Condensed Parent Only Financial Statements - Cash Flows (Details) - USD ($) $ in Millions	3 Months Ended								12 Months Ended
	Sep. 30, 2018	Jun. 30, 2018	Mar. 31, 2018	Dec. 31, 2017	Sep. 30, 2017	Jun. 30, 2017	Mar. 31, 2017	Dec. 31, 2016	Sep. 30, 2018	Sep. 30, 2017	Sep. 30, 2016	Sep. 30, 2013
Condensed Financial Statements, Captions [Line Items]
Depreciation and amortization									$ 11.6	$ 9.8	$ 8.2
Bad debts	$ 1.2	$ 1.6	$ 0.2	$ 0.1	$ 0.4	$ 0.1	$ 1.3	$ 2.5	3.1	4.3	4.4
Deferred income taxes									22.3	(9.8)	(0.8)
Amortization and extinguishment of debt issuance costs									1.0	1.9	1.1
Amortization of share-based compensation expense									6.6	6.3	5.1
Deposits and receivables from broker-dealers, clearing organizations, and counterparties									408.8	(889.1)	146.6
Receivables from subsidiaries, net									(0.8)	(0.3)	(3.1)
Notes receivable, net									6.8	8.3	59.5
Income taxes receivable									(1.3)	0.5	8.2
Financial instruments owned, at fair value									(308.7)	(125.6)	(192.9)
Other assets									(3.3)	(16.0)	(17.4)
Accounts payable and other accrued liabilities									18.6	(19.6)	7.5
Payable to customers									520.0	290.9	172.2
Financial instruments sold, not yet purchased, at fair value									153.9	(124.4)	273.9
Net cash (used in) provided by operating activities									(74.0)	13.9	(27.8)
Purchase of property and equipment									(12.5)	(16.1)	(15.4)
Net cash used in investing activities									(15.4)	(22.3)	(35.5)
Payable to lenders under loans									125.8	48.2	142.0
Payments of notes payable									(0.8)	(0.8)	(0.8)
Payments related to earn-outs on acquisitions									(5.5)	0.0	(2.9)
Share repurchase									0.0	0.0	(19.5)
Debt issuance costs									(0.4)	(0.3)	(2.1)	$ (1.7)
Exercise of stock options									2.6	3.4	3.5
Payments Related to Tax Withholding for Share-based Compensation									(0.8)	0.0	0.0
Income tax benefit on stock options and awards									0.0	0.7	0.8
Net cash provided by (used in) financing activities									120.9	5.7	121.0
Net (decrease) increase in cash and cash equivalents									27.4	(1.3)	48.1
Cash and cash equivalents at beginning of period				314.9				316.2	314.9	316.2	268.1
Cash and cash equivalents at end of period	342.3				314.9				342.3	314.9	316.2
Cash paid for interest									78.9	38.0	26.0
Income taxes (received) paid, net of cash refunds									22.2	17.1	8.5
Additional consideration payable related to acquisitions									0.0	(0.2)	(0.4)
Parent Company [Member]
Condensed Financial Statements, Captions [Line Items]
Net loss									(37.2)	10.4	(3.4)
Depreciation and amortization									4.8	3.3	2.5
Bad debts									0.0	0.0	0.2
Deferred income taxes									18.0	(10.7)	(3.3)
Amortization and extinguishment of debt issuance costs									0.7	1.7	1.0
Amortization of share-based compensation expense									6.1	5.5	5.1
Business Combination, Bargain Purchase, Gain Recognized, Amount									0.0	0.0	6.2
Deposits and receivables from broker-dealers, clearing organizations, and counterparties									0.0	(2.9)	2.8
Due to/from subsidiaries									(68.6)	27.0	(86.6)
Notes receivable, net									2.9	2.1	39.1
Income taxes receivable									(6.6)	5.4	10.3
Financial instruments owned, at fair value									(4.4)	1.3	1.7
Other assets									(0.7)	7.8	0.3
Accounts payable and other accrued liabilities									8.6	(7.8)	0.4
Payable to customers									(0.3)	(2.5)	(26.1)
Financial instruments sold, not yet purchased, at fair value									34.0	(10.6)	35.9
Net cash (used in) provided by operating activities									(43.5)	35.5	(35.0)
Capital contribution in affiliates									(4.5)	0.0	(48.4)
Purchase of property and equipment									(5.9)	(6.1)	(5.5)
Net cash used in investing activities									(10.4)	(6.1)	(53.9)
Payable to lenders under loans									58.2	13.5	108.5
Proceeds from Issuance of Senior Long-term Debt									0.0	(45.5)	0.0
Payments related to earn-outs on acquisitions									(5.5)	0.0	(2.9)
Share repurchase									0.0	0.0	(19.5)
Debt issuance costs									0.0	0.0	(1.9)
Exercise of stock options									2.6	3.4	3.5
Payments Related to Tax Withholding for Share-based Compensation									(0.8)	0.0	0.0
Income tax benefit on stock options and awards									0.0	0.7	0.8
Net cash provided by (used in) financing activities									53.7	(28.7)	87.7
Net (decrease) increase in cash and cash equivalents									(0.2)	0.7	(1.2)
Cash and cash equivalents at beginning of period				$ 2.0				$ 1.3	2.0	1.3	2.5
Cash and cash equivalents at end of period	$ 1.8				$ 2.0				1.8	2.0	1.3
Cash paid for interest									15.0	8.2	9.0
Income taxes (received) paid, net of cash refunds									(18.4)	(22.3)	(33.8)
Additional consideration payable related to acquisitions									$ 0.0	$ (0.2)	$ (0.4)