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Financial Derivatives - Schedule of Derivative Instruments, Impact on Results of Operations (Details) (USD $)
 12 Months Ended
Dec. 31, 2014
Dec. 31, 2013
Dec. 31, 2012
Derivative Instruments, Gain (Loss) [Line Items]      
(Losses)/gains on financial derivatives and hedging activities $ (21,646,000)us-gaap_GainLossOnDerivativeInstrumentsNetPretax $ 31,764,000us-gaap_GainLossOnDerivativeInstrumentsNetPretax $ (19,829,000)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 14,520,000us-gaap_ChangeInUnrealizedGainLossOnHedgedItemInFairValueHedge1
/ us-gaap_DerivativeInstrumentsGainLossByHedgingRelationshipAxis
= us-gaap_FairValueHedgingMember
/ us-gaap_HedgingDesignationAxis
= us-gaap_DesignatedAsHedgingInstrumentMember		 (18,230,000)us-gaap_ChangeInUnrealizedGainLossOnHedgedItemInFairValueHedge1
/ us-gaap_DerivativeInstrumentsGainLossByHedgingRelationshipAxis
= us-gaap_FairValueHedgingMember
/ us-gaap_HedgingDesignationAxis
= us-gaap_DesignatedAsHedgingInstrumentMember		 6,388,000us-gaap_ChangeInUnrealizedGainLossOnHedgedItemInFairValueHedge1
/ us-gaap_DerivativeInstrumentsGainLossByHedgingRelationshipAxis
= us-gaap_FairValueHedgingMember
/ us-gaap_HedgingDesignationAxis
= us-gaap_DesignatedAsHedgingInstrumentMember
Gain (Loss) on Fair Value Hedges Recognized in Earnings 11,791,000us-gaap_GainLossOnFairValueHedgesRecognizedInEarnings
/ us-gaap_DerivativeInstrumentsGainLossByHedgingRelationshipAxis
= us-gaap_FairValueHedgingMember
/ us-gaap_HedgingDesignationAxis
= us-gaap_DesignatedAsHedgingInstrumentMember		 11,308,000us-gaap_GainLossOnFairValueHedgesRecognizedInEarnings
/ us-gaap_DerivativeInstrumentsGainLossByHedgingRelationshipAxis
= us-gaap_FairValueHedgingMember
/ us-gaap_HedgingDesignationAxis
= us-gaap_DesignatedAsHedgingInstrumentMember		 5,984,000us-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)/gains on financial derivatives and hedging activities (33,437,000)us-gaap_GainLossOnDerivativeInstrumentsNetPretax
/ us-gaap_HedgingDesignationAxis
= us-gaap_NondesignatedMember		 20,456,000us-gaap_GainLossOnDerivativeInstrumentsNetPretax
/ us-gaap_HedgingDesignationAxis
= us-gaap_NondesignatedMember		 (25,813,000)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 11,600,000agm_GainLossonComponentsIncludedfromAssessmentofInterestRateFairValueHedgeEffectiveness
/ us-gaap_DerivativeByNatureAxis
= us-gaap_InterestRateSwapMember
/ us-gaap_DerivativeInstrumentsGainLossByHedgingRelationshipAxis
= us-gaap_FairValueHedgingMember		 11,800,000agm_GainLossonComponentsIncludedfromAssessmentofInterestRateFairValueHedgeEffectiveness
/ us-gaap_DerivativeByNatureAxis
= us-gaap_InterestRateSwapMember
/ us-gaap_DerivativeInstrumentsGainLossByHedgingRelationshipAxis
= us-gaap_FairValueHedgingMember		 6,100,000agm_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		 500,000us-gaap_GainLossOnFairValueHedgeIneffectivenessNet
/ us-gaap_DerivativeByNatureAxis
= us-gaap_InterestRateSwapMember
/ us-gaap_DerivativeInstrumentsGainLossByHedgingRelationshipAxis
= us-gaap_FairValueHedgingMember		 (100,000)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 (2,729,000)us-gaap_ChangeInUnrealizedGainLossOnFairValueHedgingInstruments1
/ us-gaap_DerivativeByNatureAxis
= us-gaap_InterestRateSwapMember
/ us-gaap_DerivativeInstrumentsGainLossByHedgingRelationshipAxis
= us-gaap_FairValueHedgingMember
/ us-gaap_HedgingDesignationAxis
= us-gaap_DesignatedAsHedgingInstrumentMember		 29,538,000us-gaap_ChangeInUnrealizedGainLossOnFairValueHedgingInstruments1
/ us-gaap_DerivativeByNatureAxis
= us-gaap_InterestRateSwapMember
/ us-gaap_DerivativeInstrumentsGainLossByHedgingRelationshipAxis
= us-gaap_FairValueHedgingMember
/ us-gaap_HedgingDesignationAxis
= us-gaap_DesignatedAsHedgingInstrumentMember		 (404,000)us-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)/gains on financial derivatives and hedging activities (31,111,000)us-gaap_GainLossOnDerivativeInstrumentsNetPretax
/ us-gaap_DerivativeByNatureAxis
= us-gaap_InterestRateSwapMember
/ us-gaap_HedgingDesignationAxis
= us-gaap_NondesignatedMember		 21,355,000us-gaap_GainLossOnDerivativeInstrumentsNetPretax
/ us-gaap_DerivativeByNatureAxis
= us-gaap_InterestRateSwapMember
/ us-gaap_HedgingDesignationAxis
= us-gaap_NondesignatedMember		 (24,763,000)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)/gains on financial derivatives and hedging activities (1,842,000)us-gaap_GainLossOnDerivativeInstrumentsNetPretax
/ us-gaap_DerivativeByNatureAxis
= us-gaap_ForwardContractsMember
/ us-gaap_HedgingDesignationAxis
= us-gaap_NondesignatedMember		 (1,002,000)us-gaap_GainLossOnDerivativeInstrumentsNetPretax
/ us-gaap_DerivativeByNatureAxis
= us-gaap_ForwardContractsMember
/ us-gaap_HedgingDesignationAxis
= us-gaap_NondesignatedMember		 (828,000)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)/gains on financial derivatives and hedging activities (484,000)us-gaap_GainLossOnDerivativeInstrumentsNetPretax
/ us-gaap_DerivativeByNatureAxis
= us-gaap_FutureMember
/ us-gaap_HedgingDesignationAxis
= us-gaap_NondesignatedMember		 103,000us-gaap_GainLossOnDerivativeInstrumentsNetPretax
/ us-gaap_DerivativeByNatureAxis
= us-gaap_FutureMember
/ us-gaap_HedgingDesignationAxis
= us-gaap_NondesignatedMember		 (129,000)us-gaap_GainLossOnDerivativeInstrumentsNetPretax
/ us-gaap_DerivativeByNatureAxis
= us-gaap_FutureMember
/ us-gaap_HedgingDesignationAxis
= us-gaap_NondesignatedMember
Credit Default Swap [Member] | Not Designated as Hedging Instrument [Member]      
Derivative Instruments, Gain (Loss) [Line Items]      
(Losses)/gains on financial derivatives and hedging activities $ 0us-gaap_GainLossOnDerivativeInstrumentsNetPretax
/ us-gaap_DerivativeByNatureAxis
= us-gaap_CreditDefaultSwapMember
/ us-gaap_HedgingDesignationAxis
= us-gaap_NondesignatedMember		 $ 0us-gaap_GainLossOnDerivativeInstrumentsNetPretax
/ us-gaap_DerivativeByNatureAxis
= us-gaap_CreditDefaultSwapMember
/ us-gaap_HedgingDesignationAxis
= us-gaap_NondesignatedMember		 $ (93,000)us-gaap_GainLossOnDerivativeInstrumentsNetPretax
/ us-gaap_DerivativeByNatureAxis
= us-gaap_CreditDefaultSwapMember
/ us-gaap_HedgingDesignationAxis
= us-gaap_NondesignatedMember