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Consolidated Statements of Changes in Members' Capital (Unaudited) (USD $)
3 Months Ended
Mar. 31, 2015
Mar. 31, 2014
Members' capital, beginning balance $ 78,546,247us-gaap_PartnersCapital $ 76,659,546us-gaap_PartnersCapital
Subscriptions 734,544gaifb_PartnersCapitalAccountSubscriptions 1,462,800gaifb_PartnersCapitalAccountSubscriptions
Redemptions (832,281)us-gaap_PartnersCapitalAccountRedemptions (3,904,278)us-gaap_PartnersCapitalAccountRedemptions
Net income (loss) 5,476,983us-gaap_IncomeLossAttributableToParent (8,384,583)us-gaap_IncomeLossAttributableToParent
Members' capital, ending balance 83,925,493us-gaap_PartnersCapital 65,833,485us-gaap_PartnersCapital
Class 0 Units [Member]    
Members' capital, beginning 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, beginning 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
Subscriptions 377,644gaifb_PartnersCapitalAccountSubscriptions
/ us-gaap_CapitalUnitsByClassAxis
= us-gaap_CapitalUnitClassAMember
160,000gaifb_PartnersCapitalAccountSubscriptions
/ us-gaap_CapitalUnitsByClassAxis
= us-gaap_CapitalUnitClassAMember
Subscriptions (in units) 2,418.637gaifb_PartnersCapitalAccountSubscribed
/ us-gaap_CapitalUnitsByClassAxis
= us-gaap_CapitalUnitClassAMember
1,320.227gaifb_PartnersCapitalAccountSubscribed
/ us-gaap_CapitalUnitsByClassAxis
= us-gaap_CapitalUnitClassAMember
Redemptions (107,801)us-gaap_PartnersCapitalAccountRedemptions
/ us-gaap_CapitalUnitsByClassAxis
= us-gaap_CapitalUnitClassAMember
(2,991,103)us-gaap_PartnersCapitalAccountRedemptions
/ us-gaap_CapitalUnitsByClassAxis
= us-gaap_CapitalUnitClassAMember
Redemptions (in units) (676.320)us-gaap_PartnersCapitalAccountUnitsRedeemed
/ us-gaap_CapitalUnitsByClassAxis
= us-gaap_CapitalUnitClassAMember
(25,972.022)us-gaap_PartnersCapitalAccountUnitsRedeemed
/ us-gaap_CapitalUnitsByClassAxis
= us-gaap_CapitalUnitClassAMember
Net income (loss) 4,129,634us-gaap_IncomeLossAttributableToParent
/ us-gaap_CapitalUnitsByClassAxis
= us-gaap_CapitalUnitClassAMember
(6,231,099)us-gaap_IncomeLossAttributableToParent
/ us-gaap_CapitalUnitsByClassAxis
= us-gaap_CapitalUnitClassAMember
Members' capital, ending balance 62,700,318us-gaap_PartnersCapital
/ us-gaap_CapitalUnitsByClassAxis
= us-gaap_CapitalUnitClassAMember
49,247,820us-gaap_PartnersCapital
/ us-gaap_CapitalUnitsByClassAxis
= us-gaap_CapitalUnitClassAMember
Members' capital, ending balance (in units) 392,050.086us-gaap_PartnersCapitalAccountUnits
/ us-gaap_CapitalUnitsByClassAxis
= us-gaap_CapitalUnitClassAMember
431,892.793us-gaap_PartnersCapitalAccountUnits
/ us-gaap_CapitalUnitsByClassAxis
= us-gaap_CapitalUnitClassAMember
Class 2 Units [Member]    
Members' capital, beginning 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, beginning 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
Subscriptions 356,900gaifb_PartnersCapitalAccountSubscriptions
/ us-gaap_CapitalUnitsByClassAxis
= us-gaap_CapitalUnitClassBMember
1,302,800gaifb_PartnersCapitalAccountSubscriptions
/ us-gaap_CapitalUnitsByClassAxis
= us-gaap_CapitalUnitClassBMember
Subscriptions (in units) 2,990.196gaifb_PartnersCapitalAccountSubscribed
/ us-gaap_CapitalUnitsByClassAxis
= us-gaap_CapitalUnitClassBMember
13,404.463gaifb_PartnersCapitalAccountSubscribed
/ us-gaap_CapitalUnitsByClassAxis
= us-gaap_CapitalUnitClassBMember
Redemptions (724,480)us-gaap_PartnersCapitalAccountRedemptions
/ us-gaap_CapitalUnitsByClassAxis
= us-gaap_CapitalUnitClassBMember
(913,175)us-gaap_PartnersCapitalAccountRedemptions
/ us-gaap_CapitalUnitsByClassAxis
= us-gaap_CapitalUnitClassBMember
Redemptions (in units) (5,999.518)us-gaap_PartnersCapitalAccountUnitsRedeemed
/ us-gaap_CapitalUnitsByClassAxis
= us-gaap_CapitalUnitClassBMember
(10,154.220)us-gaap_PartnersCapitalAccountUnitsRedeemed
/ us-gaap_CapitalUnitsByClassAxis
= us-gaap_CapitalUnitClassBMember
Net income (loss) 1,347,349us-gaap_IncomeLossAttributableToParent
/ us-gaap_CapitalUnitsByClassAxis
= us-gaap_CapitalUnitClassBMember
(2,153,484)us-gaap_IncomeLossAttributableToParent
/ us-gaap_CapitalUnitsByClassAxis
= us-gaap_CapitalUnitClassBMember
Members' capital, ending balance $ 21,225,175us-gaap_PartnersCapital
/ us-gaap_CapitalUnitsByClassAxis
= us-gaap_CapitalUnitClassBMember
$ 16,585,665us-gaap_PartnersCapital
/ us-gaap_CapitalUnitsByClassAxis
= us-gaap_CapitalUnitClassBMember
Members' capital, ending balance (in units) 175,236.469us-gaap_PartnersCapitalAccountUnits
/ us-gaap_CapitalUnitsByClassAxis
= us-gaap_CapitalUnitClassBMember
189,711.755us-gaap_PartnersCapitalAccountUnits
/ us-gaap_CapitalUnitsByClassAxis
= us-gaap_CapitalUnitClassBMember