Income Taxes - Deferred Tax Assets and Liabilities (Details) (USD $)	Dec. 31, 2014	Dec. 31, 2013
Components of Deferred Tax Assets [Abstract]
Deferred Tax Assets, Derivative Instruments	$ 30,921,000	$ 22,349,000
Deferred Tax Asset - basis in securities	4,218,000agm_DeferredTaxAssetbasisinsecurities	2,509,000agm_DeferredTaxAssetbasisinsecurities
Deferred Tax Assets, Unrealized Losses on Available-for-Sale Securities, Gross	0	8,762,000
Deferred Tax Assets, Tax Deferred Expense, Reserves and Accruals, Provision for Loan Losses	3,545,000	4,667,000
Deferred Tax Assets, Tax Deferred Expense, Compensation and Benefits, Share-based Compensation Cost	2,443,000	1,916,000
Deferred Tax Assets, Capital Loss Carryforwards	2,105,000	38,532,000
Deferred Tax Assets, Valuation Allowance	2,100,000	37,900,000
Deferred Tax Assets, Investments	0us-gaap_DeferredTaxAssetsInvestments	1,499,000us-gaap_DeferredTaxAssetsInvestments
Deferred Tax Assets, Other	1,205,000us-gaap_DeferredTaxAssetsOther	2,455,000us-gaap_DeferredTaxAssetsOther
Deferred Tax Assets, Gross	42,332,000us-gaap_DeferredTaxAssetsGross	44,758,000us-gaap_DeferredTaxAssetsGross
Deferred Tax Liabilities, Other Comprehensive Income	8,448,000	0
Entity Not Subject to Income Taxes, Difference in Bases, Amount	(195,000)	(353,000)
Deferred Tax Liabilities, Other	298,000us-gaap_DeferredTaxLiabilitiesOther	360,000us-gaap_DeferredTaxLiabilitiesOther
Deferred Tax Liabilities, Gross	8,941,000us-gaap_DeferredIncomeTaxLiabilities	713,000us-gaap_DeferredIncomeTaxLiabilities
Deferred tax asset, net	33,391,000us-gaap_DeferredTaxAssetsLiabilitiesNet	44,045,000us-gaap_DeferredTaxAssetsLiabilitiesNet
Capital Loss Carryforward [Member]
Components of Deferred Tax Assets [Abstract]
Deferred Tax Assets, Valuation Allowance	2,105,000	36,432,000
Amortization of Premiums on Capital Investments [Member]
Components of Deferred Tax Assets [Abstract]
Deferred Tax Assets, Valuation Allowance	$ 0	$ 1,499,000

Deferred Tax Asset - basis in securities

No definition available.

Name:	agm_DeferredTaxAssetbasisinsecurities
Namespace Prefix:	agm_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	instant

- Details

Name:	us-gaap_ComponentsOfDeferredTaxAssetsAbstract
Namespace Prefix:	us-gaap_
Data Type:	xbrli:stringItemType
Balance Type:	na
Period Type:	duration

- Definition

Amount of deferred tax liability attributable to taxable temporary differences.

+ References

Reference 1: http://www.xbrl.org/2003/role/presentationRef

-Publisher FASB

-Name Accounting Standards Codification

-Glossary Deferred Tax Liability

-URI http://asc.fasb.org/extlink&oid=6510232

Reference 2: http://www.xbrl.org/2003/role/presentationRef

-Publisher FASB

-Name Accounting Standards Codification

-Topic 740

-SubTopic 10

-Section 50

-Paragraph 2

-Subparagraph (a)

-URI http://asc.fasb.org/extlink&oid=6907707&loc=d3e32537-109319

Reference 3: http://www.xbrl.org/2003/role/presentationRef

-Publisher SEC

-Name Regulation S-X (SX)

-Number 210

-Section 03

-Paragraph 15

-Subparagraph b(2)

-Article 7

+ Details

Name:	us-gaap_DeferredIncomeTaxLiabilities
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	instant

- Definition

Amount before allocation of valuation allowances of deferred tax asset attributable to deductible capital loss carryforwards.

