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Investments - Summary of Investments (Details) - USD ($)
$ in Millions
Jun. 30, 2022
Sep. 30, 2021
Investment Holdings [Line Items]    
Total investments, at fair value $ 660.8 $ 588.3
Investments in equity method investees 744.5 814.3
Other investments 253.2 107.7
Total 1,658.5 1,510.3
Sponsored funds and separate accounts [Member]    
Investment Holdings [Line Items]    
Investments, at fair value 463.5 368.3
Investments related to long-term incentive plans [Member]    
Investment Holdings [Line Items]    
Investments, at fair value 141.0 160.0
Other equity and debt investments [Member]    
Investment Holdings [Line Items]    
Investments, at fair value $ 56.3 $ 60.0