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Financial Derivatives - Schedule of Derivative Instruments, Impact on Results of Operations (Details) (USD $)
 3 Months Ended
Mar. 31, 2015
Mar. 31, 2014
Derivative Instruments, Gain (Loss) [Line Items]    
Losses on financial derivatives and hedging activities $ (3,882,000)us-gaap_GainLossOnDerivativeInstrumentsNetPretax $ (7,578,000)us-gaap_GainLossOnDerivativeInstrumentsNetPretax
Designated as Hedging Instrument [Member] | Fair Value Hedging [Member]    
Derivative Instruments, Gain (Loss) [Line Items]    
Change in Unrealized Gain (Loss) on Hedged Item in Fair Value Hedge 8,876,000us-gaap_ChangeInUnrealizedGainLossOnHedgedItemInFairValueHedge1
/ us-gaap_DerivativeInstrumentsGainLossByHedgingRelationshipAxis
= us-gaap_FairValueHedgingMember
/ us-gaap_HedgingDesignationAxis
= us-gaap_DesignatedAsHedgingInstrumentMember		 2,750,000us-gaap_ChangeInUnrealizedGainLossOnHedgedItemInFairValueHedge1
/ us-gaap_DerivativeInstrumentsGainLossByHedgingRelationshipAxis
= us-gaap_FairValueHedgingMember
/ us-gaap_HedgingDesignationAxis
= us-gaap_DesignatedAsHedgingInstrumentMember
Gain (Loss) on Fair Value Hedges Recognized in Earnings 3,116,000us-gaap_GainLossOnFairValueHedgesRecognizedInEarnings
/ us-gaap_DerivativeInstrumentsGainLossByHedgingRelationshipAxis
= us-gaap_FairValueHedgingMember
/ us-gaap_HedgingDesignationAxis
= us-gaap_DesignatedAsHedgingInstrumentMember		 2,950,000us-gaap_GainLossOnFairValueHedgesRecognizedInEarnings
/ us-gaap_DerivativeInstrumentsGainLossByHedgingRelationshipAxis
= us-gaap_FairValueHedgingMember
/ us-gaap_HedgingDesignationAxis
= us-gaap_DesignatedAsHedgingInstrumentMember
Not Designated as Hedging Instrument [Member]    
Derivative Instruments, Gain (Loss) [Line Items]    
Losses on financial derivatives and hedging activities (6,998,000)us-gaap_GainLossOnDerivativeInstrumentsNetPretax
/ us-gaap_HedgingDesignationAxis
= us-gaap_NondesignatedMember		 (10,528,000)us-gaap_GainLossOnDerivativeInstrumentsNetPretax
/ us-gaap_HedgingDesignationAxis
= us-gaap_NondesignatedMember
Interest Rate Swap [Member] | Fair Value Hedging [Member]    
Derivative Instruments, Gain (Loss) [Line Items]    
Gain (Loss) on Components Included from Assessment of Interest Rate Fair Value Hedge Effectiveness 2,900,000agm_GainLossonComponentsIncludedfromAssessmentofInterestRateFairValueHedgeEffectiveness
/ us-gaap_DerivativeByNatureAxis
= us-gaap_InterestRateSwapMember
/ us-gaap_DerivativeInstrumentsGainLossByHedgingRelationshipAxis
= us-gaap_FairValueHedgingMember		 2,900,000agm_GainLossonComponentsIncludedfromAssessmentofInterestRateFairValueHedgeEffectiveness
/ us-gaap_DerivativeByNatureAxis
= us-gaap_InterestRateSwapMember
/ us-gaap_DerivativeInstrumentsGainLossByHedgingRelationshipAxis
= us-gaap_FairValueHedgingMember
Gain (Loss) on Fair Value Hedge Ineffectiveness, Net (200,000)us-gaap_GainLossOnFairValueHedgeIneffectivenessNet