+ References

Reference 1: http://www.xbrl.org/2003/role/presentationRef

-Publisher FASB

-Name Accounting Standards Codification

-Topic 740

-SubTopic 10

-Section 50

-Paragraph 6

-URI http://asc.fasb.org/extlink&oid=6907707&loc=d3e32621-109319

Reference 2: http://www.xbrl.org/2003/role/presentationRef

-Publisher FASB

-Name Accounting Standards Codification

-Topic 740

-SubTopic 10

-Section 25

-Paragraph 20

-URI http://asc.fasb.org/extlink&oid=29652012&loc=d3e28680-109314

Reference 3: http://www.xbrl.org/2003/role/presentationRef

-Publisher FASB

-Name Accounting Standards Codification

-Topic 740

-SubTopic 10

-Section 50

-Paragraph 8

-URI http://asc.fasb.org/extlink&oid=6907707&loc=d3e32632-109319

+ Details

Name:	us-gaap_DeferredTaxAssetsCapitalLossCarryforwards
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	instant

- Definition

Amount before allocation of valuation allowances of deferred tax asset attributable to deductible temporary differences from derivative instruments.

+ References

+ Details

Name:	us-gaap_DeferredTaxAssetsDerivativeInstruments
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	instant

- Definition

Amount before allocation of valuation allowances of deferred tax asset attributable to deductible temporary differences and carryforwards.

+ References

Reference 1: http://www.xbrl.org/2003/role/presentationRef

-Publisher FASB

-Name Accounting Standards Codification

-Topic 740

-SubTopic 10

-Section 50

-Paragraph 2

-Subparagraph (b)

-URI http://asc.fasb.org/extlink&oid=6907707&loc=d3e32537-109319

Reference 2: http://www.xbrl.org/2003/role/presentationRef

-Publisher FASB

-Name Accounting Standards Codification

-Glossary Deferred Tax Asset

-URI http://asc.fasb.org/extlink&oid=6510090

+ Details

Name:	us-gaap_DeferredTaxAssetsGross
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	instant

- Definition

Amount before allocation of valuation allowances of deferred tax asset attributable to deductible temporary differences from investments (excludes investments in subsidiaries and equity method investments).

+ References

No definition available.

+ Details

Name:	us-gaap_DeferredTaxAssetsInvestments
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	instant

- Definition

Amount after allocation of valuation allowances of deferred tax asset attributable to deductible temporary differences and carryforwards, net of deferred tax liability attributable to taxable temporary differences.

+ References

Reference 1: http://www.xbrl.org/2003/role/presentationRef

-Publisher FASB

-Name Accounting Standards Codification

-Topic 740

-SubTopic 10

-Section 50

-Paragraph 2

-URI http://asc.fasb.org/extlink&oid=6907707&loc=d3e32537-109319

+ Details

Name:	us-gaap_DeferredTaxAssetsLiabilitiesNet
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	instant

- Definition

Amount before allocation of valuation allowances of deferred tax asset attributable to deductible temporary differences not separately disclosed.

+ References

+ Details

Name:	us-gaap_DeferredTaxAssetsOther
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	instant

- Definition

Amount before allocation of valuation allowances of deferred tax asset attributable to deductible temporary differences from share-based compensation.

+ References

Reference 1: http://www.xbrl.org/2003/role/presentationRef

-Publisher FASB

-Name Accounting Standards Codification

-Topic 740

-SubTopic 10

-Section 50

-Paragraph 6

-URI http://asc.fasb.org/extlink&oid=6907707&loc=d3e32621-109319

Reference 2: http://www.xbrl.org/2003/role/presentationRef

-Publisher FASB

-Name Accounting Standards Codification

-Topic 740

-SubTopic 10

-Section 50

-Paragraph 8

-URI http://asc.fasb.org/extlink&oid=6907707&loc=d3e32632-109319

Reference 3: http://www.xbrl.org/2003/role/presentationRef

-Publisher FASB

-Name Accounting Standards Codification

-Topic 740

-SubTopic 10

-Section 25

-Paragraph 20

-Subparagraph (b)

-URI http://asc.fasb.org/extlink&oid=29652012&loc=d3e28680-109314

+ Details

Name:	us-gaap_DeferredTaxAssetsTaxDeferredExpenseCompensationAndBenefitsShareBasedCompensationCost
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	instant

- Definition

Amount before allocation of valuation allowances of deferred tax asset attributable to deductible temporary differences from the provision for loan losses.

