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Accumulated Other Comprehensive Income (Loss) (Tables)
 12 Months Ended
Sep. 30, 2020
Accumulated Other Comprehensive Income (Loss), Net of Tax [Abstract]  
Schedule of changes in accumulated other comprehensive income (loss) by component
Changes in accumulated other comprehensive income (loss) by component were as follows: 
(in millions)
 
Currency
Translation
Adjustments
 
Unrealized
Losses on
Defined Benefit
Plans
 
Unrealized
Gains on
Investments
 
Total
as of and for the fiscal years ended
September 30, 2020, 2019 and 2018
 
 
 
Balance at October 1, 2017
 
$
(281.0
)
 
$
(6.0
)
 
$
2.2

 
$
(284.8
)
Adoption of new accounting guidance
 
—

 
(0.1
)
 
—

 
(0.1
)
Other comprehensive income (loss)
 
 
 
 
 
 
 


Other comprehensive income (loss) before reclassifications, net of tax
 
(85.5
)
 
1.5

 
7.3

 
(76.7
)
Reclassifications to compensation and benefits expense, net of tax
 
—

 
0.4

 
—

 
0.4

Reclassifications to net investment and other income (losses), net of tax
 
(6.4
)
 
—

 
(3.0
)
 
(9.4
)
Total other comprehensive income (loss)
 
(91.9
)
 
1.9

 
4.3

 
(85.7
)
Balance at September 30, 2018
 
$
(372.9
)
 
$
(4.2
)
 
$
6.5

 
$
(370.6
)
Adoption of new accounting guidance
 
—

 
—

 
(8.0
)
 
(8.0
)
Other comprehensive income (loss)
 
 
 
 
 
 
 
 
Other comprehensive loss before reclassifications, net of tax
 
(53.9
)
 
(2.4
)
 
(5.4
)
 
(61.7
)
Reclassifications to compensation and benefits expense, net of tax
 
—

 
0.4

 
—

 
0.4

Reclassifications to net investment and other income (losses), net of tax
 
1.4

 
—

 
6.9

 
8.3

Total other comprehensive income (loss)
 
(52.5
)
 
(2.0
)
 
1.5

 
(53.0
)
Balance at September 30, 2019
 
$
(425.4
)
 
$
(6.2
)
 
$
—

 
$
(431.6
)
Other comprehensive income (loss)
 
 
 
 
 
 
 
 
Other comprehensive income (loss) before reclassifications, net of tax
 
23.8

 
(2.1
)
 
(1.3
)
 
20.4

Reclassifications to compensation and benefits expense, net of tax
 
—

 
0.3

 
—

 
0.3

Reclassifications to net investment and other income (losses), net of tax
 
2.0

 
—

 
1.3

 
3.3

Total other comprehensive income (loss)
 
25.8

 
(1.8
)
 
—

 
24.0

Balance at September 30, 2020
 
$
(399.6
)
 
$
(8.0
)
 
$
—

 
$
(407.6
)