While I am writing this blog the yield on the 10-year US Treasury bond briefly dipped below the 2.0% threshold. Yes, lending out your money to the US government would leave you with a return of just 2% per year. We have to go back to June of last year to find lower 10-year yields. Since then the US economy has grown at least 2.5% (real terms). ‘At least’, because the results for Q3 (positive growth of 3% annualized expected) are not yet in. This leads to the obvious question: What is going on with US bond yields?

**Rule of Thumb**

I believe current long-term yields are too low. Now, there are a million ways, if not more, to try to support this view, from just looking at long-term graphs to state-of-the-art, highly complex, statistical analyses. In this case, however, I don‘t think the latter is necessarily required.

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For instance, take the general rule of thumb that the level of long-term interest rates should mirror nominal GDP growth. Hence, the nominal interest rate should (almost) equal the sum of real GDP growth and inflation. The graph below shows that, while this relationship is far from perfect, the nominal interest rate and nominal GDP growth are related. Moreover, smarter alternatives of this basic rule of thumb, that take into account the forward-looking nature of interest rates, while GDP numbers tell something about the past, show an even stronger relationship between the nominal yield and the sum of real GDP growth and inflation.

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So, what does this rule of thumb imply for the current bond yield? Since we are already in the last quarter of 2014 it makes sense to turn to data for next year. Bloomberg reveals that in 2015 real GDP in the US is expected to grow by 3.0%. The average estimate for US inflation equals 2.1%. Just to be sure I also looked at the numbers for 2016. Growth is expected to slow marginally to 2.9%, while inflation is expected to increase slightly to 2.2%. The sum of the two is shown in the graph below.

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**Double that**

As can be derived from the graph, the sum of real GDP growth and inflation has been pretty constant this year. More importantly, for both years the estimate of nominal GDP growth indicates a nominal bond yield of well over 5.0%. That is more than double the current 10-year bond yield. Based on these numbers there can be only one conclusion, yields are too low.

It is possible, of course, that the forecasters included in the Bloomberg survey data are way too optimistic. But at this point I would like to point out that their expectations have to be totally out of whack in order to get to the current bond yield of 2.0%. For example, expectations of both real GDP growth and inflation need to be reduced by half to get close to that number. To be clear, this does happen occasionally. During the financial crisis in 2009 real GDP growth expectations fell from above 1% in September 2008 to -2.5% in the second half of 2009.

**Model Estimate**

The relationship described above is a very simplistic example of a factor model used to estimate the ‘fair value bond yield’. It does not take all that much, however, to build a more sophisticated model. Take a look at the graph below. It shows the actual bond yield and a model estimate based on the ISM new orders index (as a proxy for real GDP growth), the short-term interest rate (as a proxy for monetary policy) and inflation expectations. As the graph shows the model does a pretty good job in describing the actual bond yield, explaining over 90% of the variance in bond yield changes.

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The conclusion that follows from this model estimate has to be the same as above. The current bond yield is too low. The most recent data on the ISM index, the short-term interest rate and inflation expectations suggest a 10-year bond yield of almost 4%, a full 2% higher than the actual yield. Many varieties of this model are thinkable, but all of them yield similar results.

**Why so low?**

One question remains, of course. Why are bond yields so low? What is missing in the analysis above? There are a number of possible explanations. First, as mentioned before, expectations about future GDP growth and inflation could be far too optimistic. The graph below shows the yield on US inflation swaps, which can be considered to be market-derived inflation expectations. In recent weeks the 1-year inflation swap rate fell to 1.1% and the 2-year swap rate to 1.5%. As the graph shows swaps are by no means the holy grail of inflation expectations. As market turmoil increases mispricing starts to occur. The 2008 data are a good example of this. At the end of 2008 the 1-year inflation swap suggested an expected inflation rate of -4.5% (realized inflation in the US was -0.3%). But even in the event the inflation does turn out to be 1.1%, it would take a downward revision of the 2015 real GDP growth expectations of 2.1%(!) to 0.9% to reach the current bond yield level of 2.0%. The ISM index will have to move below 50 to realize this.

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The Fed offers another possible explanation. As the graph above revealed, the difference between the actual and estimated bond yield has been relatively large in recent years. The obvious reason for this is QE. But if recent market developments don’t make the Fed change its course, outright QE will end at the end of this month. And yet in recent weeks the difference between the model estimate and the actual yield has increased quite dramatically.

Perhaps investors are anticipating that the Fed will keep rates low for longer. Looking at the Fed futures data this seems to be the case, but only to certain extent. Despite the recent market turmoil the implied timing of the first rate hike has moved out only a couple of months, from the second to early in the fourth quarter.

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**Combination of factors**

Finding one suitable explanation for the current low bond yields is challenging. My take on it is that a combination of factors makes investors very eager to invest in bonds. The first is that investors have short memories. It’s hard to remember a state of the world in which markets and economies had to survive without subsequent periods of QE. So, whenever worries about inflation and/or GDP growth pop up, which has been the case in recent weeks, investors turn to ‘QE-mode’ again and buy US Treasuries.

Also, the Fed is the first central bank to exit its QE program. In other parts in the world QE is still (Japan) or just recently (Europe) the way to go. Some of that abundance of cash will make it across to the US Treasury market. Moreover, the decoupling of monetary policy is likely accompanied by a rising US dollar, making US Treasuries more attractive (from an unhedged perspective that is).

Long-term factors like a decrease in the working force population and aging could be of importance as well, but their influence is likely to be gradual. And in the case of the US, things are looking less grim than in many other parts of the world. It seems plausible that investors have become (too) used to a world of shaky economic fundamentals and persistent low inflation in which central banks will, in the end, come to the rescue. And that they will probably only really shy away from US Treasuries when both GDP growth and inflation rates have normalized for some time. My guess is, it will be in well in 2015 before we see that happening.