Notes Payable - Earliest Interest Reset Date of Borrowing Outstanding (Details) - USD ($) $ in Thousands	Dec. 31, 2020	Dec. 31, 2019
Debt Instrument [Line Items]
2023	$ 3,004,203	$ 3,696,699
2024	2,809,551	1,592,315
2025	$ 927,119	$ 1,202,817
Short-term debt, weighted average rate (as a percent)	0.59%	1.84%
Weighted - average rate (as a percent)	1.37%	2.28%
Notes payable	$ 21,795,677	$ 19,091,215
Total weighted - average rate (as a percent)	0.98%	2.05%
2021
Debt Instrument [Line Items]
2021	$ 12,805,994
Short-term debt, weighted average rate (as a percent)	0.55%
2022
Debt Instrument [Line Items]
2022	$ 2,123,372
Weighted - average rate (as a percent)	1.34%
2023
Debt Instrument [Line Items]
2023	$ 2,390,730
Weighted - average rate (as a percent)	1.39%
2024
Debt Instrument [Line Items]
2024	$ 884,138
Weighted - average rate (as a percent)	1.74%
2025
Debt Instrument [Line Items]
2025	$ 1,126,871
Weighted - average rate (as a percent)	1.15%
Thereafter
Debt Instrument [Line Items]
Thereafter	$ 2,464,572
Weighted - average rate (as a percent)	2.19%

Long-Term Debt, Maturity, after Year Four

No definition available.

Name:	agm_LongTermDebtMaturityAfterYearFour
Namespace Prefix:	agm_
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_DebtInstrumentLineItems
Namespace Prefix:	us-gaap_
Data Type:	xbrli:stringItemType
Balance Type:	na
Period Type:	duration

- Definition

Weighted average interest rate of debt outstanding.

+ References

No definition available.

+ Details

Name:	us-gaap_DebtWeightedAverageInterestRate
Namespace Prefix:	us-gaap_
Data Type:	num:percentItemType
Balance Type:	na
Period Type:	instant

- Definition

Amount, after unamortized (discount) premium and debt issuance costs, of long-term debt. Includes, but not limited to, notes payable, bonds payable, debentures, mortgage loans and commercial paper. Excludes capital lease obligations.

+ References

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 470
-SubTopic 20
-Section 50
-Paragraph 4
-Subparagraph (b)(3)
-URI http://asc.fasb.org/extlink&oid=120520924&loc=SL6031897-161870

Reference 2: 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(a)(16))
-URI http://asc.fasb.org/extlink&oid=120400017&loc=d3e572229-122910

Reference 3: 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(16))
-URI http://asc.fasb.org/extlink&oid=120398452&loc=d3e534808-122878

Reference 4: 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(22))
-URI http://asc.fasb.org/extlink&oid=120391452&loc=d3e13212-122682

+ Details

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

- Definition

Amount of long-term debt payable, sinking fund requirement, and other securities issued that are redeemable by holder at fixed or determinable price and date, maturing in next fiscal year following current fiscal year. Excludes interim and annual periods when interim periods are reported from current statement of financial position date (rolling approach).

+ References

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 235
-SubTopic 10
-Section S99
-Paragraph 3
-Subparagraph (SX 210.12-04.(a))
-URI http://asc.fasb.org/extlink&oid=120395691&loc=d3e24072-122690

Reference 2: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 470
-SubTopic 10
-Section 50
-Paragraph 1
-URI http://asc.fasb.org/extlink&oid=6802200&loc=d3e1835-112601

+ Details

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

- Definition

Amount of long-term debt payable, sinking fund requirement, and other securities issued that are redeemable by holder at fixed or determinable price and date, maturing in fourth fiscal year following current fiscal year. Excludes interim and annual periods when interim periods are reported from current statement of financial position date (rolling approach).

+ References

+ Details

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

- Definition

Amount of long-term debt payable, sinking fund requirement, and other securities issued that are redeemable by holder at fixed or determinable price and date, maturing in third fiscal year following current fiscal year. Excludes interim and annual periods when interim periods are reported from current statement of financial position date (rolling approach).

+ References

+ Details

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

- Definition

Amount of long-term debt payable, sinking fund requirement, and other securities issued that are redeemable by holder at fixed or determinable price and date, maturing in second fiscal year following current fiscal year. Excludes interim and annual periods when interim periods are reported from current statement of financial position date (rolling approach).

+ References

+ Details

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

- Definition

Weighted average interest rate of long-term debt outstanding calculated at point in time.

+ References

No definition available.

+ Details

Name:	us-gaap_LongtermDebtWeightedAverageInterestRate
Namespace Prefix:	us-gaap_
Data Type:	num:percentItemType
Balance Type:	na
Period Type:	instant

- Definition

Reflects the total carrying amount as of the balance sheet date of debt having initial terms less than one year or the normal operating cycle, if longer.

+ 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(19)(a))
-URI http://asc.fasb.org/extlink&oid=120391452&loc=d3e13212-122682

Reference 2: 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(a)(16)(a)(1))
-URI http://asc.fasb.org/extlink&oid=120400017&loc=d3e572229-122910

Reference 3: 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(13))
-URI http://asc.fasb.org/extlink&oid=120398452&loc=d3e534808-122878

+ Details

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

- Definition

Weighted average interest rate of short-term debt outstanding calculated at point in time.

+ References

+ Details

Name:	us-gaap_ShortTermDebtWeightedAverageInterestRate
Namespace Prefix:	us-gaap_
Data Type:	num:percentItemType
Balance Type:	na
Period Type:	instant

- Details

Name:	us-gaap_LongtermDebtTypeAxis=agm_DueWithinOneYearMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_LongtermDebtTypeAxis=agm_DueYearOneMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_LongtermDebtTypeAxis=agm_DueYearTwoMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_LongtermDebtTypeAxis=agm_DueYearThreeMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_LongtermDebtTypeAxis=agm_DueYearFourMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_LongtermDebtTypeAxis=agm_DueAfterFourYearsMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type: