Implied forward Treasury bill rates showed a very large drop of more than 0.41% in 2017 versus last week in the wake of a drop in current Treasury yields of 0.18% to 0.28% at maturities from 2 years to 30 years. All of the drop in Treasury yields was due to a drop in expected short term Treasury rate levels. There was no change in the risk premium or term premium in long term Treasuries. That premium, the reward for "going long" in excess of expected short term Treasuries was unchanged at 0.69% at 30 years this week. Forward 1 month T-bill rates now rise steadily until February, 2022, with the peak at 2.41%, down 0.29% and 5 months later than projected last week. The largest drop in implied forward 1 month T-bill rates was 0.43% in October 2017. The implied forecast also shows forward 10 year U.S. Treasury yields rising to 2.56% in 2025, down 0.15% from last week.

Here are the highlights of this week's implied forecast:

- Over the next 120 months, the maximum implied forward 1 month T-bill rate is 2.41%.
- The implied forward 1 month T-bill rate increases until reaching a peak at February 28, 2022.
- The largest decrease in implied forward 1 month T-bills versus last week's forecast is -0.43% on October 31, 2017.
- The U.S. Treasury 10 year yield decreased this week by -0.26%.
- All of this decrease was fueled by lower expectations for short term Treasuries over the next ten years. None of it was due to a change in the U.S. Treasury "term premium" or "risk premium" at ten years.
- The 30 year U.S. Treasury term premium is currently 0.69%.
- The 10 year U.S. Treasury yield is projected to reach 1.99% in 1 year, a change of 0.22% from current levels.
- Looking ahead 10 years, the 10 year U.S. Treasury yield implied by current bond prices is 2.56%, a change of 0.79% from current levels.

The details behind these highlights are explained below.

**Note: Forward Rate Calculations are Not a Forecast**

Many readers who are not familiar with forward rate calculations assume they are a forecast of interest rates with no more credibility than any other forecast. Forward rates, which we often label an "implied forecast," involve no judgment. Forward rates are the mechanical calculation of break-even yields such that investing in any maturity U.S. Treasury and rolling it over for 30 years will yield the same amount of cash in 30 years as investing in any other maturity. For example, if one is given the 4 week U.S. Treasury bill yield and the 13 week Treasury bill yield today, one can calculate how much the 9 week Treasury bill must yield in 4 weeks for a strategy of buying the 3 month Treasury bill or the one month Treasury bill, followed by reinvestment in a 9 week bill, to yield the same amount of cash in 13 weeks. This calculation involves no more judgment than the calculation of the yield to maturity on a bond.

How does one use forward rates to forecast interest rates or to simulate them forward for asset and liability management or other risk management purposes? A series of authors beginning with Ho and Lee in 1985 and then followed by Heath, Jarrow, and Morton in a number of papers beginning in the late 1980s answered this question. The future path of interest rates must bear a specific link to forward rates that depends on the number of random factors driving interest rate movements and the nature of the volatility of those factors. Forward rates play an important role, however, in understanding where actual rates will end up. In this note we use a 9 factor Heath Jarrow and Morton model of the U.S. Treasury curve with constant coefficients. We derive those coefficients and the parameters which determine expectations using U.S. Department of the Treasury data from 1962 through September 30, 2014.

The empirical relationship between forward rates and actual rates is very thoroughly discussed by a number of respected researchers. For an introduction to the topic, we encourage readers to review recent Federal Reserve research by Swanson (2007), Rosenberg and Maurer (2008), Kim and Orphanides (2007), and Adrian, Crump, Mills and Moensch (2014). We refer readers with a technical background to Kim and Wright (2005) and the 2005 and 2008 papers by John Cochrane and Monika Piazzesi on this topic. Other excellent papers include Adrian, Crump and Moensch (2013), Durham (2014), Rudebusch, Sack and Swanson (2007), and Cochrane (2007).

