Income Taxes - Deferred Tax Assets and Liabilities (Details) - USD ($) $ in Thousands	Dec. 31, 2022	Dec. 31, 2021
Components of Deferred Tax Assets [Abstract]
Basis difference related to hedge items	$ 53,360	$ 0
Unrealized losses on available-for-sale securities	26,371	0
Allowance for losses	3,603	3,452
Stock-based compensation	1,755	1,462
Basis differences related to financial derivatives	0	64,795
Unrealized losses on cash flow hedges	0	1,427
Basis difference related to structured securitizations	0	35
Capital loss carryforwards	32	32
Valuation allowance	(32)	(32)
Other	1,444	358
Total deferred tax assets	88,172	72,810
Deferred tax liability:
Basis differences related to financial derivatives	49,526	0
Unrealized gains on cash flow hedges	12,855	0
Basis difference related to structured securitizations	7,782	0
Basis differences related to hedged items	0	54,446
Unrealized gains on available-for-sale securities	0	2,451
Other	5	44
Total deferred tax liability	70,168	56,941
Net deferred tax asset	18,004	15,869
Capital Loss Carryforward
Components of Deferred Tax Assets [Abstract]
Compensation and Benefits	$ 1,639	$ 1,281

Deferred Tax Asset, Basis Difference Related To Structed Securitization

No definition available.

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

- Definition

Deferred Tax Assets, Unrealized Loss on Cash Flow Hedge

+ References

No definition available.

+ Details

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

- Definition

Deferred Tax Liabilities, Basis Difference Related To Structed Securitization

+ References

No definition available.

+ Details

Name:	agm_DeferredTaxLiabilitiesBasisDifferenceRelatedToStructedSecuritization
Namespace Prefix:	agm_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	instant

- Definition

Deferred Tax Liabilities, Differences Related to Hedged Items

+ References

No definition available.

+ Details

Name:	agm_DeferredTaxLiabilitiesDifferencesRelatedToHedgedItems
Namespace Prefix:	agm_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	instant

- References

No definition available.

+ Details

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

- References

No definition available.

+ Details

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

- Definition

Amount, after allocation of valuation allowances and deferred tax liability, of deferred tax asset attributable to deductible differences and carryforwards, with jurisdictional netting.

+ References

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 740
-SubTopic 10
-Section 45
-Paragraph 6
-URI https://asc.fasb.org/extlink&oid=123427490&loc=d3e31931-109318

Reference 2: http://www.xbrl.org/2003/role/disclosureRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 740
-SubTopic 10
-Section 45
-Paragraph 4
-URI https://asc.fasb.org/extlink&oid=123427490&loc=d3e31917-109318

+ Details

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

- Definition

Amount of deferred tax liability attributable to taxable temporary differences.

+ References

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 210
-SubTopic 10
-Section S99
-Paragraph 1
-Subparagraph (SX 210.5-02(26)(b))
-URI https://asc.fasb.org/extlink&oid=120391452&loc=d3e13212-122682

Reference 2: http://www.xbrl.org/2003/role/disclosureRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 740
-SubTopic 10
-Section 50
-Paragraph 2
-Subparagraph (a)
-URI https://asc.fasb.org/extlink&oid=121826272&loc=d3e32537-109319

Reference 3: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 944
-SubTopic 210
-Section S99
-Paragraph 1
-Subparagraph (SX 210.7-03(15)(b)(2))
-URI https://asc.fasb.org/extlink&oid=126734703&loc=d3e572229-122910

Reference 4: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 942
-SubTopic 210
-Section S99
-Paragraph 1
-Subparagraph (SX 210.9-03(15)(2))
-URI https://asc.fasb.org/extlink&oid=126897435&loc=d3e534808-122878

Reference 5: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 210
-SubTopic 10
-Section S99
-Paragraph 1
-Subparagraph (SX 210.5-02(26)(a))
-URI https://asc.fasb.org/extlink&oid=120391452&loc=d3e13212-122682

+ 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://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 740
-SubTopic 10
-Section 50
-Paragraph 8
-URI https://asc.fasb.org/extlink&oid=121826272&loc=d3e32632-109319

Reference 2: http://www.xbrl.org/2009/role/commonPracticeRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 740
-SubTopic 10
-Section 50
-Paragraph 6
-URI https://asc.fasb.org/extlink&oid=121826272&loc=d3e32621-109319

+ 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

Reference 1: http://www.xbrl.org/2009/role/commonPracticeRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 740
-SubTopic 10
-Section 50
-Paragraph 6
-URI https://asc.fasb.org/extlink&oid=121826272&loc=d3e32621-109319

Reference 2: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 740
-SubTopic 10
-Section 50
-Paragraph 8
-URI https://asc.fasb.org/extlink&oid=121826272&loc=d3e32632-109319

+ 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/disclosureRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 740
-SubTopic 10
-Section 50
-Paragraph 2
-Subparagraph (b)
-URI https://asc.fasb.org/extlink&oid=121826272&loc=d3e32537-109319

+ 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 hedging transactions.

+ References

+ Details

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

- Definition

Amount, before allocation of valuation allowance, of deferred tax asset attributable to deductible temporary differences, classified as other.

+ 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 employee compensation.

+ References

+ Details

Name:	us-gaap_DeferredTaxAssetsTaxDeferredExpenseCompensationAndBenefitsEmployeeCompensation
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

+ 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 allowance, of deferred tax asset attributable to deductible temporary difference from allowance for credit loss on financing receivable.

+ References

+ 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 allowance, of deferred tax asset attributable to deductible temporary difference from unrealized loss on investment in debt security measured at fair value with change in fair value recognized in other comprehensive income (available-for-sale).

+ 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

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 740
-SubTopic 10
-Section 50
-Paragraph 2
-Subparagraph (c)
-URI https://asc.fasb.org/extlink&oid=121826272&loc=d3e32537-109319

+ 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 from derivatives.

+ References

+ Details

Name:	us-gaap_DeferredTaxLiabilitiesDerivatives
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 classified as other.

+ 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

+ Details

Name:	us-gaap_DeferredTaxLiabilitiesOtherComprehensiveIncome
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 on trading securities.

+ References

+ Details

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

- Details

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