Well, here's an interesting little tidbit. (But first, a note from our sponsors: some channels didn't pick up my article from last Wednesday, "Fun With The CPI," so follow that link if you'd like to read it.)

The Fed adds permanent reserves by buying securities, as we all know by now. The Open Market Desk buys securities and credits the Fed account of the selling institution. Conversely, when the Fed subtracts reserves permanently, it sells securities and debits the account of the buying institution.

As of February 6th, the Fed owned $1.782 trillion in face value of Treasury and agency mortgage-backed securities. At the closing prices from Friday, those securities are worth $2.069 trillion, plus accrued interest which I didn't bother to calculate.

So let's revisit for a second the question of how the Fed would unwind the quantitative easing and actually tighten policy. In order to do that, the Fed would first need to vaporize the $1.58 trillion that exists in excess reserves, before they could actually affect the required reserves which is where the rubber meets the road for monetary policy (at least, in the absence of the "portfolio balance channel").

We have reviewed some of the options before: sell the securities held in the System Open Market Account (SOMA); conduct massive and long-dated repo operations; sell bills or pay interest on deposits at the Fed (or raise IOER). Some people have suggested that the Fed could just "let the securities in the SOMA roll off": i.e., let the bonds mature and don't reinvest the proceeds. I was curious how long, after Operation Twist, such a passive approach would take.

The current value of Excess Reserves is $1.58 trillion. If Excess Reserves did not move for any other reason, it would take until November of 2039 before we saw that many bonds mature. To be fair, with coupon payments and such it would take less time, but we're still looking at a couple of decades. So that's not an option, at least by itself.

Then I noticed something interesting. Some economists have suggested that when the economy begins to improve, the Desk could simply start selling securities into the market, since with a stronger economy the Treasury would presumably be running a smaller deficit (now, that's blind faith if ever there was such a thing) and auctioning fewer securities, so the Fed could take up the slack without impacting the market very much. Leaving aside the question that it isn't clear that market rates would be in the range they are now if the Fed actually stopped buying (after all, that's the whole point of the portfolio balance channel - that investors won't pay the high price the Fed has set so they buy riskier securities), I'm not sure it's even possible that the Fed could drain the excess reserves even if they sold every single bond on their balance sheet. Here's why.

The SOMA portfolio has a DV01 of approximately $1.56billion, based on the reported holdings and Bloomberg's calculated modified duration. For those unfamiliar with bond math, this means that every 1/100th of 1% rise in interest rates causes the value of the Fed's holdings to decline $1.56bln.

The current market value of the portfolio, as I said, is $2.07 trillion, while Excess Reserves are $1.58 trillion. But the problem is that the 'market value' of the portfolio assumes the portfolio is liquidated at mid-market prices. Ask the London Whale how well that works when you are a big player. Ask Long Term Capital.

But forget about the market impact. Suppose interest rates were to rise 300bps, so that the 10-year was around 5% and, with expected inflation remaining (again, let's go with the blind faith argument) around 2.5%, real interest rates were up to around 2.5%. That would be a fairly neutral valuation for an economy with decent prospects and contained inflation, growing at its sustainable natural growth rate.

The SOMA portfolio, valued 300bps higher in yield, would be worth $2.07T - $1.56B * 300 = 1.60T. In other words, if the Fed sold every single bond in its portfolio, 300bps higher, it would just barely be able to drain all of the excess reserves. Yes, I did ignore the question of convexity, but since the MBS tend to have negative convexity that balances the positive convexity of the Treasuries, I suspect that isn't a huge effect over this small a move.

So the Fed, in this circumstance, would have used all of its gunpowder just getting back to the point where traditional tools would begin to work again. This is an entirely natural outcome, by the way! If a behemoth market participant lurches into the market to buy securities, and then lurches to sell them, and repeats that pattern over and over, it loses value because it is consuming liquidity in both directions. It is going to be buying high (and again, that's the Fed's goal here: to pay more than anyone else wants to pay) and selling low. So in this case, if rates rise 300bps, the Fed will be unwinding its entire portfolio and have no securities left to sell to actually drain the liquidity that matters.

This is obviously a thought experiment - I can't imagine the Fed could unwind that sort of portfolio with only a 300bp market impact. But it just highlights, for me, the fact that the 'end game' for the FOMC almost must involve raising the interest paid on excess reserves - the other tools aren't only impractical in size, but may be de facto impotent (because, remember, the first thing that needs to happen is that Excess Reserves are drained, before policy has traction again through the traditional channels).

I am sure someone else has pointed out this little mathematics dilemma before, but I don't think it had previously occurred to me. I guess I'd always stopped at the mechanics/feasibility of selling $2 trillion in securities, and never asked whether that would actually do the job. I don't think it would! It is not actually true that a 500-lb gorilla sits "anywhere he wants," as the old joke goes - he can't sit anywhere that won't hold a 500-lb gorilla.

Now, the Committee doesn't really seem to believe in traditional monetary policy any more, so it may be that they figure the reverse of the "portfolio balance channel" effect will be good enough: raise the returns to the 'less risky' part of the market enough to pull capital out of the risky parts of the market. But I find it hard to convince myself that, as much as they clearly intended to push housing and equity market prices higher, they'd be willing to do the opposite. And I do believe that other stakeholders (e.g., Congress) would be less accommodating in that direction. Which brings me back again to the conclusion I keep coming to: does the Fed theoretically have the tools to reverse QE? Yes, although they have one fewer than I thought yesterday. But is it plausible that the Fed will have the will to use those tools, to the degree they'd need to be used, to reverse QE? I really don't believe they'd be willing to crash the housing and stock markets, just to cool down inflation.

We do live in interesting times. And they will remain interesting for a long, long time.