Bond yields have risen significantly in the last two months. Between the beginning of May and June 24 the 10-year Treasury yield increased by more than one percent. Since then the yield has come down a little to just over 2.50%, still more than 70 basis points higher than at the beginning of the year.

The reason for this rise in interest rates is pretty obvious. Ever since Bernanke told us that there will come a time when the Fed will (slowly) reduce the size of its asset purchases, the bond market has been pretty turbulent. And, even though, the Fed has not yet set a date for when it will actually start to taper its bond purchases, the fact that Bernanke dared to mention it was enough for a strong sell off in bonds.

So, now that the 10-year bond yield has crossed the 2.50% threshold for the first time since August 2011, has it gone too far? Well, to be honest, it is pretty hard to build this case as I will try to explain. Let’s start with the bond yield fundamentals. Imagine, and this could be pretty difficult after five years of extraordinary stimulus, that there was no quantitative easing. What would the bond yield look like in this scenario?

**Modeling bond yields**

In brief, interest rates are a reflection of economic growth, inflation and monetary policy. In general, higher economic growth, higher inflation and higher short-term interest rates are accompanied by higher bond yields, and vice versa. This implies that finding good proxies for each of these factors should make it possible to replicate the bond yield at any given time.

To represent the economic conditions I take the ISM New Orders Index. Historically, this index has shown a strong relationship with (future) economic growth. As inflation input I take the Core CPI, the Consumer Price Index ex food and energy, as measured by the Bureau of Labor Statistics. Finally, the 3M-Libor is used as an input related to the monetary policy of the Fed. Together, these three factors are put together in a simple model that estimates (not forecasts) the current 10-year bond yield.

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The estimation results of the model are shown in the graph below. As can be derived from the graph, the model does a good job in replicating the 10-year bond yield. In fact, the model fit, as measured by the R-squared of a simple linear regression, is almost 90%. But just a simple look at the graph will tell you as well that there is a decent fit between the fair value and actual bond yield.

The models tells us that, based on the ISM New Order Index, the Core CPI and the 3M-Libor, the 10-year bond yield should be 3.0%, which is 50 basis points higher than the current yield. According to the model, if anything the 10-year bond yield is too low.

**Forward looking input**

One caveat of the model could be that it does incorporate enough forward looking factors. This could lead to potential deviations since financial markets are by nature forward looking. Although the strong fit of the model before 2011 does not make it very likely, let’s just take a quick look at some more forward looking data.

Bloomberg is a good source for finding forward looking CPI data. The current expectation for the Core Personal Expenditure Price Index (PCE), the preferred inflation gauge of the Fed, for this year is 1.3% (Bloomberg does not keep track of the Core CPI). For 2014 it is 1.8%. With the current Core PCE at 1.1% it is reasonable to assume that inflation is expected to go up, not down. Incorporating forward looking inflation data would, therefore, result in a higher, not lower, fair value bond yield.

We can do a similar exercise for the 3M-Libor. Since the Libor-rate is used as an input related to the Federal Funds Target Rate the implied Fed rates derived from the Fed futures seems an obvious place to look for forward looking factors. In the next graph I plotted the implied probabilities for different Fed Funds Target Rates at the December 17 2014 meeting of the Fed. I chose this meeting as the discussion about the first rate hike pivots around this FOMC meeting.

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The graph shows two sets of implied probabilities, one from April 29 the day before the second-last FOMC meeting and the other from June 29. Not surprisingly, the recent FOMC meetings in which the bond tapering was put forward have resulted in a substantial increase in implied probabilities of future rate hikes. On April 29 there was only a 3% chance that the Fed Funds Target Rate would be 0.50% in December 2014. The chance of anything higher than that was zilch. But on June 29 the probability of a Fed rate of 0.50% was over 30%, and there was a cumulative probability of 20% of rates higher than that. So, like for the CPI, incorporating an explicit forward looking Fed indicator, would likely result in a higher fair value yield estimate. To sum up; looking at traditional fundamental factors would lead to the conclusion that current yields are not too high.

**The effect of Quantitative Easing**

Now, back to the first graph. As explained above it does not take into account the unprecedented amount of quantitative easing that the Fed has demonstrated. Hence, the model, arguably, leaves out the most important factor for bond yields in recent years. These bond purchases are the main explanation for the gap that has opened up between the fair value yield estimation of the model and the actual 10-year yield.

In order to determine if current bond yields have risen too much we have to know the impact of the Fed bond purchases. Economist Jan Hatzius from Goldman Sachs has done some extensive research on this topic. Drawing on a dozen academic studies Hatzius estimates that it takes about $1 trillion in bond purchases to move the long-term interest rates by 40 basis points, 0.40%.

Let’s put this number to work. The graph below, taken from the website of the Federal Reserve Bank of St. Louis, shows that since the start of Quantitative Easing back in 2008, the Fed has increased its bond holdings by approximately $1.4 trillion. This would then translate to a 0.56% (1.4 * 0.40%) effect on the long-term interest rates. In case of the 10-year bond yield this would imply a 0.56% deviation from the fair value estimate of the model of 3.0%, which leaves 2.44%. This is very close to the current 10-year yield of 2.50%, demonstrating that the current yields have not risen too much. Moreover, when taking into account that the Fed has also bought large quantities of short-term bonds, which are also part of the $1.4 trillion total, the impact of 0.56% is probably overstated.

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**Conclusion**

Although (long-term) interest rates have risen sharply in recent months, yields are not too high from a fundamental perspective. A simple model that incorporates factors that are related to economic growth, inflation and the general monetary policy shows yields are currently a bit too low. When the effect of the unconventional Fed measures is taken into account, the current 10-year bond yield lies pretty close to its fair value. This, of course, does not mean the bond yield can’t go down again. Deterioration in the economic outlook could send yields lower and technically speaking the Fed has also kept the option open to increase, rather than decrease, its bond purchases. That said; given de current economic development and the signs of tapering by the Fed, current bond yields have probably not risen too much.