+ References

Reference 1: http://www.xbrl.org/2003/role/presentationRef

-Publisher FASB

-Name Accounting Standards Codification

-Topic 740

-SubTopic 10

-Section 50

-Paragraph 6

-URI http://asc.fasb.org/extlink&oid=6907707&loc=d3e32621-109319

Reference 2: http://www.xbrl.org/2003/role/presentationRef

-Publisher FASB

-Name Accounting Standards Codification

-Topic 740

-SubTopic 10

-Section 50

-Paragraph 8

-URI http://asc.fasb.org/extlink&oid=6907707&loc=d3e32632-109319

Reference 3: http://www.xbrl.org/2003/role/presentationRef

-Publisher FASB

-Name Accounting Standards Codification

-Topic 740

-SubTopic 10

-Section 25

-Paragraph 20

-Subparagraph (b)

-URI http://asc.fasb.org/extlink&oid=29652012&loc=d3e28680-109314

+ Details

Name:	us-gaap_DeferredTaxAssetsTaxDeferredExpenseReservesAndAccrualsProvisionForLoanLosses
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	instant

- Definition

Amount before allocation of valuation allowances of deferred tax asset attributable to deductible temporary differences from unrealized losses on available-for-sale securities.

+ References

+ Details

Name:	us-gaap_DeferredTaxAssetsUnrealizedLossesOnAvailableforSaleSecuritiesGross
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	instant

- Definition

Amount of deferred tax assets for which it is more likely than not that a tax benefit will not be realized.

+ References

+ Details

Name:	us-gaap_DeferredTaxAssetsValuationAllowance
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	instant

- Definition

Amount of deferred tax liability attributable to taxable temporary differences not separately disclosed.

+ References

+ Details

Name:	us-gaap_DeferredTaxLiabilitiesOther
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	instant

- Definition

Amount of deferred tax liability attributable to taxable temporary differences from unrealized gains in other comprehensive income.

+ References

Reference 1: http://www.xbrl.org/2003/role/presentationRef

-Publisher FASB

-Name Accounting Standards Codification

-Topic 740

-SubTopic 20

-Section 45

-Paragraph 11

-Subparagraph (b)

-URI http://asc.fasb.org/extlink&oid=18498875&loc=d3e39076-109324

Reference 2: http://www.xbrl.org/2003/role/presentationRef

-Publisher FASB

-Name Accounting Standards Codification

-Topic 740

-SubTopic 10

-Section 50

-Paragraph 6

-URI http://asc.fasb.org/extlink&oid=6907707&loc=d3e32621-109319

Reference 3: http://www.xbrl.org/2003/role/presentationRef

-Publisher FASB

-Name Accounting Standards Codification

-Topic 740

-SubTopic 10

-Section 25

-Paragraph 20

-URI http://asc.fasb.org/extlink&oid=29652012&loc=d3e28680-109314

Reference 4: http://www.xbrl.org/2003/role/presentationRef

-Publisher FASB

-Name Accounting Standards Codification

-Topic 740

-SubTopic 10

-Section 50

-Paragraph 8

-URI http://asc.fasb.org/extlink&oid=6907707&loc=d3e32632-109319

+ Details

Name:	us-gaap_DeferredTaxLiabilitiesOtherComprehensiveIncome
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	instant

- Definition

Represents the net difference between the tax bases and the reported amounts of the assets and liabilities of an entity that is not subject to income taxes because its income is taxed directly to its owners.

+ References

Reference 1: http://www.xbrl.org/2003/role/presentationRef

-Publisher FASB

-Name Accounting Standards Codification

-Topic 740

-SubTopic 10

-Section 50

-Paragraph 16

-URI http://asc.fasb.org/extlink&oid=6907707&loc=d3e32796-109319

+ Details

Name:	us-gaap_EntityNotSubjectToIncomeTaxesDifferenceInBasesAmount
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	instant

- Details

Name:	us-gaap_ValuationAllowanceByDeferredTaxAssetAxis=agm_AmortizationofPremiumsonCapitalInvestmentsMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_ValuationAllowanceByDeferredTaxAssetAxis=us-gaap_CapitalLossCarryforwardMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type: