Guarantees - Schedule of Long-Term Standby Purchase Commitments (Details) - LTSPCs - USD ($) $ in Thousands	3 Months Ended	9 Months Ended
Mar. 31, 2020	Sep. 30, 2020	Dec. 31, 2019
Guarantor Obligations [Line Items]
Maximum principal amount		$ 2,882,212	$ 3,002,349
Weighted-average remaining maturity	15 years 2 months 12 days	15 years 1 month 6 days
Guarantee and commitment obligation
Guarantor Obligations [Line Items]
Guarantee and commitment obligation		$ 33,360	$ 34,470

Weighted average remaining maturity, Loans underlying guarantees not held by transferor

No definition available.

Name:	agm_WeightedAverageRemainingMaturityLoansUnderlyingGuaranteesNotHeldByTransferor
Namespace Prefix:	agm_
Data Type:	xbrli:durationItemType
Balance Type:	na
Period Type:	duration

- Definition

The current carrying amount of the liability for the freestanding or embedded guarantor's obligations under the guarantee or each group of similar guarantees.

+ References

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 460
-SubTopic 10
-Section 50
-Paragraph 4
-Subparagraph (c)
-URI http://asc.fasb.org/extlink&oid=121555522&loc=d3e12069-110248

+ Details

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

- Definition

Line items represent financial concepts included in a table. These concepts are used to disclose reportable information associated with domain members defined in one or many axes to the table.

+ References

No definition available.

+ Details

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

- Definition

Maximum potential amount of future payments (undiscounted) the guarantor could be required to make under the guarantee or each group of similar guarantees before reduction for potential recoveries under recourse or collateralization provisions.

+ References

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 460
-SubTopic 10
-Section 50
-Paragraph 4
-Subparagraph (b)(1)
-URI http://asc.fasb.org/extlink&oid=121555522&loc=d3e12069-110248

+ Details

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

- Details

Name:	us-gaap_GuaranteeObligationsByNatureAxis=agm_LongTermStandbyPurchaseCommitmentsMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	agm_UnrecordedMaximumPotentialExposureOnGuaranteesAxis=agm_GuaranteeobligationsissuedafterJanuary12003Member
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type: