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Accounting Policies - Earnings Per Share Anti-Dilutive (Details)
12 Months Ended
Dec. 31, 2014
Dec. 31, 2013
Dec. 31, 2012
Stock Options and SARs [Members]      
Antidilutive Securities Excluded from Computation of Earnings Per Share [Line Items]      
Antidilutive securities excluded from earnings per share (shares) 109,143us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareAmount
/ us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareByAntidilutiveSecuritiesAxis
= agm_StockOptionsAndStockAppreciationRightsMember
33,730us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareAmount
/ us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareByAntidilutiveSecuritiesAxis
= agm_StockOptionsAndStockAppreciationRightsMember
317,253us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareAmount
/ us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareByAntidilutiveSecuritiesAxis
= agm_StockOptionsAndStockAppreciationRightsMember
Performance Shares [Member]      
Antidilutive Securities Excluded from Computation of Earnings Per Share [Line Items]      
Antidilutive securities excluded from earnings per share (shares) 36,784us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareAmount
/ us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareByAntidilutiveSecuritiesAxis
= us-gaap_PerformanceSharesMember
26,696us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareAmount
/ us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareByAntidilutiveSecuritiesAxis
= us-gaap_PerformanceSharesMember
79,300us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareAmount
/ us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareByAntidilutiveSecuritiesAxis
= us-gaap_PerformanceSharesMember