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Posts Tagged ‘negative convexity’

We’re the Government, and We’re Here to Help

March 24, 2014 1 comment

Today’s article will be brief (some might say blessedly so). The topic is the publication of an article on the NY Fed’s blog entitled “Convexity Event Risks in a Rising Interest Rate Environment.”

Long-time readers may recall that I wrote an article last year, with 10-year notes at 2.12%, called “Bonds and the ‘Convexity Trade’,” in which I commented that “the bond market is very vulnerable to a convexity trade to higher yields…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.” Within a few weeks, 10-year note yields hit 2.60% and eventually topped out at 3%.

Now, the Fed tells me that this selloff was “more gradual and therefore inconsistent with a sell-off driven primarily by convexity hedging.” I suppose in a way I can agree. The sell-off was primarily driven by the fact that the Fed had abused the hell out of the bond market and pushed it to unsustainable levels. But I don’t think that’s what they’re saying.

Indeed, the Fed is actually claiming credit for the fact that the selloff was only 140bps. You see, the reason that we didn’t get a convexity-based selloff – or at least, we only got the one, and not the one I was really concerned about, on a push over 3% – is because the Fed had bought so many mortgage-backed securities that there weren’t enough current-coupon MBS left to cause a debacle!

How wonderfully serendipitous it is that even the most egregious failures of the Federal Reserve turn out to benefit society in heretofore unexpected ways. You will recall that one of the main reasons given by the Federal Reserve to purchase mortgages in the first place was to help unfreeze the mortgage market, and to provoke additional mortgage origination. In that, it evidently failed, for if it had succeeded then the total amount of negative convexity in public hands would not have changed very dramatically. In fact, it would have been worse since the new origination would have been current coupons and replacing higher coupons.

The real reason that the convexity-spurred selloff wasn’t worse isn’t because the Fed had taken all of the current coupon MBS out of the market, but because the Fed continued to buy even in the move to higher yields. A negative-convexity selloff has two parts: the increased demand for hedging, and the decreased supply of counterparties to take the other side as the ball gets rolling. In this case, one big buyer remained, which emboldened dealers who knew they wouldn’t be stuck “holding the bag.” That is the reason that the selloff was “only” 140bps and not worse.

However, the observation that the Fed’s policy was a failure, as it did not stimulate vast amounts of new mortgage activity, remains. It is true that there is less negative convexity in the mortgage market than there would otherwise have been in the absence of Fed buying. But that’s an indictment, not exoneration.

Is A Bond Rally Due?

July 29, 2013 1 comment

As we head into a very busy week of economic data, the bond market remains drippy with the 10-year yield up to 2.59%. (Just writing that makes me laugh. Who would have thought, only a few years ago, that 2.59% was a high-ish yield?)

How we got here, from the ultra-low levels of the last two years, is well-traveled territory. The Fed’s swing from “QE-infinity” to “someday, maybe, we might not buy as many bonds” helped trigger a run for the exits, and then negative convexity inflection points kept the rout going for a long time. Most lately, the threat of muni bond convexity has been looming as the next big concern.

But my message today is actually one of good cheer. The worst of the bond selloff was now more than three weeks ago, without a further low being established. In my experience, convexity-inspired selloffs typically end not with a sharp rebound but with a sideways trade as “trapped” long positions gradually work their way out and buyers start to nibble. But it remains a buyer’s market for several weeks, at least.

We are getting far enough along in that process that I suspect we have a rally due. This has nothing to do with any economic data coming up. There is enough data coming this week, from Consumer Confidence to Payrolls to GDP to the Fed statement, that both bulls and bears will be able to find something to point to. And I am not pointing to technicals, exactly. I am just saying that markets rarely move in a straight line, and even bear markets – such as the one I think we have now entered, in bonds – have nice rallies from time to time.

But here’s a reason to expect this to happen relatively soon. The chart below is a neat “seasonal heat map” chart from Bloomberg showing the monthly yield change for the last 10 years and the average monthly change on the top line.

heatmapFor a long time, I have been following the rule of thumb I learned as a mere babe in the bond market, and that’s that the best time of the year to buy bonds is the first few days of September. From at least the late 1970s until today, September until mid-October has been the strongest seasonal period of the year (not every year, but with enough consistency that you wanted to avoid being short in September). But the heat map above shows that this tendency may have shifted. The month that has seen the best average bond market performance over the last decade has been August, with yields falling an average of 22bps with rallies in 8 of the last 10 years. If we were sitting with 10-year yields at 1.59%, I would be less interested in this observation, but at 2.59% I am looking for the counter-trade.

To be sure, yields in the big picture are headed higher, not lower. But I am looking for signs that the recent selloff has over-discounted the immediate threat of ebbing Federal Reserve purchases. And I don’t expect growth to suddenly leap forward here, either.

As an aside, 10-year TIPS yields have also experienced one of their best months in August, with the other clear positive month being January. But, because nominal yields have been so strong, August has been the worst month for breakevens, with 10-year breakevens falling 10bps on average over the last ten years. No other month has seen breakevens decline as much as 6bps, on average.

Now, although I am a bond bear in the big picture, I don’t think that the housing market is doomed because interest rates will go up one or two or three percent. I am fascinated by how many analysts seem to think that unless 10-year rates are below 3%, the housing market will collapse. I argued about six weeks ago that higher mortgage rates should not impact sales of homes very much as long as the interest rate is less than the expected capital gain the homeowner expects to make on the home. (Higher rates will, however, cut fairly quickly into speculative building activity, which is much more rates-sensitive). And here is another reason not to worry too much about the housing market. A story in Bloomberg last week says that adjustable-rate mortgages are booming again, with mortgagees taking them out at the highest pace since 2008. Faced with higher rates, and a Fed with is not likely to raise short rates for a long while – as they have taken pains to keep reminding us – homebuyers have rationally decided to take the cheaper money and let the future refinancing take care of itself.

Whether that is sowing the seeds of a future debacle I will leave to other pundits to debate. From my perspective, the important point is that higher rates are not likely to slow home sales, or the recent rise in home prices, very much…unless they get a lot higher.

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.

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