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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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