities Measured at Fair Value |  | 261.7 | 178.1
Fair Value, Recurring [Member] | Level 2 [Member] |  |  |
Assets [Abstract] |  |  |
Total Assets Measured at Fair Value |  | 226.9 | 168.5
Liability [Abstract] |  |  |
Securities sold short |  | 0.0 | 0.0
Contingent consideration liabilities |  | 0.0 | 0.0
Total Liabilities Measured at Fair Value |  | 0.0 | 0.0
Fair Value, Recurring [Member] | Level 3 [Member] |  |  |
Assets [Abstract] |  |  |
Total Assets Measured at Fair Value |  | 5.0 | 7.8
Liability [Abstract] |  |  |
Securities sold short |  | 0.0 | 0.0
Contingent consideration liabilities |  | 21.5 | 28.2
Total Liabilities Measured at Fair Value |  | 21.5 | 28.2
Fair Value, Recurring [Member] | NAV as a Practical Expedient [Member] |  |  |
Assets [Abstract] |  |  |
Total Assets Measured at Fair Value |  | 96.3 | 108.8
Liability [Abstract] |  |  |
Securities sold short |  | 0.0 | 0.0
Contingent consideration liabilities |  | 0.0 | 0.0
Total Liabilities Measured at Fair Value |  | 0.0 | 0.0
Fair Value, Recurring [Member] | Sponsored funds and separate accounts [Member] |  |  |
Assets [Abstract] |  |  |
Investments, at fair value |  | 752.9 | 509.1
Fair Value, Recurring [Member] | Sponsored funds and separate accounts [Member] | Level 1 [Member] |  |  |
Assets [Abstract] |  |  |
Investments, at fair value |  | 497.2 | 306.3
Fair Value, Recurring [Member] | Sponsored funds and separate accounts [Member] | Level 2 [Member] |  |  |
Assets [Abstract] |  |  |
Investments, at fair value |  | 214.7 | 157.4
Fair Value, Recurring [Member] | Sponsored funds and separate accounts [Member] | Level 3 [Member] |  |  |
Assets [Abstract] |  |  |
Investments, at fair value |  | 3.2 | 5.2
Fair Value, Recurring [Member] | Sponsored funds and separate accounts [Member] | NAV as a Practical Expedient [Member] |  |  |
Assets [Abstract] |  |  |
Investments, at fair value |  | 37.8 | 40.2
Fair Value, Recurring [Member] | Investments related to long-term incentive plans [Member] |  |  |
Assets [Abstract] |  |  |
Investments, at fair value |  | 261.1 | 271.6
Fair Value, Recurring [Member] | Investments related to long-term incentive plans [Member] | Level 1 [Member] |  |  |
Assets [Abstract] |  |  |
Investments, at fair value |  | 227.5 | 242.5
Fair Value, Recurring [Member] | Investments related to long-term incentive plans [Member] | Level 2 [Member] |  |  |
Assets [Abstract] |  |  |
Investments, at fair value |  | 2.9 | 0.0
Fair Value, Recurring [Member] | Investments related to long-term incentive plans [Member] | Level 3 [Member] |  |  |
Assets [Abstract] |  |  |
Investments, at fair value |  | 0.0 | 0.0
Fair Value, Recurring [Member] | Investments related to long-term incentive plans [Member] | NAV as a Practical Expedient [Member] |  |  |
Assets [Abstract] |  |  |
Investments, at fair value |  | 30.7 | 29.1
Fair Value, Recurring [Member] | Other equity and debt investments [Member] |  |  |
Assets [Abstract] |  |  |
Investments, at fair value |  | 50.5 | 57.3
Fair Value, Recurring [Member] | Other equity and debt investments [Member] | Level 1 [Member] |  |  |
Assets [Abstract] |  |  |
Investments, at fair value |  | 11.6 | 4.1
Fair Value, Recurring [Member] | Other equity and debt investments [Member] | Level 2 [Member] |  |  |
Assets [Abstract] |  |  |
Investments, at fair value |  | 9.3 | 11.1
Fair Value, Recurring [Member] | Other equity and debt investments [Member] | Level 3 [Member] |  |  |
Assets [Abstract] |  |  |
Investments, at fair value |  | 1.8 | 2.6
Fair Value, Recurring [Member] | Other equity and debt investments [Member] | NAV as a Practical Expedient [Member] |  |  |
Assets [Abstract] |  |  |
Investments, at fair value |  | $ 27.8 | $ 39.5
[1] | As of June 30, 2025, there were $16.1 million of other investments which were adjusted to fair value on a nonrecurring basis and excluded from the table above.

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