Assets and Liabilities, at Fair Value - Narrative (Details) - USD ($) $ in Millions	12 Months Ended
	Sep. 30, 2022	Sep. 30, 2021	Sep. 30, 2020
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Accounts payable and other accrued liabilities	$ 400.6	$ 305.1
Equity investments in exchange stock - cost	3.7	3.7
Financial instruments owned	4,167.3	4,354.6
Additional consideration payable related to acquisitions	3.6	2.6
Remeasurement losses		1.1	$ 0.6
Carrying value	$ 339.1	336.9
Senior Notes Due Twenty Twenty Five
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Debt instrument, interest rate, stated percentage	8.625%
Level 2
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Long-term debt, fair value	$ 352.3
Fair Value, Measurements, Recurring
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Financial instruments owned	4,167.3	4,354.6
Fair Value, Measurements, Recurring | Exchange firm common stock
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Financial instruments owned	10.6	11.6
Fair Value, Measurements, Recurring | Level 3
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Financial instruments owned	0.0	0.0
Fair Value, Measurements, Recurring | Level 3 | Exchange firm common stock
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Financial instruments owned	0.0	0.0
Fair Value, Measurements, Recurring | Level 2
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Financial instruments owned	3,895.8	3,865.4
Fair Value, Measurements, Recurring | Level 2 | Exchange firm common stock
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Financial instruments owned	0.0	0.0
Contingent Consideration | Fair Value, Measurements, Recurring
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Accounts payable and other accrued liabilities		2.8
Contingent Consideration | Fair Value, Measurements, Recurring | Level 3
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Accounts payable and other accrued liabilities	$ 0.0	2.8
Contingent Consideration | Fair Value, Measurements, Recurring | Level 2
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Accounts payable and other accrued liabilities		$ 0.0