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Great question, Erik. Here are my own thoughts (not to be attributed to FRB St. Louis or the Federal Reserve System). https://twitter.com/ErikVoorhees/status/1387469641933545474
The Federal Reserve is obliged to do the best it can, given the tools at its disposal, to fulfil its Congressional mandates of "price stability" and "full employment." Note that Fed Chair must testify before Congress twice a year. Fed is held accountable by Congress.
"Price stability" is defined a "2% PCE inflation rate (long run)." "Full employment" is trickier to quantify (which Fed readily admits). It looks at a wide range of measures to get a feel for it. Here is the Fed's "Nicene Creed:" https://www.federalreserve.gov/monetarypolicy/files/fomc_longerrungoals.pdf
Now, we could have a legitimate debate about whether Congress should have mandated these things or whether Fed is interpreting them correctly. But this is not what you are asking. We can come back to this another time.
For the purpose of your question, note that Congress tells Fed what it wants and what tools the Fed can use to achieve these Congressional mandates. Fed Chair gets grilled by Congress twice a year to make sure he/she performing as expected.
What tools does the Fed have? First off, Fed is not permitted to "give money away." Only Congress can do that. Fed is restricted by FRA only to make loans against "good" collateral and to purchase a limited set of securities (primarily USTs and Treasury-insured securities).
So, Fed (specifically, the FOMC) looks out at the world and sees: (1) PCE inflation below target for over a decade, remains low today, with market-based measures of inflation expectations roughly on target; (2) employment still far below what anyone would call "full employment."
Given this data, given Fed's mandate, given Fed's tools, FOMC has decided to keep its policy rate low (zero) and to continue with its securities purchases (puts downward pressure on long rates).
FOMC is sensitive to the fact that in the last expansion, the most rapid wage gains were being experienced by lower income groups. Fed does not want to prematurely abort a recovery that's improving living standards of lower-income Americans.
See Jay Powell's comments here: https://www.rev.com/blog/transcripts/fed-chair-jerome-powell-press-conference-transcript-april-28-market-update
Now, this monetary policy may very well be contributing to the stock market boom you're alluding to. But Fed does not presently have a mandate to use its policy tools to influence the stock market. To some people, it seems Fed does implicitly support stock market. Not exactly.
For example, if stock market plunges, it usually does so on "bad news." Bad news is usually associated with disinflationary pressure and declines in employment. Fed reacts to these latter two objects, not the decline is stock valuations per se.
So, yes, S&P500 doing great. Welcome to America. Fed's job though is to concentrate on inflation and employment. I hope this goes some way to answering your question.
Again, you may disagree with the mandates and how they are interpreted. You may even disagree with very existence of the Fed. It is your right as an American to lobby your Congressional representatives and let them know how you feel about this.
But also feel free to reach out to your local Federal Reserve Branch (there are 12 of us https://www.federalreserve.gov/aboutthefed/federal-reserve-system.htm ). There are people in our research divisions (and other departments) that would be happy to discuss your concerns.
PS. I forgot to mention that another way of looking at the $120B of money being pumped into the economy is to understand that it also means $120B of interest-bearing securities are being sucked out of the economy. The Fed actually makes a profit on this activity and remits this
profit to the Treasury (last year, almost $90B). https://www.wsj.com/articles/fed-sent-88-5-billion-in-profits-to-u-s-treasury-in-2020-11610384401
