Fair Value Measurements - Schedule of Assets and Liabilities Measured at Fair Value on a Recurring Basis (Details) - USD ($) $ in Millions	Dec. 31, 2024	Sep. 30, 2024
Sponsored funds and separate accounts [Member]
Assets [Abstract]
Investments, at fair value	$ 469.1	$ 509.1
Investments related to long-term incentive plans [Member]
Assets [Abstract]
Investments, at fair value	266.3	271.6
Other equity and debt investments [Member]
Assets [Abstract]
Investments, at fair value	71.5	57.3
Fair Value, Recurring [Member]
Assets [Abstract]
Total Assets Measured at Fair Value	806.9	838.0
Liability [Abstract]
Securities sold short	244.9	178.1
Contingent consideration liabilities	27.5	28.2
Total Liabilities Measured at Fair Value	272.4	206.3
Fair Value, Recurring [Member] \| Level 1 [Member]
Assets [Abstract]
Total Assets Measured at Fair Value	512.2	552.9
Liability [Abstract]
Securities sold short	244.9	178.1
Contingent consideration liabilities	0.0	0.0
Total Liabilities Measured at Fair Value	244.9	178.1
Fair Value, Recurring [Member] \| Level 2 [Member]
Assets [Abstract]
Total Assets Measured at Fair Value	185.3	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	6.3	7.8
Liability [Abstract]
Securities sold short	0.0	0.0
Contingent consideration liabilities	27.5	28.2
Total Liabilities Measured at Fair Value	27.5	28.2
Fair Value, Recurring [Member] \| NAV as a Practical Expedient [Member]
Assets [Abstract]
Total Assets Measured at Fair Value	103.1	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	469.1	509.1
Fair Value, Recurring [Member] \| Sponsored funds and separate accounts [Member] \| Level 1 [Member]
Assets [Abstract]
Investments, at fair value	257.6	306.3
Fair Value, Recurring [Member] \| Sponsored funds and separate accounts [Member] \| Level 2 [Member]
Assets [Abstract]
Investments, at fair value	171.3	157.4
Fair Value, Recurring [Member] \| Sponsored funds and separate accounts [Member] \| Level 3 [Member]
Assets [Abstract]
Investments, at fair value	4.7	5.2
Fair Value, Recurring [Member] \| Sponsored funds and separate accounts [Member] \| NAV as a Practical Expedient [Member]
Assets [Abstract]
Investments, at fair value	35.5	40.2
Fair Value, Recurring [Member] \| Investments related to long-term incentive plans [Member]
Assets [Abstract]
Investments, at fair value	266.3	271.6
Fair Value, Recurring [Member] \| Investments related to long-term incentive plans [Member] \| Level 1 [Member]
Assets [Abstract]
Investments, at fair value	237.1	242.5
Fair Value, Recurring [Member] \| Investments related to long-term incentive plans [Member] \| Level 2 [Member]
Assets [Abstract]
Investments, at fair value	0.0	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	29.2	29.1
Fair Value, Recurring [Member] \| Other equity and debt investments [Member]
Assets [Abstract]
Investments, at fair value	71.5	57.3
Fair Value, Recurring [Member] \| Other equity and debt investments [Member] \| Level 1 [Member]
Assets [Abstract]
Investments, at fair value	17.5	4.1
Fair Value, Recurring [Member] \| Other equity and debt investments [Member] \| Level 2 [Member]
Assets [Abstract]
Investments, at fair value	14.0	11.1
Fair Value, Recurring [Member] \| Other equity and debt investments [Member] \| Level 3 [Member]
Assets [Abstract]
Investments, at fair value	1.6	2.6
Fair Value, Recurring [Member] \| Other equity and debt investments [Member] \| NAV as a Practical Expedient [Member]
Assets [Abstract]
Investments, at fair value	$ 38.4	$ 39.5

Fair value portion of probable future economic benefits obtained or controlled by an entity as a result of past transactions or events.

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Amount of liability recognized arising from contingent consideration in a business combination.

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Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
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Fair value of financial and nonfinancial obligations.

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Amount of investment in debt security measured at fair value with change in fair value recognized in net income (trading) and investment in equity security measured at fair value with change in fair value recognized in net income (FV-NI).

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Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Topic 210
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