I am new to this, so bear with me. The key question nagging the Fed currently is how to unwind the asset positions it has taken and get back to a "normal" balance sheet. As is well-known, the total quantity of the Fed's assets before the onset of the financial crisis was about $900 billion, and this quantity has grown to about $2.3 trillion. Further, the Fed's assets have traditionally consisted primarily of U.S. Treasury securities, but now include a substantial quantity of mortgage backed securities (MBS) - about $1 trillion - and about $170 billion in agency securities (primarily the debts of Fannie Mae and Freddie Mac). To finance the purchases of these assets, the Fed has increased the quantity of bank reserves to a whopping $1.2 trillion. There are basically three approaches to unwinding the Fed's recent unusual interventions. I will address each in turn.
(1) HOLD STRATEGY: Hold the MBS and agency securities until maturity. Maturity is a long time in the future, as the duration of these assets runs in the range of 7 to 10 years. The key question here is: What happens to the large stock of reserves held by the banks in the meantime? These reserves currently bear an interest rate which is roughly the interest rate on Treasury bills, and reserves are being willingly held by the banks. Indeed, it is useful to think of these reserves as being equivalent to T-bills, which is of course why we have not seen severe inflationary consequences from the massive increase in the stock of base money. What happens when monetary policy starts to tighten (in terms of the fed funds rate target), and nominal interest rates rise? Then, if the interest rate on reserves were to remain constant, reserves would become increasingly unattractive to banks. In the process of trying to rid themselves of reserves, prices of goods and services would have to rise, and some reserves would be converted into currency. This of course is the Fed's nightmare - reserves unleashed must create inflation. This, the "hold" strategy implies that the interest rate on reserves must rise to induce the banks to hold reserves. One idea that has been floated is to create reserve accounts that are essentially term deposits, with a maturity of perhaps 1 month. Proponents of this approach argue that it would temporarily "lock up" reserves so that they cannot be unleashed to generate inflation. Now, a key problem in the tightening period will be that short rates will be increasing, while the Fed is locked into fixed nominal long-term returns on its large portfolio of MBS and agency securities. Fed profits will decline, and could even become negative if short-term nominal interest rates become high enough. How does the Fed deal with negative profits? It prints more money. Note that a problem with "locking up" reserves in term deposits is that the term deposits cannot be used in interbank transactions, so the Fed has to pay a higher interest rate on the term deposits than on reserves - there is nothing good about that.
(2) SELL STRATEGY: The Fed could choose to sell all its MBS and agency securities, either all at once or over a period of time. Under some conditions this could make no difference at all for market interest rates, prices, or quantities. What difference would it make if we took the MBS and agency securities off the Fed balance sheet, and replaced the reserves currently on banks' balance sheets with these assets. Maybe we think that it will make a difference because reserves are somehow more liquid than the MBS and agency securities. However, banks are in the business of liquidity transformation. What makes the Fed better at transforming liquidity than the private banking system? The only remaining argument is that the interventions by the Fed were in part an implicit subsidy to the housing market - the Fed essentially bought the MBS and agency securities at too high a price. In that case, why not take its losses now by selling the assets? The Fed will suffer a loss, it will have to print money to make up the difference, and prices will rise. We can take the price increase all at once, or we can take it over a period of time, with gradual sales of the assets.
(3) BUY MORE STRATEGY: The Fed could choose to buy more MBS and agency securities, and further subsidize the housing sector. This comes with a cost of course - credit is being allocated towards housing and away from other uses, including the financing of non-residential construction and investment in machinery and equipment. Housing has traditionally been subsidized to an egregious extent in the U.S., and I don't think we need more of this.
In conclusion, strategy (2) seems the correct option, with strategy (1) in some sense the limit of strategy (2). A large inflation is inevitable and it seems the only choice is having (i) a very large inflation in the near term, with less inflation over the medium horizon or (ii) somewhat higher inflation over a longer horizon. What results depends on how fast the Fed sells off its portfolio of unconventional assets.