Not affiliated with the federal government? You do know about the Federal Reserve Act of 1913 don't you? Member banks are required to buy stock in their district Federal Reserve Bank and keep a certain amount of money on "reserve" at the Fed as set by the Governors. The Fed Board of Governors is appointed by the president and confirmed by the senate.
My larger intent behind the affiliation remark was "The Fed pumps $1.5T into overnight repro markets" is not a Government action and it is not government money - and theoretically all decisioning Fed decisioning is to be 100% apolitical. These outrageous figures that individuals are conflating with "Wall Street Bailouts" are not government affiliated and are not government funds.
Its board is appointed by the President, so you can't really say it isn't affiliated with the government to some degree.
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EDIT: as expanded on below my main intent behind the Federal Reserve <> Government affiliation remark is that the Feds decisioning and repro market fund pumping is not government affiliated.