Equity - Equity-based Incentive Compensation Plans (Details) (USD $)	12 Months Ended
Dec. 31, 2014	Dec. 31, 2013	Dec. 31, 2012
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Share-based Compensation, Shares Authorized under Stock Option Plans, Exercise Price Range, Lower Range Limit	$ 29.37	$ 30.20	$ 21.69
Share-based Compensation, Shares Authorized under Stock Option Plans, Exercise Price Range, Upper Range Limit	$ 35.60	$ 37.17	$ 32.85
Officers and certain employees [Member]
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Share-based Compensation Arrangement by Share-based Payment Award, Terms of Award	P10Y0M0D

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

Description of pertinent provisions of equity-based compensation awards that have actual or potential impact upon the company's financial statements.

+ References

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

-Publisher FASB

-Name Accounting Standards Codification

-Topic 718

-SubTopic 10

-Section 50

-Paragraph 2

-Subparagraph (a)

-URI http://asc.fasb.org/extlink&oid=6415400&loc=d3e5070-113901

+ Details

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

- Definition

The floor of a customized range of exercise prices for purposes of disclosing shares potentially issuable under outstanding stock option awards on all stock option plans and other required information pertaining to awards in the customized range.

+ References

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

-Publisher FASB

-Name Accounting Standards Codification

-Topic 718

-SubTopic 10

-Section 50

-Paragraph 2

-Subparagraph (g)

-URI http://asc.fasb.org/extlink&oid=6415400&loc=d3e5070-113901

+ Details

Name:	us-gaap_ShareBasedCompensationSharesAuthorizedUnderStockOptionPlansExercisePriceRangeLowerRangeLimit
Namespace Prefix:	us-gaap_
Data Type:	num:perShareItemType
Balance Type:	na
Period Type:	duration

- Definition

The ceiling of a customized range of exercise prices for purposes of disclosing shares potentially issuable under outstanding stock option awards on all stock option plans and other required information pertaining to awards in the customized range.

+ References

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

-Publisher FASB

-Name Accounting Standards Codification

-Topic 718

-SubTopic 10

-Section 50

-Paragraph 2

-Subparagraph (g)

-URI http://asc.fasb.org/extlink&oid=6415400&loc=d3e5070-113901

+ Details

Name:	us-gaap_ShareBasedCompensationSharesAuthorizedUnderStockOptionPlansExercisePriceRangeUpperRangeLimit
Namespace Prefix:	us-gaap_
Data Type:	num:perShareItemType
Balance Type:	na
Period Type:	duration

- Details

Name:	agm_TermOfGrantAxis=agm_OfficersAndCertainEmployeesMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type: