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Financial Derivatives - Narrative (Details) (USD $)
Mar. 31, 2015
Dec. 31, 2014
Derivative [Line Items]    
Financial derivatives, at fair value $ 95,493,000us-gaap_DerivativeFairValueOfDerivativeLiability $ 84,844,000us-gaap_DerivativeFairValueOfDerivativeLiability
Derivative, Collateral [Abstract]    
Collateral Pledged 48,870,000us-gaap_CollateralAlreadyPostedAggregateFairValue 46,627,000us-gaap_CollateralAlreadyPostedAggregateFairValue
Additional Collateral, Aggregate Fair Value 47,900,000us-gaap_AdditionalCollateralAggregateFairValue 46,800,000us-gaap_AdditionalCollateralAggregateFairValue
Notional Disclosures [Abstract]    
Derivative, Notional Amount 7,370,529,000invest_DerivativeNotionalAmount 6,837,571,000invest_DerivativeNotionalAmount
Excluding netting [Member] | Including accrued interest [Member]    
Derivative [Line Items]    
Credit exposure to interest rate swap counterparties 8,700,000agm_CreditExposureToInterestRateSwapCounterparties
/ us-gaap_DerivativeByNatureAxis
= agm_IncludingAccruedInterestMember
/ us-gaap_TypeOfArrangementAxis
= agm_ExcludingNettingMember
6,100,000agm_CreditExposureToInterestRateSwapCounterparties
/ us-gaap_DerivativeByNatureAxis
= agm_IncludingAccruedInterestMember
/ us-gaap_TypeOfArrangementAxis
= agm_ExcludingNettingMember
Financial derivatives, at fair value 105,300,000us-gaap_DerivativeFairValueOfDerivativeLiability
/ us-gaap_DerivativeByNatureAxis
= agm_IncludingAccruedInterestMember
/ us-gaap_TypeOfArrangementAxis
= agm_ExcludingNettingMember
99,400,000us-gaap_DerivativeFairValueOfDerivativeLiability
/ us-gaap_DerivativeByNatureAxis
= agm_IncludingAccruedInterestMember
/ us-gaap_TypeOfArrangementAxis
= agm_ExcludingNettingMember
Netting [Member] | Including accrued interest [Member]    
Derivative [Line Items]    
Credit exposure to interest rate swap counterparties 300,000agm_CreditExposureToInterestRateSwapCounterparties
/ us-gaap_DerivativeByNatureAxis
= agm_IncludingAccruedInterestMember
/ us-gaap_TypeOfArrangementAxis
= agm_NettingMember
400,000agm_CreditExposureToInterestRateSwapCounterparties
/ us-gaap_DerivativeByNatureAxis
= agm_IncludingAccruedInterestMember
/ us-gaap_TypeOfArrangementAxis
= agm_NettingMember
Financial derivatives, at fair value 96,800,000us-gaap_DerivativeFairValueOfDerivativeLiability
/ us-gaap_DerivativeByNatureAxis
= agm_IncludingAccruedInterestMember
/ us-gaap_TypeOfArrangementAxis
= agm_NettingMember
93,400,000us-gaap_DerivativeFairValueOfDerivativeLiability
/ us-gaap_DerivativeByNatureAxis
= agm_IncludingAccruedInterestMember
/ us-gaap_TypeOfArrangementAxis
= agm_NettingMember
Uncollateralized [Member]    
Derivative [Line Items]    
Credit exposure to interest rate swap counterparties 300,000agm_CreditExposureToInterestRateSwapCounterparties
/ us-gaap_TypeOfArrangementAxis
= agm_UncollateralizedMember
400,000agm_CreditExposureToInterestRateSwapCounterparties
/ us-gaap_TypeOfArrangementAxis
= agm_UncollateralizedMember
Cash [Member]    
Derivative, Collateral [Abstract]    
Collateral Received 0us-gaap_ObligationToReturnSecuritiesReceivedAsCollateral
/ us-gaap_FinancialInstrumentsOwnedAndPledgedAsCollateralAxis
= us-gaap_CashMember
0us-gaap_ObligationToReturnSecuritiesReceivedAsCollateral
/ us-gaap_FinancialInstrumentsOwnedAndPledgedAsCollateralAxis
= us-gaap_CashMember
Collateral Pledged 48,900,000us-gaap_CollateralAlreadyPostedAggregateFairValue
/ us-gaap_FinancialInstrumentsOwnedAndPledgedAsCollateralAxis
= us-gaap_CashMember
46,600,000us-gaap_CollateralAlreadyPostedAggregateFairValue
/ us-gaap_FinancialInstrumentsOwnedAndPledgedAsCollateralAxis
= us-gaap_CashMember
Securities Pledged as Collateral [Member]    
Derivative, Collateral [Abstract]    
Collateral Pledged 0us-gaap_CollateralAlreadyPostedAggregateFairValue
/ us-gaap_FinancialInstrumentsOwnedAndPledgedAsCollateralAxis
= us-gaap_SecuritiesPledgedAsCollateralMember
0us-gaap_CollateralAlreadyPostedAggregateFairValue
/ us-gaap_FinancialInstrumentsOwnedAndPledgedAsCollateralAxis
= us-gaap_SecuritiesPledgedAsCollateralMember
Exchange Cleared [Member]    
Notional Disclosures [Abstract]    
Derivative, Notional Amount 4,200,000,000invest_DerivativeNotionalAmount
/ us-gaap_TransactionTypeAxis
= us-gaap_ExchangeClearedMember
4,000,000,000invest_DerivativeNotionalAmount
/ us-gaap_TransactionTypeAxis
= us-gaap_ExchangeClearedMember
Interest Rate Swap [Member]    
Notional Disclosures [Abstract]    
Derivative, Notional Amount $ 7,300,000,000invest_DerivativeNotionalAmount
/ us-gaap_DerivativeInstrumentRiskAxis
= us-gaap_InterestRateSwapMember
$ 6,800,000,000invest_DerivativeNotionalAmount
/ us-gaap_DerivativeInstrumentRiskAxis
= us-gaap_InterestRateSwapMember