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Accounting Policies - Earnings Per Share Anti-Dilutive (Details)
3 Months Ended
Mar. 31, 2015
Mar. 31, 2014
Stock Options and SARs [Members]    
Antidilutive Securities Excluded from Computation of Earnings Per Share [Line Items]    
Antidilutive securities excluded from earnings per share (shares) 201,401us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareAmount
/ us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareByAntidilutiveSecuritiesAxis
= agm_StockOptionsAndStockAppreciationRightsMember
32,983us-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) 30,514us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareAmount
/ us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareByAntidilutiveSecuritiesAxis
= us-gaap_PerformanceSharesMember
31,594us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareAmount
/ us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareByAntidilutiveSecuritiesAxis
= us-gaap_PerformanceSharesMember