Condensed Parent Only Financial Statements - Cash Flows (Details) - USD ($) $ in Millions	9 Months Ended	12 Months Ended
	Jun. 30, 2019	Sep. 30, 2019	Sep. 30, 2018	Sep. 30, 2017	Sep. 30, 2013	Sep. 30, 2016
Condensed Cash Flow Statements, Captions [Line Items]
Cash paid for interest		$ 153.2	$ 78.9	$ 38.0
Depreciation and amortization		14.0	11.6	9.8
Deferred income taxes		(3.7)	(22.3)	9.8
Amortization and extinguishment of debt issuance costs		1.5	1.0	1.9
Amortization of share-based compensation expense		8.1	6.6	6.3
Business Combination, Bargain Purchase, Gain Recognized, Amount	$ (5.4)
Deposits with and receivables from broker-dealers, clearing organizations, and counterparties		(241.7)	(292.9)	186.3
Notes receivable, net		0.9	6.8	8.3
Income taxes receivable		(4.2)	(1.3)	0.5
Financial instruments owned, at fair value		(113.3)	(308.7)	(125.6)
Other assets		(8.3)	(3.3)	(16.0)
Accounts payable and other accrued liabilities		6.7	18.6	(19.6)
Payable to clients		(46.8)	520.0	290.9
Financial instruments sold, not yet purchased, at fair value		(156.1)	153.9	(124.4)
Net cash (used in) provided by operating activities		195.6	(473.6)	1,037.4
Purchase of property and equipment		(11.9)	(12.5)	(16.1)
Net cash used in investing activities		(40.8)	(15.4)	(22.3)
Payments of notes payable		(0.8)	(0.8)	(0.8)
Deferred payments on acquisitions		0.0	(5.5)	0.0
Share repurchase		(3.8)	0.0	0.0
Debt issuance costs		(3.3)	(0.4)	(0.3)	$ (1.7)
Exercise of stock options		1.2	2.6	3.4
Withholding taxes on stock option exercises		0.0	(0.8)	0.0
Income tax benefit on stock options and awards		0.0	0.0	0.7
Net cash provided by (used in) financing activities		9.6	120.9	5.7
Cash and cash equivalents at end of period		(471.3)	(342.3)
Income taxes (received) paid, net of cash refunds		24.6	22.2	17.1
Additional consideration payable related to acquisitions		1.8	0.0	(0.2)
Parent Company [Member]
Condensed Cash Flow Statements, Captions [Line Items]
Cash paid for interest		18.9	15.0	8.2
Net loss		15.3	(37.2)	10.4
Depreciation and amortization		5.2	4.8	3.3
Deferred income taxes		(0.6)	(18.0)	10.7
Amortization and extinguishment of debt issuance costs		1.2	0.7	1.7
Amortization of share-based compensation expense		7.1	6.1	5.5
Business Combination, Bargain Purchase, Gain Recognized, Amount		(5.4)	0.0	0.0
Deposits with and receivables from broker-dealers, clearing organizations, and counterparties		0.0	0.0	(2.9)
Receivables from subsidiaries, net		0.0	(0.8)	(0.3)
Due to/from subsidiaries		8.3	(68.6)	27.0
Notes receivable, net		(1.0)	2.9	2.1
Income taxes receivable		(0.8)	(6.6)	5.4
Financial instruments owned, at fair value		4.4	(4.4)	1.3
Other assets		(4.4)	(0.7)	7.8
Accounts payable and other accrued liabilities		4.6	8.6	(7.8)
Payable to clients		(1.4)	(0.3)	(2.5)
Financial instruments sold, not yet purchased, at fair value		25.2	34.0	(10.6)
Net cash (used in) provided by operating activities		58.4	(43.5)	35.5
Capital contribution in affiliates		(75.8)	(4.5)	0.0
Purchase of property and equipment		(6.2)	(5.9)	(6.1)
Net cash used in investing activities		(82.0)	(10.4)	(6.1)
Payable to lenders under loans		(138.2)	58.2	13.5
Proceeds from Issuance of Senior Long-term Debt		0.0	0.0	(45.5)
Deferred payments on acquisitions		0.0	(5.5)	0.0
Share repurchase		(3.8)	0.0	0.0
Debt issuance costs		(3.0)	0.0	0.0
Exercise of stock options		1.2	2.6	3.4
Withholding taxes on stock option exercises		0.0	0.8	0.0
Income tax benefit on stock options and awards		0.0	0.0	0.7
Net cash provided by (used in) financing activities		23.8	53.7	(28.7)
Net (decrease) increase in cash and cash equivalents		0.2	(0.2)	0.7
Cash and cash equivalents at end of period		(2.0)	(1.8)	(2.0)		$ (1.3)
Income taxes (received) paid, net of cash refunds		(23.9)	(18.4)	(22.3)
Additional consideration payable related to acquisitions		$ 1.8	$ 0.0	$ (0.2)