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Consolidated Statements of Changes in Members' Capital (USD $)
12 Months Ended
Dec. 31, 2014
Dec. 31, 2013
Members' capital, beginning balance $ 76,659,546us-gaap_PartnersCapital $ 93,947,400us-gaap_PartnersCapital
Subscriptions 11,652,795gaifb_PartnersCapitalAccountSubscriptions 2,467,801gaifb_PartnersCapitalAccountSubscriptions
Redemptions (20,262,759)us-gaap_PartnersCapitalAccountRedemptions (28,314,081)us-gaap_PartnersCapitalAccountRedemptions
Net income 10,496,665us-gaap_IncomeLossAttributableToParent 8,558,426us-gaap_IncomeLossAttributableToParent
Members' capital, ending balance 78,546,247us-gaap_PartnersCapital 76,659,546us-gaap_PartnersCapital
Class 0 Units [Member]    
Members' capital, beginning balance 58,310,022us-gaap_PartnersCapital
/ us-gaap_CapitalUnitsByClassAxis
= us-gaap_CapitalUnitClassAMember
75,558,523us-gaap_PartnersCapital
/ us-gaap_CapitalUnitsByClassAxis
= us-gaap_CapitalUnitClassAMember
Members' capital, beginning balance (in units) 456,544.588us-gaap_PartnersCapitalAccountUnits
/ us-gaap_CapitalUnitsByClassAxis
= us-gaap_CapitalUnitClassAMember
657,725.570us-gaap_PartnersCapitalAccountUnits
/ us-gaap_CapitalUnitsByClassAxis
= us-gaap_CapitalUnitClassAMember
Subscriptions 8,734,000gaifb_PartnersCapitalAccountSubscriptions
/ us-gaap_CapitalUnitsByClassAxis
= us-gaap_CapitalUnitClassAMember
705,000gaifb_PartnersCapitalAccountSubscriptions
/ us-gaap_CapitalUnitsByClassAxis
= us-gaap_CapitalUnitClassAMember
Subscriptions (in units) 68,503.746gaifb_PartnersCapitalAccountSubscribed
/ us-gaap_CapitalUnitsByClassAxis
= us-gaap_CapitalUnitClassAMember
5,806.281gaifb_PartnersCapitalAccountSubscribed
/ us-gaap_CapitalUnitsByClassAxis
= us-gaap_CapitalUnitClassAMember
Redemptions (16,433,428)us-gaap_PartnersCapitalAccountRedemptions
/ us-gaap_CapitalUnitsByClassAxis
= us-gaap_CapitalUnitClassAMember
(24,940,235)us-gaap_PartnersCapitalAccountRedemptions
/ us-gaap_CapitalUnitsByClassAxis
= us-gaap_CapitalUnitClassAMember
Redemptions (in units) (134,740.565)us-gaap_PartnersCapitalAccountUnitsRedeemed
/ us-gaap_CapitalUnitsByClassAxis
= us-gaap_CapitalUnitClassAMember
(206,987.263)us-gaap_PartnersCapitalAccountUnitsRedeemed
/ us-gaap_CapitalUnitsByClassAxis
= us-gaap_CapitalUnitClassAMember
Net income 7,690,247us-gaap_IncomeLossAttributableToParent
/ us-gaap_CapitalUnitsByClassAxis
= us-gaap_CapitalUnitClassAMember
6,986,734us-gaap_IncomeLossAttributableToParent
/ us-gaap_CapitalUnitsByClassAxis
= us-gaap_CapitalUnitClassAMember
Members' capital, ending balance 58,300,841us-gaap_PartnersCapital
/ us-gaap_CapitalUnitsByClassAxis
= us-gaap_CapitalUnitClassAMember
58,310,022us-gaap_PartnersCapital
/ us-gaap_CapitalUnitsByClassAxis
= us-gaap_CapitalUnitClassAMember
Members' capital, ending balance (in units) 390,307.769us-gaap_PartnersCapitalAccountUnits
/ us-gaap_CapitalUnitsByClassAxis
= us-gaap_CapitalUnitClassAMember
456,544.588us-gaap_PartnersCapitalAccountUnits
/ us-gaap_CapitalUnitsByClassAxis
= us-gaap_CapitalUnitClassAMember
Class 2 Units [Member]    
Members' capital, beginning balance 18,349,524us-gaap_PartnersCapital
/ us-gaap_CapitalUnitsByClassAxis
= us-gaap_CapitalUnitClassBMember
18,388,877us-gaap_PartnersCapital
/ us-gaap_CapitalUnitsByClassAxis
= us-gaap_CapitalUnitClassBMember
Members' capital, beginning balance (in units) 186,461.512us-gaap_PartnersCapitalAccountUnits
/ us-gaap_CapitalUnitsByClassAxis
= us-gaap_CapitalUnitClassBMember
203,657.512us-gaap_PartnersCapitalAccountUnits
/ us-gaap_CapitalUnitsByClassAxis
= us-gaap_CapitalUnitClassBMember
Subscriptions 2,918,795gaifb_PartnersCapitalAccountSubscriptions
/ us-gaap_CapitalUnitsByClassAxis
= us-gaap_CapitalUnitClassBMember
1,762,801gaifb_PartnersCapitalAccountSubscriptions
/ us-gaap_CapitalUnitsByClassAxis
= us-gaap_CapitalUnitClassBMember
Subscriptions (in units) 31,364.710gaifb_PartnersCapitalAccountSubscribed
/ us-gaap_CapitalUnitsByClassAxis
= us-gaap_CapitalUnitClassBMember
18,904.473gaifb_PartnersCapitalAccountSubscribed
/ us-gaap_CapitalUnitsByClassAxis
= us-gaap_CapitalUnitClassBMember
Redemptions (3,829,331)us-gaap_PartnersCapitalAccountRedemptions
/ us-gaap_CapitalUnitsByClassAxis
= us-gaap_CapitalUnitClassBMember
(3,373,846)us-gaap_PartnersCapitalAccountRedemptions
/ us-gaap_CapitalUnitsByClassAxis
= us-gaap_CapitalUnitClassBMember
Redemptions (in units) (39,580.431)us-gaap_PartnersCapitalAccountUnitsRedeemed
/ us-gaap_CapitalUnitsByClassAxis
= us-gaap_CapitalUnitClassBMember
(36,100.473)us-gaap_PartnersCapitalAccountUnitsRedeemed
/ us-gaap_CapitalUnitsByClassAxis
= us-gaap_CapitalUnitClassBMember
Net income 2,806,418us-gaap_IncomeLossAttributableToParent
/ us-gaap_CapitalUnitsByClassAxis
= us-gaap_CapitalUnitClassBMember
1,571,692us-gaap_IncomeLossAttributableToParent
/ us-gaap_CapitalUnitsByClassAxis
= us-gaap_CapitalUnitClassBMember
Members' capital, ending balance $ 20,245,406us-gaap_PartnersCapital
/ us-gaap_CapitalUnitsByClassAxis
= us-gaap_CapitalUnitClassBMember
$ 18,349,524us-gaap_PartnersCapital
/ us-gaap_CapitalUnitsByClassAxis
= us-gaap_CapitalUnitClassBMember
Members' capital, ending balance (in units) 178,245.791us-gaap_PartnersCapitalAccountUnits
/ us-gaap_CapitalUnitsByClassAxis
= us-gaap_CapitalUnitClassBMember
186,461.512us-gaap_PartnersCapitalAccountUnits
/ us-gaap_CapitalUnitsByClassAxis
= us-gaap_CapitalUnitClassBMember