Some of the Feds liabilities are our assets, the Federal Reserve Notes in our wallets or under your mattress perhaps.
https://www.exchangewire.com/wp-content/uploads/2013/02/cash1-300x181.pngStarting at about 58% of Fed liabilities in 1945, currency in circulation would reach well over 90% by 2000. It is now less than 30%. Reserves were about a third of Fed liabilities in 1945, dropped to less than 5% in the 90s as the Fed ruled that sweep accounts (money market deposit accounts) were " Under the Federal Reserve's Regulation D, MMDA accounts are personal saving deposits and, hence, have a zero statutory reserve requirement." With the Fed undertaking large scale asset purchases (LSAP) vis-a-vis permanent open market operations (POMO) as a response to the Financial Crisis, reserves would rise up to over 60% of the Fed's liabilities. ($12B on 9/3/2008 to $2.8T on 7/30/2014).
https://fred.stlouisfed.org/graph/?g=y9lFDark lines are quarterly data, lighter lines are weekly data. Here is a better view of the weekly data.
https://fred.stlouisfed.org/graph/?g=y9nqBesides the rise of reserves as a liability, there was a rise in the Treasury General Account (TGA), almost as high as currency. Also reverse repo rose esp after 2014 as the Fed used RRP to drain reserves to keep short term rates from DROPPING BELOW THEIR TARGET RANGE. Repo, adding reserves and RRP removing reserves; temporary open market operations (TOMO, were the Fed's main policy tools before the GFC to maintain Feds Funds target(RRP, TGA and Currency remove reserves; Repo and Fed POMO of Tresuries, Agency debt, and TBA GSE Pass-throughs increase reserves. Ceteris paribus). So yeah, about 30% of the Fed's liabilities are our asset.
"I don’t find it strange that the Fed tried to reduce the balance sheet one time, and the market promptly dropped 20%" I take it you are referring to the end of 2018.
https://fred.stlouisfed.org/graph/fredgraph.png?g=y9r4Except that didn't happen.
https://fred.stlouisfed.org/graph/fredgraph.png?g=y9r5Fed assets peaked in Jan 2015, gradually declining until the beginning of 2018. The FED then accelerated the runoff until the Repo problem in Sept 2019, dropping 17%. Reserve balances with the Fed dropped over 50%. Even with the market sell off the Fed continued to reduce assets and reserves; raised the Fed Funds twice. Yet the market rebounded.
I'll deal with stock buybacks later. For the record, XOM has yet to declare any asset impairment, but on the last earnings call announced there could be $25-30B in the future. Also under US GAAP rules reversal of a loss is prohibited for all the assets to be held and used.