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As expected, there has been quite a bit of discussion regarding the theoretical implications of the Fed's new plan to purchase $40 billion of agency mortgage back securities per month until such a time as the "outlook for the labor market improves substantially." Although any predictions about how a policy will ultimately play out are by definition theoretical (we cannot ever know for sure what the future holds), we can use available data coupled with a few basic and I think reasonable assumptions to make some relatively reliable predictions about what the future holds for the Fed and its balance sheet.

First consider the following excerpt from the Fed's statement (cited above):

"[In addition to the new MBS purchases], the Committee...will continue through the end of the year its program to extend the average maturity of its holdings of securities...and it is maintaining its existing policy of reinvesting principal payments from its holdings of agency debt and agency mortgage-backed securities in agency mortgage-backed securities. These actions...will increase the Committee's holdings of longer-term securities by about $85 billion each month through the end of the year."

Given this information, we can determine with a relative degree of accuracy, what the Fed's balance sheet is likely to look like going forward. First, note that the Fed sterilizes its $45 billion in monthly long-term Treasury purchases by selling an equivalent amount of 3-year-and-in Treasuries -- this is of course, Operation Twist:

"the Committee intends to purchase Treasury securities with remaining maturities of 6 years to 30 years at the current pace and to sell or redeem an equal amount of Treasury securities with remaining maturities of approximately 3 years or less."

By my math, the Fed only has around $123 billion in 3-month to 3-year Treasury notes left to sell before it runs out. This means that at the current rate ($45 billion per month), the Fed will run out of ammunition to sterilize its long-term purchases by the end of the year. Given this, and given that it is difficult to imagine that the Fed would cease to purchase the long-term Treasuries it buys each month while still buying unlimited amounts of MBS, the Fed will likely continue to buy long-term Treasuries into next year only without sterilizing them.

Alternatively, the Fed could begin to sell longer-dated notes, but of course it will eventually run out of these too and given the current environment wherein the world cheers unsterilized asset purchases it seems logical to assume that it will simply choose to continue on the current course of buying long-term Treasuries to the tune of $45 billion each month alongside its purchase of $40 billion in monthly MBS. Indeed the Fed has already hinted at this:

"If the outlook for the labor market does not improve substantially, the Committee will continue its purchases of agency mortgage-backed securities, undertake additional asset purchases, and employ its other policy tool..." (emphasis mine)

From here the math is fairly simple. First, multiply $40 billion by three and add $23 billion to get $143 billion. This is $40 billion in MBS purchases in October, November, and December and $23 billion in MBS purchases to be carried out from now until the end of September. Notice there are no additional purchases to add to the $143 billion total because the Fed is able, via its stock of some $123 billion in 3-month to 3-year Treasuries, to sterilize the remainder of its 2012 long-term Treasury purchases.

Next, we must calculate the assets the Fed will purchase in 2013. Assuming the Fed will run out of short-term bonds to sell in December and will resort to unsterilized purchases of $45 billion in long-term Treasuries per month in addition to the $40 billion in MBS purchases, we can multiply $85 billion by 12 to get $1.02 trillion. Now add the $143 billion from the remainder of 2012 and the Fed will add a total of $1.163 trillion in assets to its balance sheet over the course of the next 15 and a half months. This puts the Fed's balance sheet at an astounding $3.988 trillion by the end of 2013.

There are two things to note here. First, in this scenario the Fed's DV01 would be nearly $4 billion. Put simply, this means that for every 1 basis point that Treasury yields move up, the Fed takes a $4 billion hit on its holdings. Anyone who thinks it is possible for the Fed to 'wind down' its holdings and/or raise rates in the future should consider that. Second, and this is a familiar refrain by now, this type of balance sheet expansion stokes inflation. In light of all this, I think it is more than reasonable to bet on a decline in the U.S. dollar going forward. Additionally, as noted by numerous commentators, if there ever was a time to buy gold (GLD) this is it.

Source: What QE3 Means For The Fed's Balance Sheet: $4 Trillion Here We Come