Accumulated Other Comprehensive Income (Loss) - Changes in Accumulated Other Comprehensive Income (Loss) by Component (Details) - USD ($) $ in Millions	12 Months Ended
	Sep. 30, 2021	Sep. 30, 2020	Sep. 30, 2019	Sep. 30, 2018
Accumulated Other Comprehensive Income (Loss) [Line Items]
Balance at beginning of year	$ (407.6)	$ (431.6)	$ (370.6)
Adoption of new accounting guidance	11,223.4	10,114.5
Other comprehensive income before reclassifications, net of tax	28.7	20.4	(61.7)
Reclassifications to compensation and benefits expense, net of tax	(0.7)	0.3	0.4
Reclassifications to net investment and other income (losses), net of tax	2.0	3.3	8.3
Total other comprehensive income (loss)	30.0	24.0	(53.0)
Balance at end of year	(377.6)	(407.6)	(431.6)
ASU 2016-01 [Member]
Accumulated Other Comprehensive Income (Loss) [Line Items]
Adoption of new accounting guidance				$ (8.0)
Currency Translation Adjustments [Member]
Accumulated Other Comprehensive Income (Loss) [Line Items]
Balance at beginning of year	(399.6)	(425.4)	(372.9)
Other comprehensive income before reclassifications, net of tax	27.1	23.8	(53.9)
Reclassifications to compensation and benefits expense, net of tax	0.0	0.0	0.0
Reclassifications to net investment and other income (losses), net of tax	2.0	2.0	1.4
Total other comprehensive income (loss)	29.1	25.8	(52.5)
Balance at end of year	(370.5)	(399.6)	(425.4)
Currency Translation Adjustments [Member] | ASU 2016-01 [Member]
Accumulated Other Comprehensive Income (Loss) [Line Items]
Adoption of new accounting guidance				0.0
Unrealized Losses on Defined Benefit Plans [Member]
Accumulated Other Comprehensive Income (Loss) [Line Items]
Balance at beginning of year	(8.0)	(6.2)	(4.2)
Other comprehensive income before reclassifications, net of tax	1.6	(2.1)	(2.4)
Reclassifications to compensation and benefits expense, net of tax	(0.7)	0.3	0.4
Reclassifications to net investment and other income (losses), net of tax	0.0	0.0	0.0
Total other comprehensive income (loss)	0.9	(1.8)	(2.0)
Balance at end of year	(7.1)	(8.0)	(6.2)
Unrealized Losses on Defined Benefit Plans [Member] | ASU 2016-01 [Member]
Accumulated Other Comprehensive Income (Loss) [Line Items]
Adoption of new accounting guidance				0.0
Unrealized Gains on Investments [Member]
Accumulated Other Comprehensive Income (Loss) [Line Items]
Balance at beginning of year	0.0	0.0	6.5
Other comprehensive income before reclassifications, net of tax	0.0	(1.3)	(5.4)
Reclassifications to compensation and benefits expense, net of tax	0.0	0.0	0.0
Reclassifications to net investment and other income (losses), net of tax	0.0	1.3	6.9
Total other comprehensive income (loss)	0.0	0.0	1.5
Balance at end of year	$ 0.0	$ 0.0	$ 0.0
Unrealized Gains on Investments [Member] | ASU 2016-01 [Member]
Accumulated Other Comprehensive Income (Loss) [Line Items]
Adoption of new accounting guidance				$ (8.0)