Condensed Parent Only Financial Statements - Cash Flows (Details) - USD ($) $ in Millions	3 Months Ended								12 Months Ended
	Sep. 30, 2017	Jun. 30, 2017	Mar. 31, 2017	Dec. 31, 2016	Sep. 30, 2016	Jun. 30, 2016	Mar. 31, 2016	Dec. 31, 2015	Sep. 30, 2017	Sep. 30, 2016	Sep. 30, 2015	Sep. 30, 2013
Condensed Financial Statements, Captions [Line Items]
Depreciation and amortization									$ 9.8	$ 8.2	$ 7.2
Bad debts	$ 0.4	$ 0.1	$ 1.3	$ 2.5	$ (0.2)	$ 0.0	$ 2.6	$ 2.0	4.3	4.4	7.3
Deferred income taxes									(9.8)	(0.8)	5.0
Amortization and extinguishment of debt issuance costs									1.9	1.1	0.9
Amortization of share-based compensation expense									6.3	5.1	3.6
Gain on acquisition					(6.2)	$ 0.0	$ 0.0	0.0	0.0	(6.2)	0.0
Deposits and receivables from broker-dealers, clearing organizations, and counterparties									(889.1)	146.6	44.9
Receivables from subsidiaries, net									(0.3)	(3.1)	0.0
Notes receivable, net									8.3	59.5	(14.5)
Income taxes receivable									0.5	8.2	0.0
Financial instruments owned, at fair value									(125.6)	(192.9)	(565.0)
Other assets									(16.0)	(17.4)	(16.2)
Accounts payable and other accrued liabilities									(19.6)	7.5	23.2
Payable to customers									290.9	172.2	332.1
Financial instruments sold, not yet purchased, at fair value									(124.4)	273.9	177.5
Net cash (used in) provided by operating activities									13.9	(27.8)	37.9
Purchase of property and equipment									(16.1)	(15.4)	(9.1)
Net cash used in investing activities									(22.3)	(35.5)	(15.5)
Payable to lenders under loans									48.2	142.0	15.5
Proceeds from notes payable									0.0	0.0	4.0
Payments of notes payable									(0.8)	(0.8)	(0.4)
Payments related to earn-outs on acquisitions									0.0	(2.9)	(2.2)
Share repurchase									0.0	(19.5)	(4.7)
Debt issuance costs									(0.3)	(2.1)	(0.2)	$ (1.7)
Exercise of stock options									3.4	3.5	2.5
Income tax benefit on stock options and awards									0.7	0.8	0.5
Net cash provided by (used in) financing activities									5.7	121.0	15.0
Net (decrease) increase in cash and cash equivalents									(1.3)	48.1	36.8
Cash and cash equivalents at beginning of period				316.2				268.1	316.2	268.1	231.3
Cash and cash equivalents at end of period	314.9				316.2				314.9	316.2	268.1
Cash paid for interest									38.0	26.0	15.8
Income taxes (received) paid, net of cash refunds									17.1	8.5	15.3
Additional consideration payable related to acquisitions									(0.2)	(0.4)	1.9
Parent Company [Member]
Condensed Financial Statements, Captions [Line Items]
Net loss									10.4	(3.4)	(27.7)
Depreciation and amortization									3.3	2.5	1.8
Bad debts									0.0	0.2	1.6
Deferred income taxes									(10.7)	(3.3)	4.6
Amortization and extinguishment of debt issuance costs									1.7	1.0	0.8
Amortization of share-based compensation expense									5.5	5.1	3.6
Gain on acquisition									0.0	(6.2)	0.0
Deposits and receivables from broker-dealers, clearing organizations, and counterparties									(2.9)	2.8	0.0
Due to/from subsidiaries									27.0	(86.6)	33.2
Notes receivable, net									2.1	39.1	(7.8)
Income taxes receivable									5.4	10.3	(11.4)
Financial instruments owned, at fair value									1.3	1.7	(3.0)
Other assets									7.8	0.3	(3.9)
Accounts payable and other accrued liabilities									(7.8)	0.4	12.6
Payable to customers									(2.5)	(26.1)	4.9
Financial instruments sold, not yet purchased, at fair value									(10.6)	35.9	0.0
Net cash (used in) provided by operating activities									35.5	(35.0)	9.3
Capital contribution in affiliates									0.0	(48.4)	(22.4)
Capital withdrawals from affiliates									0.0	0.0	7.8
Purchase of property and equipment									(6.1)	(5.5)	(7.8)
Net cash used in investing activities									(6.1)	(53.9)	(22.4)
Payable to lenders under loans									13.5	108.5	13.0
Proceeds from Issuance of Senior Long-term Debt									(45.5)	0.0	0.0
Payments related to earn-outs on acquisitions									0.0	(2.9)	(2.2)
Share repurchase									0.0	(19.5)	(4.7)
Debt issuance costs									0.0	(1.9)	(0.1)
Exercise of stock options									3.4	3.5	2.5
Income tax benefit on stock options and awards									0.7	0.8	0.5
Net cash provided by (used in) financing activities									(28.7)	87.7	12.6
Net (decrease) increase in cash and cash equivalents									0.7	(1.2)	(0.5)
Cash and cash equivalents at beginning of period				$ 1.3				$ 2.5	1.3	2.5	3.0
Cash and cash equivalents at end of period	$ 2.0				$ 1.3				2.0	1.3	2.5
Cash paid for interest									8.2	9.0	11.9
Income taxes (received) paid, net of cash refunds									(22.3)	(33.8)	(12.9)
Additional consideration payable related to acquisitions									$ (0.2)	$ (0.4)	$ 1.9