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Revenue from Contracts with Clients - Schedule of Principal Gains, Net Related To Income and Expense of Dividends (Details) - Equity position - USD ($) $ in Millions | 12 Months Ended
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Sep. 30, 2023 | Sep. 30, 2022 | Sep. 30, 2021
Disaggregation of Revenue [Line Items] |  |  |
Dividend (loss)/income net of dividend expense reported within Principal Gains, net | $ (1.3) | $ 8.3 | $ 1.4
Long |  |  |
Disaggregation of Revenue [Line Items] |  |  |
Dividend (loss)/income net of dividend expense reported within Principal Gains, net | 32.0 | 142.3 | 282.7
Short |  |  |
Disaggregation of Revenue [Line Items] |  |  |
Dividend (loss)/income net of dividend expense reported within Principal Gains, net | $ (33.3) | $ (134.0) | $ (281.3)

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