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Consolidated Statements of Financial Condition (Unaudited) (Parenthetical) (USD $)
Mar. 31, 2015
Dec. 31, 2014
Class 0 Units [Member]    
Members' capital:    
Capital units, issued (in units) 392,050.086gaifb_CapitalUnitsIssued
/ us-gaap_CapitalUnitsByClassAxis
= us-gaap_CapitalUnitClassAMember
390,307.769gaifb_CapitalUnitsIssued
/ us-gaap_CapitalUnitsByClassAxis
= us-gaap_CapitalUnitClassAMember
Capital units, outstanding (in units) 392,050.086us-gaap_CapitalUnitsOutstanding
/ us-gaap_CapitalUnitsByClassAxis
= us-gaap_CapitalUnitClassAMember
390,307.769us-gaap_CapitalUnitsOutstanding
/ us-gaap_CapitalUnitsByClassAxis
= us-gaap_CapitalUnitClassAMember
Capital units, value (in dollars per unit) $ 159.93gaifb_CapitalUnitsStatedValue
/ us-gaap_CapitalUnitsByClassAxis
= us-gaap_CapitalUnitClassAMember
$ 149.37gaifb_CapitalUnitsStatedValue
/ us-gaap_CapitalUnitsByClassAxis
= us-gaap_CapitalUnitClassAMember
Class 2 Units [Member]    
Members' capital:    
Capital units, issued (in units) 175,236.469gaifb_CapitalUnitsIssued
/ us-gaap_CapitalUnitsByClassAxis
= us-gaap_CapitalUnitClassBMember
178,245.791gaifb_CapitalUnitsIssued
/ us-gaap_CapitalUnitsByClassAxis
= us-gaap_CapitalUnitClassBMember
Capital units, outstanding (in units) 175,236.469us-gaap_CapitalUnitsOutstanding
/ us-gaap_CapitalUnitsByClassAxis
= us-gaap_CapitalUnitClassBMember
178,245.791us-gaap_CapitalUnitsOutstanding
/ us-gaap_CapitalUnitsByClassAxis
= us-gaap_CapitalUnitClassBMember
Capital units, value (in dollars per unit) $ 121.12gaifb_CapitalUnitsStatedValue
/ us-gaap_CapitalUnitsByClassAxis
= us-gaap_CapitalUnitClassBMember
$ 113.58gaifb_CapitalUnitsStatedValue
/ us-gaap_CapitalUnitsByClassAxis
= us-gaap_CapitalUnitClassBMember