I think the term is a bit misleading as it describes loans outstanding minus deposits on account. Most of that, except maybe 30%, is a shared liability between depositors and borrowers. But the Fed has ledger prices it can raise.
The actual liabilities of Janet and her minions are their salaries, about 5-10 billion a year. If they fail to make rent and salary, the judge will yell them to print up the do-re-me and meet contracts. So, Fed failure is a wind down, like anything else in no arbitrage cash.
Another way to account for the Fed is to take the 15 billion in its expenses and call that ledger fee and it comes to much less than 1/2% of spending, a very low amount since our ledger fees are currently about 2%.
The Fed can hold gains/loss on an accumulated basis and let it go negative. Statistics of queue tell use that, we have queue in and queue out, at stability we can measure the likelihood to the one or the other queues expanding beyond variance bounds. That is a prior contract,the Fed is bound to take gains or losses, and cannot be liable except for fraud.
What fraud? Secret conversations that set prices without an equally observable trade book, discretion. If the Fed assumes discretion, in favor of certain parties, then the liability hold to the party. The Fed, via discretion, has created an imbalance in the loans to deposits, favoring government as the borrower. That is fraud in the sandbox.
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