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Fees and Related Party Transactions (Details) - USD ($)
3 Months Ended
Mar. 31, 2019
Mar. 31, 2018
Advisory Fees [Abstract]    
Advisory fees at annual rate of the Members' Capital 1.50%  
Advisory fees $ 102,095 $ 142,186
Sponsor Fees [Abstract]    
Sponsor Fees $ 54,113 74,114
Incentive Allocation [Abstract]    
Percentage of incentive allocation 20.00%  
Incentive Allocation allocated to the Fund by GAIT $ 0 0
Administrator's Fee [Abstract]    
Administrator's fees $ 9,250 $ 12,229
Class 0 Units [Member]    
Sponsor Fees [Abstract]    
Sponsor fees at annual rate of the Members' Capital 0.50%  
Class 2 Units [Member]    
Sponsor Fees [Abstract]    
Sponsor fees at annual rate of the Members' Capital 1.25%