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Investments - Summary of Investments (Details) - USD ($)
$ in Millions
Sep. 30, 2022
Sep. 30, 2021
Investment Holdings [Line Items]    
Total investments, at fair value $ 613.5 $ 588.3
Investments in equity method investees 771.5 814.3
Other investments 266.3 107.7
Total 1,651.3 1,510.3
Sponsored funds and separate accounts [Member]    
Investment Holdings [Line Items]    
Investments, at fair value 413.0 368.3
Investment related to long-term incentive plans [Member]    
Investment Holdings [Line Items]    
Investments, at fair value 143.3 160.0
Other equity and debt investments [Member]    
Investment Holdings [Line Items]    
Investments, at fair value $ 57.2 $ 60.0