Consolidated Statements of Comprehensive Income - USD ($) $ in Millions	12 Months Ended
	Sep. 30, 2020	Sep. 30, 2019	Sep. 30, 2018
Statement of Comprehensive Income [Abstract]
Net income	$ 169.6	$ 85.1	$ 55.5
Other comprehensive loss, net of tax:
Foreign currency translation adjustment	(4.5)	(0.8)	(9.0)
Pension liabilities adjustment	(0.2)	(0.8)	0.3
Reclassification of adjustment for losses (gains) included in net income:
Periodic pension costs (included in compensation and benefits)	0.1	0.1	0.1
Foreign currency gains realized upon dissolution of subsidiaries (included in principal gains, net)	0.0	(0.2)	0.0
Reclassification adjustment for losses (gains) included in net income	0.1	(0.1)	0.1
Other comprehensive loss	(4.6)	(1.7)	(8.6)
Comprehensive income	$ 165.0	$ 83.4	$ 46.9