**The Analysis**

The implied forecast takes the Treasury yield curve as a given and does not attempt to reverse the impact on the curve of quantitative easing by the Federal Reserve. See Jarrow and Li (2012) and Chadha, Turner and Zampolli (2013) for estimates of the impact of quantitative easing on Treasury yield levels.

We explain the background for these calculations in the rest of this note. The implied forecast allows investors in exchange traded U.S. Treasury funds (NYSEARCA:TLT) (NYSEARCA:TBT) (NYSEARCA:TMF) (NYSEARCA:TMV) (NYSEARCA:IEF) (NYSEARCA:SHY), bond funds (NYSEARCA:BOND), (NASDAQ:BND), municipal bonds (NYSE:NUV) and exchange traded mortgage funds (BATS:REM) to assess likely total returns over the next 120 months.

Today's implied forecast for U.S. Treasury yields is based on the January 15, 2015 constant maturity Treasury yields that were reported by the Department of the Treasury at 4 p.m. Eastern Daylight Time January 15, 2015. The U.S. Treasury "forecast" is the implied forward coupon bearing U.S. Treasury yields derived using the maximum smoothness forward rate smoothing approach developed by Adams and van Deventer (*Journal of Fixed Income*, 1994) and corrected in van Deventer and Imai, *Financial Risk Analytics* (1996). Kamakura Corporation recently announced new research by Managing Director Robert Jarrow which confirms that the maximum smoothness forward rate approach is consistent with the no arbitrage conditions on interest rate movements derived by Heath, Jarrow and Morton [1992]. There are other yield curve smoothing methods in common use which violate the no arbitrage restrictions. Among the methods which cannot meet the "no arbitrage" standard are the Svensson, Nelson-Siegel, and Merrill Lynch exponential smoothing approaches.

**U.S. Treasury Yield Implied Forecast**

This graph shows the projected current path for 1 month implied forward Treasury bill rates in blue. Last week's implied forward path is shown in red.

We can plot forward rates versus the best estimates of the market's true expected rates using the Heath, Jarrow and Morton model discussed above. One can see in this graph of 3 month forward U.S. Treasury bill rates and estimated expectations for the actual 3 month U.S. Treasury bill rates that expected rates are well below forward rates:

**Today's Kamakura U.S. Treasury Yield Implied Forecast**

The Kamakura 10 year implied forecast of U.S. Treasury yields is based on this data from the Federal Reserve H15 statistical release:

The table above shows the reasons for the change in rates, the change due to differences in expectations and the change due to differences in the U.S. Treasury term premium. The excess of actual Treasury yields over the yields that would prevail with no risk premium or term premium is shown in this graph:

The magnitude of the U.S. Treasury term premium is plotted in this graph. This is the reward for committing to long term U.S. Treasury yields above and beyond the market's expectations for short term Treasury yields over each holding period plotted:

The graph below shows in 3 dimensions the implied movement of the U.S. Treasury yield curve 120 months into the future at each month end:

These yield curve movements are consistent with the continuous forward rates and zero coupon yields implied by the U.S. Treasury coupon bearing yields above:

In numerical terms, implied forecasts for the first 60 months of U.S. Treasury yield curves are as follows:

The implied forecast yields for months 61 to 120 are given here:

**Background Information on Input Data and Smoothing**

The Federal Reserve H15 statistical release is the source of most of the data used in this analysis. The Kamakura approach to forward rate derivation and the maximum smoothness forward rate approach to yield curve smoothing is detailed in Chapter 5 of van Deventer, Imai and Mesler (2013).

Younger readers may not be familiar with the dramatic movements in interest rates that have occurred in modern U.S. economic history. Older readers were once familiar with these rate movements, but they may have forgotten them. Kamakura Corporation has provided a video that shows the daily movements in forward rates from 1962 through August 2011. To view the video, follow this link.

**Disclosure:** The author has no positions in any stocks mentioned, and no plans to initiate any positions within the next 72 hours.

The author wrote this article themselves, and it expresses their own opinions. The author is not receiving compensation for it (other than from Seeking Alpha). The author has no business relationship with any company whose stock is mentioned in this article.