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Investments of Operating Entities and Consolidated Funds - Derivatives (Details)
12 Months Ended
Dec. 05, 2016
Dec. 31, 2018
USD ($)
contract
Dec. 31, 2017
USD ($)
contract
Dec. 31, 2016
USD ($)
Mar. 10, 2014
USD ($)
Derivative [Line Items]          
Warrants issued       $ 15,200,000  
Cost of hedge transaction and warrant, net         $ 20,500,000
Stockholders' Equity Note, Stock Split, Conversion Ratio 0.25        
Receivable on derivative contracts, at fair value   $ 25,125,000 $ 69,177,000    
Payable for derivative contracts, at fair value   16,082,000 42,750,000    
Receivable on derivative contracts, at fair value   4,416,000 2,520,000    
Payable for derivative contracts, at fair value, Consolidated Funds   1,663,000 7,130,000    
Equity Swap          
Derivative [Line Items]          
Receivable on derivative contracts, at fair value   2,477,000 1,754,000    
Payable for derivative contracts, at fair value, Consolidated Funds   713,000 7,042,000    
Futures          
Derivative [Line Items]          
Derivative Asset, Notional Amount   42,288,209 3,819,350    
Receivable on derivative contracts, at fair value   334,000 58,000    
Derivative Liability, Notional Amount   0 16,796,000    
Payable for derivative contracts, at fair value   0 242,000    
Currency Forwards          
Derivative [Line Items]          
Derivative Asset, Notional Amount   394,875 233,136    
Receivable on derivative contracts, at fair value   1,000 5,000    
Derivative Liability, Notional Amount   96,406,000 62,439,000    
Payable for derivative contracts, at fair value   709,000 874,000    
Receivable on derivative contracts, at fair value   186,000 524,000    
Payable for derivative contracts, at fair value, Consolidated Funds   96,000 11,000    
Swaps          
Derivative [Line Items]          
Derivative Asset, Notional Amount   13,702,458 164,664,203    
Receivable on derivative contracts, at fair value   917,000 10,942,000    
Derivative Liability, Notional Amount   52,905,000 11,595,000    
Payable for derivative contracts, at fair value   $ 2,162,000 $ 71,000    
Options          
Derivative [Line Items]          
Derivative Asset, Number of Instruments Held | contract [1]   654,506 283,112    
Receivable on derivative contracts, at fair value [1]   $ 23,130,000 $ 58,172,000    
Receivable on derivative contracts, at fair value   1,753,000 242,000    
Payable for derivative contracts, at fair value, Consolidated Funds   $ 854,000 $ 77,000    
Option          
Derivative [Line Items]          
Derivative Liability, Number of Instruments Held | contract [2]   90,730 57,043    
Payable for derivative contracts, at fair value [2]   $ 13,211,000 $ 41,563,000    
Pay to hold          
Derivative [Line Items]          
Derivative Asset, Number of Instruments Held | contract   0 0    
Receivable on derivative contracts, at fair value   $ 743,000 $ 0    
Receivable on derivatives contracts, at fair value [Member]          
Derivative [Line Items]          
Receivable on derivative contracts, at fair value   25,125,000 69,177,000    
Derivative Asset, Fair Value, Gross Asset   25,125,000 69,177,000    
Derivative Asset, Fair Value, Amount Offset Against Collateral [3]   0 0    
Financial Instruments, Owned and Pledged as Collateral, at Fair Value   0 0    
Derivative Asset, Fair Value, Amount Not Offset Against Collateral [4]   1,662,000 10,948,000    
Derivative asset, net of offset   23,463,000 58,229,000    
Payable for derivatives contracts, at fair value [Member]          
Derivative [Line Items]          
Payable for derivative contracts, at fair value   16,082,000 42,750,000    
Financial Instruments, Owned and Pledged as Collateral, at Fair Value   0 0    
Derivative Liability, Fair Value, Gross Liability   16,082,000 42,750,000    
Derivative Liability, Fair Value, Amount Offset Against Collateral [3]   0 0    
Derivative Liability, Fair Value, Amount Not Offset Against Collateral [4]   2,871,000 1,031,000    
Derivative Liability, net of offset   13,211,000 41,719,000    
Receivables from Brokers-Dealers and Clearing Organizations          
Derivative [Line Items]          
Collateral posted   11,200,000 13,500,000    
Other Income [Member]          
Derivative [Line Items]          
Realized and unrealized gains/(losses) related to derivatives trading activities   14,300,000 $ 3,900,000 $ (11,200,000)  
2019 convertible note | Convertible Debt          
Derivative [Line Items]          
Call Option, Fair Value         $ 35,700,000
Derivative, Loss on Derivative   $ 600,000      
[1] Includes index, equity, commodity future and cash conversion options.
[2] Includes index, equity, commodity future and cash conversion options.
[3] Includes financial instruments subject to enforceable master netting provisions that are permitted to be offset to the extent an event of default has occurred.
[4] Includes the amount of collateral held or posted.