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Investments - Summary of Investments (Details) - USD ($) $ in Millions | Dec. 31, 2024 | Sep. 30, 2024
--- | --- | ---
Investment Holdings [Line Items] |  |
Total investments, at fair value | $ 806.9 | $ 838.0
Investments in equity method investees | 1,175.5 | 1,219.7
Other investments | 410.1 | 280.7
Investments | 2,392.5 | 2,338.4
Sponsored funds and separate accounts [Member] |  |
Investment Holdings [Line Items] |  |
Investments, at fair value | 469.1 | 509.1
Investments related to long-term incentive plans [Member] |  |
Investment Holdings [Line Items] |  |
Investments, at fair value | 266.3 | 271.6
Other equity and debt investments [Member] |  |
Investment Holdings [Line Items] |  |
Investments, at fair value | $ 71.5 | $ 57.3

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