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Schedule II - Condensed Financial Information of Registrant - Condensed Statements of Cash Flows of Registrant (Details) (USD $)
In Millions, unless otherwise specified
 12 Months Ended
Sep. 30, 2013
Sep. 30, 2012
Sep. 30, 2011
Cash flows from operating activities:      
Net (loss) income $ (69.0) $ 110.7 $ 7.3
Adjustments to reconcile net (loss) income to operating cash flows:      
Depreciation and amortization 358.6 268.2 95.5
Stock compensation 61.5 31.2 30.5
Amortization of debt issuance costs 18.1 12.8 15.0
Amortization of debt discount 3.0 1.3 5.4
Write-off of debt issuance costs on retired debt 32.4 2.9 15.4
Write-off of debt discount on retired debt (3.1) (0.5) 9.0
Loss gain from the change in the fair value of the equity conversion feature of preferred stock       27.9
Changes in operating assets and liabilities:      
Net change in cash due to operating activities 522.3 622.5 155.5
Cash flows from investing activities:      
Proceeds from investments sold, matured or repaid 9,432.2 6,206.7 1,699.9
Cost of investments acquired (8,940.8) (5,972.7) (1,809.0)
Capital expenditures (100.1) (53.5) (38.2)
Net change in cash due to investing activities (2,010.8) (185.6) 532.0
Cash flows from financing activities:      
Dividends paid on preferred stock (33.4) (31.7)   
Repayment of senior secured notes, including tender / call premium   0 0
Proceeds from issuance of preferred stock, net of issuance cost     386.0
Common stock repurchased 12.3    
Payments Related to Tax Withholding for Share-based Compensation 22.3 3.9 2.5
Other financing activities, net    (1.0) 28.6
Net change in cash due to financing activities 1,922.0 (102.7) 192.1
Net change in cash and cash equivalents 429.0 333.3 880.5
Cash and cash equivalents at beginning of period 1,470.7 1,137.4 256.9
Cash and cash equivalents at end of period 1,899.7 1,470.7 1,137.4
HGI
      
Cash flows from operating activities:      
Net (loss) income (45.8) 89.5 42.0
Adjustments to reconcile net (loss) income to operating cash flows:      
Depreciation and amortization 0.2 0.1 0.1
Stock compensation 11.7 1.9 0.1
Amortization of debt issuance costs 2.7 2.9 1.8
Amortization of debt discount 0.5 0.6 0.6
Write-off of debt issuance costs on retired debt 10.8 0 0
Write-off of debt discount on retired debt 2.1 0 0
Deferred income taxes 0 3.6 0.4
Equity in net income of subsidiaries (263.7) (354.6) (75.0)
Dividends from subsidiaries 127.1 69.5 20.0
Loss gain from the change in the fair value of the equity conversion feature of preferred stock 101.6 156.6 (27.9)
Changes in operating assets and liabilities:      
Prepaid expenses and other current assets 0 (4.6) 0.1
Accounts payable and accrued and other current liabilities 51.4 27.0 15.7
Other operating 11.6 (1.7) 1.8
Net change in cash due to operating activities 10.2 (9.2) (20.3)
Cash flows from investing activities:      
Proceeds from investments sold, matured or repaid 34.0 108.9 101.0
Cost of investments acquired 0 (68.0) (121.9)
Capital contributions to consolidated subsidiaries (454.4) (36.3) (727.2)
Return of capital from subsidiary 126.8 88.0 0
(Advances to) repayments from consolidated subsidiaries 0 49.3 (49.3)
Capital expenditures (0.4) 0 (0.3)
Net change in cash due to investing activities (294.0) 141.9 (797.7)
Cash flows from financing activities:      
Dividends paid on preferred stock (33.4) (31.7) 0
Proceeds from senior secured notes 923.9 0 498.4
Repayment of senior secured notes, including tender / call premium (545.9)    
Proceeds from issuance of preferred stock, net of issuance cost 0 0 385.9
Debt issuance costs (25.1) 0 (16.2)
Common stock repurchased (12.3)    
Payments Related to Tax Withholding for Share-based Compensation (2.3)    
Other financing activities, net 0 0 0.4
Net change in cash due to financing activities 304.9 (31.7) 868.5
Net change in cash and cash equivalents 21.1 101.0 50.5
Cash and cash equivalents at beginning of period 235.8 134.8 84.3
Cash and cash equivalents at end of period $ 256.9 $ 235.8 $ 134.8