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

Reclass of Stranded Tax Effects from AOCI to Retained Earnings related to ASU 2018-02

No definition available.

Name:	agm_ReclassofStrandedTaxEffectsfromAOCItoRetainedEarnings
Namespace Prefix:	agm_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	duration

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.

No definition available.

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

Accumulated change in equity from transactions and other events and circumstances from non-owner sources, net of tax effect, at period end. Excludes Net Income (Loss), and accumulated changes in equity from transactions resulting from investments by owners and distributions to owners. Includes foreign currency translation items, certain pension adjustments, unrealized gains and losses on certain investments in debt and equity securities, other than temporary impairment (OTTI) losses related to factors other than credit losses on available-for-sale and held-to-maturity debt securities that an entity does not intend to sell and it is not more likely than not that the entity will be required to sell before recovery of the amortized cost basis, as well as changes in the fair value of derivatives related to the effective portion of a designated cash flow hedge.

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 220
-SubTopic 10
-Section 45
-Paragraph 11
-URI http://asc.fasb.org/extlink&oid=114867106&loc=d3e637-108580

Reference 2: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 220
-SubTopic 10
-Section 45
-Paragraph 14A
-URI http://asc.fasb.org/extlink&oid=114867106&loc=SL7669686-108580

Reference 3: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 220
-SubTopic 10
-Section 45
-Paragraph 14
-URI http://asc.fasb.org/extlink&oid=114867106&loc=d3e681-108580

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

Amount after tax of increase (decrease) to equity or (increase) decrease to net assets, resulting from the cumulative effect adjustment of a new accounting principle applied in the period of adoption.

No definition available.

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

Amount after tax, before reclassification adjustments of other comprehensive income (loss).

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 220
-SubTopic 10
-Section 45
-Paragraph 14A
-URI http://asc.fasb.org/extlink&oid=114867106&loc=SL7669686-108580

Reference 2: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 220
-SubTopic 10
-Section 55
-Paragraph 15
-URI http://asc.fasb.org/extlink&oid=109228884&loc=d3e1436-108581

Name:	us-gaap_OtherComprehensiveIncomeLossBeforeReclassificationsNetOfTax
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	duration

Amount after tax and reclassification adjustments of other comprehensive income (loss).

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 220
-SubTopic 10
-Section 45
-Paragraph 1A
-Subparagraph (b)
-URI http://asc.fasb.org/extlink&oid=114867106&loc=SL7669619-108580

Reference 2: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 505
-SubTopic 10
-Section 50
-Paragraph 2
-URI http://asc.fasb.org/extlink&oid=109259400&loc=d3e21463-112644

Reference 3: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 220
-SubTopic 10
-Section 55
-Paragraph 15
-URI http://asc.fasb.org/extlink&oid=109228884&loc=d3e1436-108581

Reference 4: http://www.xbrl.org/2003/role/disclosureRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 220
-SubTopic 10
-Section 45
-Paragraph 1B
-Subparagraph (b)
-URI http://asc.fasb.org/extlink&oid=114867106&loc=SL7669625-108580

Name:	us-gaap_OtherComprehensiveIncomeLossNetOfTax
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	duration

Amount before tax of reclassification adjustments of other comprehensive income (loss).

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 220
-SubTopic 10
-Section 45
-Paragraph 14A
-URI http://asc.fasb.org/extlink&oid=114867106&loc=SL7669686-108580

Reference 2: http://www.xbrl.org/2003/role/disclosureRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 220
-SubTopic 10
-Section 45
-Paragraph 17B
-URI http://asc.fasb.org/extlink&oid=114867106&loc=SL34724394-108580

Name:	us-gaap_ReclassificationFromAccumulatedOtherComprehensiveIncomeCurrentPeriodBeforeTax
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	duration

Amount after tax of reclassification adjustments of other comprehensive income (loss).

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 220
-SubTopic 10
-Section 45
-Paragraph 17B
-URI http://asc.fasb.org/extlink&oid=114867106&loc=SL34724394-108580

Reference 2: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 220
-SubTopic 10
-Section 45
-Paragraph 14A
-URI http://asc.fasb.org/extlink&oid=114867106&loc=SL7669686-108580

Reference 3: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 220
-SubTopic 10
-Section 55
-Paragraph 15
-URI http://asc.fasb.org/extlink&oid=109228884&loc=d3e1436-108581

Name:	us-gaap_ReclassificationFromAccumulatedOtherComprehensiveIncomeCurrentPeriodNetOfTax
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	duration

Amount of tax expense (benefit) of reclassification adjustment from accumulated other comprehensive income (loss).

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 220
-SubTopic 10
-Section 45
-Paragraph 12
-URI http://asc.fasb.org/extlink&oid=114867106&loc=d3e640-108580

Reference 2: http://www.xbrl.org/2003/role/disclosureRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 220
-SubTopic 10
-Section 45
-Paragraph 17A
-URI http://asc.fasb.org/extlink&oid=114867106&loc=SL34724391-108580

Reference 3: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 740
-SubTopic 20
-Section 45
-Paragraph 11
-Subparagraph (b)
-URI http://asc.fasb.org/extlink&oid=109238882&loc=d3e39076-109324

Name:	us-gaap_ReclassificationFromAociCurrentPeriodTax
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	duration

Name:	us-gaap_StatementEquityComponentsAxis=us-gaap_RetainedEarningsMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

Name:	us-gaap_StatementEquityComponentsAxis=us-gaap_AccumulatedNetInvestmentGainLossIncludingPortionAttributableToNoncontrollingInterestMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

Name:	us-gaap_FinancialInstrumentAxis=us-gaap_AvailableforsaleSecuritiesMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

Name:	us-gaap_FinancialInstrumentAxis=us-gaap_HeldtomaturitySecuritiesMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

Name:	us-gaap_StatementEquityComponentsAxis=us-gaap_AccumulatedNetGainLossFromCashFlowHedgesIncludingPortionAttributableToNoncontrollingInterestMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

Name:	us-gaap_StatementEquityComponentsAxis=us-gaap_AociIncludingPortionAttributableToNoncontrollingInterestMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

Name:	us-gaap_ReclassificationOutOfAccumulatedOtherComprehensiveIncomeAxis=us-gaap_ReclassificationOutOfAccumulatedOtherComprehensiveIncomeMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

Name:	us-gaap_IncomeStatementLocationAxis=us-gaap_GainLossOnDerivativeInstrumentsMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type: