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Revenue from Contracts with Clients - Schedule of Income and Expense (Details) - Equity Positions - USD ($)
$ in Millions
 12 Months Ended
Sep. 30, 2024
Sep. 30, 2023
Sep. 30, 2022
Disaggregation of Revenue [Line Items]      
Dividend income/(loss) net of dividend expense reported within Principal Gains, net $ 1.1 $ (1.3) $ 8.3
Long      
Disaggregation of Revenue [Line Items]      
Dividend income/(loss) net of dividend expense reported within Principal Gains, net 192.3 32.0 142.3
Short      
Disaggregation of Revenue [Line Items]      
Dividend income/(loss) net of dividend expense reported within Principal Gains, net $ (191.2) $ (33.3) $ (134.0)