In traditional QE, the FED will buy the bank's bonds and give them cash for it.
Actually they give them a bank instrument that is a reserve. They do not swap for cash. The bank got the security because it had to get rid of the cash into something that generates a return.
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Yeah it sounded wrong when I wrote it but I wasn't quite sure.
But I feel like that opens up another can of worms like if the banks need to spend their money on something that generates yield... aren't they going to eventually stop buying bonds and start entering defi protocols?