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Schedule II - Condensed Financial Information of Registrant - Condensed Statements of Cash Flows of Registrant (Details) - USD ($)
$ in Millions
 9 Months Ended 12 Months Ended
Jun. 30, 2015
Jun. 30, 2014
Sep. 30, 2015
Sep. 30, 2014
Sep. 30, 2013
Cash flows from operating activities:          
Net (loss) income     $ (512.4) $ 101.7 $ (69.0)
Adjustments to reconcile net (loss) income to operating cash flows:          
Depreciation and amortization     263.7 302.6 358.7
Stock compensation     91.8 91.1 61.5
Amortization of debt issuance costs     22.1 21.0 18.1
Amortization of debt discount     4.8 4.6 3.0
Write-off of discount (premium) and debt issuance costs on retired debt     12.8 9.2 29.3
Gain On Contingent Purchase Price Adjustment     8.5 (0.5)  
Changes in operating assets and liabilities:          
Net change in cash due to operating activities     283.6 607.9 522.3
Cash flows from investing activities:          
Proceeds from investments sold, matured or repaid     5,453.7 5,609.2 9,432.2
Cost of investments acquired     (6,398.3) (7,221.4) (8,940.8)
Capital expenditures     (116.2) (98.2) (100.1)
Net change in cash due to investing activities     (2,003.9) (1,920.6) (2,010.8)
Cash flows from financing activities:          
Dividends paid on preferred stock       (28.6) (17.4)
Payments of Debt Issuance Costs     (46.5) (19.3) (100.4)
Common stock repurchased     (22.2) (65.6) (12.3)
Share based award tax withholding payments     (21.0) (31.5) (22.3)
Other financing activities, net     6.2 2.8  
Net change in cash due to financing activities     1,627.8 740.4 1,922.0
Net change in cash and cash equivalents     (122.2) (580.5) 429.0
Cash and cash equivalents at beginning of period $ 1,319.2 $ 1,899.7 1,319.2 1,899.7 1,470.7
Cash and cash equivalents at end of period 1,197.0 1,319.2 1,197.0 1,319.2 1,899.7
HGI          
Cash flows from operating activities:          
Net (loss) income     (556.8) (10.3) (45.8)
Adjustments to reconcile net (loss) income to operating cash flows:          
Depreciation and amortization     0.5 0.2 0.2
Stock compensation     25.0 27.0 11.7
Amortization of debt issuance costs     4.4 3.5 2.7
Amortization of debt discount     1.8 1.5 0.5
Write-off of discount (premium) and debt issuance costs on retired debt     0.0 0.0 10.8
Write-off of debt discount on retired debt     0.0 0.0 2.1
Equity in net income of subsidiaries     357.2 (207.7) (263.7)
Dividends from subsidiaries     65.7 118.0 127.1
Loss from the change in the fair value of the equity conversion feature of preferred stock     0.0 12.7 101.6
Gain On Contingent Purchase Price Adjustment     (8.5) (0.5)  
Changes in operating assets and liabilities:          
Accounts payable and accrued and other current liabilities     (35.4) 43.5 51.4
Other operating     64.4 (0.7) 11.6
Net change in cash due to operating activities     (81.7) (12.8) 10.2
Cash flows from investing activities:          
Proceeds from investments sold, matured or repaid     0.0 0.0 34.0
Capital contributions to consolidated subsidiaries     (406.4) (115.5) (454.4)
Return of capital from subsidiary     0.0 0.0 126.8
Capital expenditures     (1.2) (0.3) (0.4)
Net change in cash due to investing activities     (407.6) (115.8) (294.0)
Cash flows from financing activities:          
Dividends paid on preferred stock     0.0 (28.6) (33.4)
Proceeds from senior secured notes     409.6 400.0 923.9
Repayment of senior secured notes, including tender / call premium     0.0 0.0 (545.9)
Payments of Debt Issuance Costs     (6.8) (10.4) (25.1)
Common stock repurchased     (22.1) (65.6) (12.3)
Share based award tax withholding payments     (18.3) (6.5) (2.3)
Other financing activities, net     4.1 2.8 0.0
Net change in cash due to financing activities     366.5 291.7 304.9
Net change in cash and cash equivalents     (122.8) 163.1 21.1
Cash and cash equivalents at beginning of period $ 420.0 $ 256.9 420.0 256.9 235.8
Cash and cash equivalents at end of period     $ 297.2 $ 420.0 $ 256.9