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Investments - Summary of Investments (Details) - USD ($)
$ in Millions
Mar. 31, 2021
Sep. 30, 2020
Investment Holdings [Line Items]    
Total investments, at fair value $ 554.3 $ 504.8
Investments in equity method investees 785.5 682.2
Other investments 94.1 83.5
Total 1,433.9 1,270.5
Sponsored funds and separate accounts    
Investment Holdings [Line Items]    
Investments, at fair value 332.6 303.4
Investments related to long-term incentive plans    
Investment Holdings [Line Items]    
Investments, at fair value 164.0 146.6
Other equity and debt investments    
Investment Holdings [Line Items]    
Investments, at fair value $ 57.7 $ 54.8