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Bonds and the “Convexity Trade”

May 29, 2013 5 comments

It has been a long time since we have had to worry about and think about the phenomenon of mortgage convexity and the effect that it can have on the bond market. But with 10-year interest rates up 50bps in less than 1 month, and some of the selloff recently being attributed to “convexity-related selling,” it is worth reminiscing.

We need to start with the concept of “negative convexity.” This is a fancy way of saying that a market position gets shorter (or less long) when the market is going up, and longer (or less short) when the market is going down. That’s obviously a bad thing: you would prefer to be longer when the market is going up and less long when the market is going down (and, not surprisingly, we call that positive convexity).

Now, a portfolio of current-coupon residential mortgages in the US exhibits the property of negative convexity because the homeowner has the right to pre-pay the mortgage at any time, and for any reason – for example, because the home is being sold, or because the homeowner wants to refinance at a lower rate. Indeed, holders of mortgage-backed securities expect that in any collection of mortgages, a certain number of them will pre-pay for non-economic reasons (such as the house being sold) and the rest will be pre-paid when economic circumstances permit. Suppose that in a pool of mortgages, the average mortgage is expected to be paid off in (just to make up a number, not intended to be an accurate or current figure) ten years. This means that the security backed by those mortgages (MBS for short) would have a duration of about ten years, so that a 1% decline in interest rates would, in the absence of convexity, cause prices to rise about 10%.[1]

Now, that’s really just a guess based on where interest rates are currently. As interest rates change, so does the duration of the bond. If mortgage interest rates fall significantly, then most of the mortgages in that MBS would pre-pay and the duration of the security would fall sharply. Suppose that after a sufficient decline in interest rates, the same pool of mortgages in that MBS is expected to be pre-paid on average in only 3 years. Now a further 1% decline in interest rates will only cause the price of the MBS to rise about 3%. This is negative convexity, and what is significant here is how holders of MBS respond. In order to maintain a similar market exposure, the owner of the MBS needs to buy more bonds, swaps, or MBS to maintain his duration. That is, into a rally, the MBS owner needs to buy more. This is “buying high,” and it’s the manifestation of one side of that negative convexity.

Suppose that instead interest rates rise sharply. Now, instead of expecting those mortgages to economically pre-pay over the next 10 years, we realize that the opportunities for these homeowners to refinance just went away (at least for a while); consequently, we now expect the mortgages to pay off in 15 years on average, rather than 10. A further rise of 1% in interest rates will cause prices to fall 15% rather than 10%. Again, the MBS holders need to respond, and they do so by selling bonds, swaps, or MBS to maintain duration. That is, into a selloff, the MBS owner needs to sell more. This is “selling low,” and it’s the manifestation of the other side of that negative convexity.

Put together, a manager of a large MBS portfolio is earning a higher-than-average coupon, but is also systematically buying high and selling low on his hedges and losing a little money each time. More importantly for our case here is that if the market moves enough to trigger the hedging activity then we say that “the convexity trade” has caused a significant amount of selling into a selloff, or a significant amount of buying into a rally, and this essentially means fuel is being added to the fire and the move is worsened. The mortgage market is massive, and especially with dealers having less capacity for market-making risk-taking a big convexity trade could cause a huge move. In the 2000s, I recall two massive selloffs of at least 125bps over a period of just a few weeks, in which every 5bps seemed to bring out another huge seller and push the market another 5bps.

Figuring out exactly what the trigger level is at which the convexity trade kicks in is the domain of mortgage analysts, and there is a lot of brainpower and computing power put to this analysis. These folks can tell you that “a 10-year note rate of 2.25% will cause the market to get longer by 150bln 10-year note equivalents [just to be clear, this is a made up example],” which in turn implies that there will be substantially more selling when interest rates approach that level.

Now, I don’t know what the current trigger levels are, but I can tell you a few more things from years of experience.

