Revenue from Contracts with Clients - Schedule of Principal Gains, Net Related To Income and Expense of Dividends (Details) - Equity securities - USD ($) $ in Millions	3 Months Ended		6 Months Ended
	Mar. 31, 2024	Mar. 31, 2023	Mar. 31, 2024	Mar. 31, 2023
Disaggregation of Revenue [Line Items]
Dividend (loss)/income, net reported within Principal Gains, net	$ 1.1	$ (0.9)	$ 2.5	$ 0.1
Dividend income on long equity positions
Disaggregation of Revenue [Line Items]
Dividend (loss)/income, net reported within Principal Gains, net	65.8	3.2	86.0	17.4
Dividend expense on short equity positions
Disaggregation of Revenue [Line Items]
Dividend (loss)/income, net reported within Principal Gains, net	$ (64.7)	$ (4.1)	$ (83.5)	$ (17.3)