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Fair Value Measurements - Schedule of Assets and Liabilities Measured at Fair Value on a Recurring Basis (Details) - USD ($) $ in Millions		Mar. 31, 2025	Sep. 30, 2024
Liability [Abstract]
Equity Securities without Readily Determinable Fair Value, Amount	[1]	$ 39.7
Sponsored funds and separate accounts [Member]
Assets [Abstract]
Investments, at fair value		278.0	$ 509.1
Investments related to long-term incentive plans [Member]
Assets [Abstract]
Investments, at fair value		258.2	271.6
Other equity and debt investments [Member]
Assets [Abstract]
Investments, at fair value		100.2	57.3
Fair Value, Recurring [Member]
Assets [Abstract]
Total Assets Measured at Fair Value		596.7	838.0
Liability [Abstract]
Securities sold short		116.6	178.1
Contingent consideration liabilities		27.5	28.2
Total Liabilities Measured at Fair Value		144.1	206.3
Fair Value, Recurring [Member] | Level 1 [Member]
Assets [Abstract]
Total Assets Measured at Fair Value		294.1	552.9
Liability [Abstract]
Securities sold short		116.6	178.1
Contingent consideration liabilities		0.0	0.0
Total Liabilities Measured at Fair Value		116.6	178.1
Fair Value, Recurring [Member] | Level 2 [Member]
Assets [Abstract]
Total Assets Measured at Fair Value		192.3	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		10.6	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		99.7	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		278.0	509.1
Fair Value, Recurring [Member] | Sponsored funds and separate accounts [Member] | Level 1 [Member]
Assets [Abstract]
Investments, at fair value		54.7	306.3
Fair Value, Recurring [Member] | Sponsored funds and separate accounts [Member] | Level 2 [Member]
Assets [Abstract]
Investments, at fair value		178.0	157.4
Fair Value, Recurring [Member] | Sponsored funds and separate accounts [Member] | Level 3 [Member]
Assets [Abstract]
Investments, at fair value		9.0	5.2
Fair Value, Recurring [Member] | Sponsored funds and separate accounts [Member] | NAV as a Practical Expedient [Member]
Assets [Abstract]
Investments, at fair value		36.3	40.2
Fair Value, Recurring [Member] | Investments related to long-term incentive plans [Member]
Assets [Abstract]
Investments, at fair value		258.2	271.6
Fair Value, Recurring [Member] | Investments related to long-term incentive plans [Member] | Level 1 [Member]
Assets [Abstract]
Investments, at fair value		226.2	242.5
Fair Value, Recurring [Member] | Investments related to long-term incentive plans [Member] | Level 2 [Member]
Assets [Abstract]
Investments, at fair value		2.8	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		60.5	57.3
Fair Value, Recurring [Member] | Other equity and debt investments [Member] | Level 1 [Member]
Assets [Abstract]
Investments, at fair value		13.2	4.1
Fair Value, Recurring [Member] | Other equity and debt investments [Member] | Level 2 [Member]
Assets [Abstract]
Investments, at fair value		11.5	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		$ 34.2	$ 39.5
[1] As of March 31, 2025, there were $39.7 million of other investments which were adjusted to fair value on a nonrecurring basis and excluded from the table above.

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