First is that the market’s negative convexity is greatest when the market has rallied to a new level and stayed there for a long time, allowing most borrowers to refinance their mortgages to the current coupon. The chart of 10-year yields below (Source: Bloomberg) illustrates this point. In 2008, 10-year note yields fell below 2.5%, but did so very quickly and few people had a chance to refinance (plus, mortgage spreads were quite wide and credit was hard to get), so the mortgage market maintained something like its prior equilibrium.

10yy

However, over 2010 and especially after mid-2011, rates got substantially lower and stayed lower; mortgage credit also got somewhat easier than in early 2009 (although obviously underwater homeowners cannot refinance, and this limited the amount of refinancing activity so that MBS prepay speeds weren’t as rapid as the pre-2008 models had expected). We have now been at these levels for some time, so that I suspect the market’s average coupon is substantially lower today than it was two years ago. This means the bond market is very vulnerable to a convexity trade to higher yields, especially once the ball gets rolling. The recent move to new high yields for the last 12 months could trigger such a phenomenon. If it does, then we will see 10-year note rates above 3% in fairly short order.

The second point is somewhat more subtle. The nature of the negative convexity in the higher rate direction is different from the nature of the negative convexity in the lower rate direction. When rates fall, we are looking at borrowers refinancing, which means that we can stair-step lower: rates fall, borrowers refinance, rates fall further, borrowers refinance again, etcetera. But when rates rise, the duration increase is caused by a lack of activity. Borrowers eschew refinancing. And this, fundamentally, can only happen once no matter how far rates move. If it is not economical to refinance with rates 2% higher, then few borrowers will refinance. But at 5% higher rates, there is no additional effect: once your model expects essentially zero refinancing, the convexity trade is over until you get substantial new origination of mortgages, and this takes longer. Therefore, in a selloff the convexity trade is somewhat self-limiting. It sure doesn’t feel like it at the time, but it is.

This is a long article but it is worth reflecting on because of the conclusion, and that is this: if rates rise because the Fed begins to raise rates (or finds it doesn’t have enough will to keep them low, once the bond market expects much higher inflation), then there is no “cap” on how high they can go. But if rates rise in a sloppy fashion because of a convexity trade, there really is a cap. It would be ugly to see interest rates rise another 100bps (and really, really bad for stocks I think), but if they did so because of the convexity trade then we would probably get a bunch of that move reversed thereafter.

I don’t have a strong opinion about whether we are at that point yet, and I no longer have access to great mortgage analysts. But Fed speakers should tread very lightly, as I doubt the first trigger point is terribly far away and you surely don’t want to hit it.

There is one reason I don’t think that the bond market selloff we have seen to date is heavily driven by convexity-related flows, and that is that TIPS yields have risen faster than nominal bond yields. Over the period during which nominal 10-year yields have risen 50bps, 10-year TIPS yields have actually risen 58bps. If the trade was a convexity-driven trade, it would be primarily affecting nominal yields, which means that while TIPS would be suffering, they would be suffering less than nominal bonds, rather than more. (The flip side is that if you are bearish here because you think the convexity trade might kick in, you should also expect breakevens to widen substantially when that trade does kick in). Indeed, TIPS at -0.13% is the best bargain we have seen in quite some time (see chart, source Bloomberg).

GTII10

Indeed, our multi-asset strategy has kicked the TIPS component all the way up to 11%, which is the highest it has been in a long while. TIPS are not cheap, but they are cheaper, and they are extremely cheap relative to nominal bonds. And they are not yet as cheap as i-Series savings bonds, although the yield advantage of those bonds has dropped from the 159bps it was when I wrote about it here to “only” 93bps. But that’s still a great arb, and so I continue to advocate i-bonds.


[1] I am abstracting from the niceties of Macaulay versus modified versus option-adjusted duration here for the purposes of exposition.

Limits On The 500-pound Gorilla

February 10, 2013 11 comments

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.

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