/ us-gaap_DerivativeByNatureAxis
= us-gaap_InterestRateSwapMember
/ us-gaap_DerivativeInstrumentsGainLossByHedgingRelationshipAxis
= us-gaap_FairValueHedgingMember		 (29,000)us-gaap_GainLossOnFairValueHedgeIneffectivenessNet
/ us-gaap_DerivativeByNatureAxis
= us-gaap_InterestRateSwapMember
/ us-gaap_DerivativeInstrumentsGainLossByHedgingRelationshipAxis
= us-gaap_FairValueHedgingMember
Interest Rate Swap [Member] | Designated as Hedging Instrument [Member] | Fair Value Hedging [Member]    
Derivative Instruments, Gain (Loss) [Line Items]    
Change in Unrealized Gain (Loss) on Fair Value Hedging Instruments (5,760,000)us-gaap_ChangeInUnrealizedGainLossOnFairValueHedgingInstruments1
/ us-gaap_DerivativeByNatureAxis
= us-gaap_InterestRateSwapMember
/ us-gaap_DerivativeInstrumentsGainLossByHedgingRelationshipAxis
= us-gaap_FairValueHedgingMember
/ us-gaap_HedgingDesignationAxis
= us-gaap_DesignatedAsHedgingInstrumentMember		 200,000us-gaap_ChangeInUnrealizedGainLossOnFairValueHedgingInstruments1
/ us-gaap_DerivativeByNatureAxis
= us-gaap_InterestRateSwapMember
/ us-gaap_DerivativeInstrumentsGainLossByHedgingRelationshipAxis
= us-gaap_FairValueHedgingMember
/ us-gaap_HedgingDesignationAxis
= us-gaap_DesignatedAsHedgingInstrumentMember
Interest Rate Swap [Member] | Not Designated as Hedging Instrument [Member]    
Derivative Instruments, Gain (Loss) [Line Items]    
Losses on financial derivatives and hedging activities (5,956,000)us-gaap_GainLossOnDerivativeInstrumentsNetPretax
/ us-gaap_DerivativeByNatureAxis
= us-gaap_InterestRateSwapMember
/ us-gaap_HedgingDesignationAxis
= us-gaap_NondesignatedMember		 (9,548,000)us-gaap_GainLossOnDerivativeInstrumentsNetPretax
/ us-gaap_DerivativeByNatureAxis
= us-gaap_InterestRateSwapMember
/ us-gaap_HedgingDesignationAxis
= us-gaap_NondesignatedMember
Forward Contracts [Member] | Not Designated as Hedging Instrument [Member]    
Derivative Instruments, Gain (Loss) [Line Items]    
Losses on financial derivatives and hedging activities (786,000)us-gaap_GainLossOnDerivativeInstrumentsNetPretax
/ us-gaap_DerivativeByNatureAxis
= us-gaap_ForwardContractsMember
/ us-gaap_HedgingDesignationAxis
= us-gaap_NondesignatedMember		 (852,000)us-gaap_GainLossOnDerivativeInstrumentsNetPretax
/ us-gaap_DerivativeByNatureAxis
= us-gaap_ForwardContractsMember
/ us-gaap_HedgingDesignationAxis
= us-gaap_NondesignatedMember
Future [Member] | Not Designated as Hedging Instrument [Member]    
Derivative Instruments, Gain (Loss) [Line Items]    
Losses on financial derivatives and hedging activities $ (256,000)us-gaap_GainLossOnDerivativeInstrumentsNetPretax
/ us-gaap_DerivativeByNatureAxis
= us-gaap_FutureMember
/ us-gaap_HedgingDesignationAxis
= us-gaap_NondesignatedMember		 $ (128,000)us-gaap_GainLossOnDerivativeInstrumentsNetPretax
/ us-gaap_DerivativeByNatureAxis
= us-gaap_FutureMember
/ us-gaap_HedgingDesignationAxis
= us-gaap_NondesignatedMember