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Accounting Policies - Earnings Per Share (Details) (USD $)
In Thousands, except Per Share data, unless otherwise specified
3 Months Ended 12 Months Ended
Dec. 31, 2014
Sep. 30, 2014
Jun. 30, 2014
Mar. 31, 2014
Dec. 31, 2013
Sep. 30, 2013
Jun. 30, 2013
Mar. 31, 2013
Dec. 31, 2014
Dec. 31, 2013
Dec. 31, 2012
Accounting Policies [Abstract]                      
Net income attributable to common stockholders (Basic) $ 5,647us-gaap_NetIncomeLossAvailableToCommonStockholdersBasic $ 11,586us-gaap_NetIncomeLossAvailableToCommonStockholdersBasic $ 20,205us-gaap_NetIncomeLossAvailableToCommonStockholdersBasic $ 813us-gaap_NetIncomeLossAvailableToCommonStockholdersBasic $ 12,485us-gaap_NetIncomeLossAvailableToCommonStockholdersBasic $ 15,413us-gaap_NetIncomeLossAvailableToCommonStockholdersBasic $ 27,745us-gaap_NetIncomeLossAvailableToCommonStockholdersBasic $ 16,190us-gaap_NetIncomeLossAvailableToCommonStockholdersBasic $ 38,251us-gaap_NetIncomeLossAvailableToCommonStockholdersBasic $ 71,833us-gaap_NetIncomeLossAvailableToCommonStockholdersBasic $ 43,894us-gaap_NetIncomeLossAvailableToCommonStockholdersBasic
Net income attributable to common stockholders (Dilutive)                 $ 38,251us-gaap_NetIncomeLossAvailableToCommonStockholdersDiluted $ 71,833us-gaap_NetIncomeLossAvailableToCommonStockholdersDiluted $ 43,894us-gaap_NetIncomeLossAvailableToCommonStockholdersDiluted
Earnings Per Share, Basic [Abstract]                      
Stock options, SARs and restricted stock                 447us-gaap_IncrementalCommonSharesAttributableToShareBasedPaymentArrangements 393us-gaap_IncrementalCommonSharesAttributableToShareBasedPaymentArrangements 540us-gaap_IncrementalCommonSharesAttributableToShareBasedPaymentArrangements
Stock options, SARs and restricted stock (in usd per share)                 $ (0.13)agm_EarningsPerShareOnIncrementalCommonSharesAttributableToShareBasedPaymentArrangements $ (0.23)agm_EarningsPerShareOnIncrementalCommonSharesAttributableToShareBasedPaymentArrangements $ (0.21)agm_EarningsPerShareOnIncrementalCommonSharesAttributableToShareBasedPaymentArrangements
Weighted Average Number of Shares Outstanding, Basic                 10,920us-gaap_WeightedAverageNumberOfSharesOutstandingBasic 10,816us-gaap_WeightedAverageNumberOfSharesOutstandingBasic 10,479us-gaap_WeightedAverageNumberOfSharesOutstandingBasic
Basic earnings per common share $ 0.52us-gaap_EarningsPerShareBasic $ 1.06us-gaap_EarningsPerShareBasic $ 1.85us-gaap_EarningsPerShareBasic $ 0.07us-gaap_EarningsPerShareBasic $ 1.14us-gaap_EarningsPerShareBasic $ 1.42us-gaap_EarningsPerShareBasic $ 2.57us-gaap_EarningsPerShareBasic $ 1.51us-gaap_EarningsPerShareBasic $ 3.50us-gaap_EarningsPerShareBasic $ 6.64us-gaap_EarningsPerShareBasic $ 4.19us-gaap_EarningsPerShareBasic
Weighted Average Number of Shares Outstanding, Diluted                 11,367us-gaap_WeightedAverageNumberOfDilutedSharesOutstanding 11,209us-gaap_WeightedAverageNumberOfDilutedSharesOutstanding 11,019us-gaap_WeightedAverageNumberOfDilutedSharesOutstanding
Diluted earnings per common share $ 0.50us-gaap_EarningsPerShareDiluted $ 1.02us-gaap_EarningsPerShareDiluted $ 1.78us-gaap_EarningsPerShareDiluted $ 0.07us-gaap_EarningsPerShareDiluted $ 1.11us-gaap_EarningsPerShareDiluted $ 1.37us-gaap_EarningsPerShareDiluted $ 2.48us-gaap_EarningsPerShareDiluted $ 1.45us-gaap_EarningsPerShareDiluted $ 3.37us-gaap_EarningsPerShareDiluted $ 6.41us-gaap_EarningsPerShareDiluted $ 3.98us-gaap_EarningsPerShareDiluted