Projected one month Treasury bill rates showed a flattening this week, with rates in 2020 down by as much as 0.18% and rates in 2024 up by 0.02%. Forward one month T-bill rates are now projected to peak beyond the ten year horizon of the forecast, rising steadily to 3.77% in April 2024. This ends a seven week stretch of implied one month bill peaks inside of our 10-year forecast horizon. The forecast shows projected 10-year U.S. Treasury yields rising steadily to 3.83% in 2024, down 0.14% from last week. We also present three potential scenarios consistent with the implied forecast that represent alternative paths for interest rates. This kind of multi-factor scenario generation is essential for comprehensive asset and liability management at banks, insurance firms, pension funds, and endowments. These scenarios are consistent with a multi-factor rate model benchmarked in 52 years of U.S. history, discussed below. For an update of the outlook for mortgages and the valuation of mortgage servicing rights, please see Kamakura Corporation's weekly mortgage forecast.
Here are the highlights of this week's implied forecast:
- Over the next 120 months, the maximum implied forward one month T-bill rate is 3.77%.
- The implied forward one month T-bill rate increases steadily over the next 120 months and reaches this peak at April 30 2024.
- The largest increase in implied forward one month T-bills versus last week's forecast is 0.02% on April 30 2024.
- The largest decrease in implied forward one month T-bills versus last week's forecast is -0.18% on October 31, 2020.
- The U.S. Treasury 10-year yield decreased this week by 0.11%.
- The 10-year U.S. Treasury yield is projected to reach 2.87% in one year, a change of 0.37% versus today's yield level.
- Looking ahead 10 years the 10-year U.S. Treasury yield implied by current bond prices is 3.83%, a change of 1.33% from current levels.
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 forecast allows investors in exchange traded U.S. Treasury funds (NYSEARCA:TLT) (NYSEARCA:TBT), bond funds (NYSEARCA:BOND)(NYSEARCA:BND), municipal bonds (NYSE:NUV) and exchange traded mortgage funds (NYSEARCA:REM) to assess likely total returns over the next 120 months.
Today's forecast for U.S. Treasury yields is based on the May 15, 2014 constant maturity Treasury yields that were reported by the Department of the Treasury at 4 p.m. Eastern Daylight Time May 15, 2014. The U.S. Treasury "forecast" is the implied future 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).
U.S. Treasury Yield Forecast
This graph shows the projected current path for one month implied forward Treasury bill rates in blue. Last week's implied forward path is shown in red.
3 Scenarios around the Forward Rate Curve
In the rest of this section, we highlight three of the infinite number of scenarios that could come about. We ensure that these scenarios are consistent with an efficient, no arbitrage market for U.S. Treasury as described by Heath, Jarrow and Morton (1992). We start with the current U.S. Treasury curve. We assume that a 9 factor model drives U.S. Treasury rates at maturities ranging from 3 months to 30 years. The basis for this model is the study released by Kamakura Corporation on March 5, 2014, that proves at least 9 factors are needed to accurately model quarterly rate changes. The study makes use of more than 52 years of daily data from the U.S. Department of the Treasury and the Board of Governors of the Federal Reserve. The 9 factors used are 6 more factors than the Federal Reserve used in its 2014 Comprehensive Capital Analysis and Review stress tests and 3 more factors than required by the December 2010 version of the Basel II market risk framework (see page 12, paragraph b) of the Bank for International Settlements. We use more factors for maximum consistency with U.S. yield curve history. The parameters of the model are estimated by Kamakura Corporation using quarterly data from 1962 to the present, with an optimization of parameters on the 2001-2013 low rate period. The model parameters are available by subscription from Kamakura Risk Information Services. The consensus "implied forecast" is shown later in this report. We now turn to three specific scenarios selected by Kamakura's analytics team for their special features.
Scenario A: A Rise to August 2016 and Then a Rate Decline
The Federal Reserve's Comprehensive Capital Analysis and Review (CCAR) process focuses on three specific scenarios provided by the Federal Reserve. In this section of our weekly commentary, we start with the forward curve for the current date, which we explain below in our implied forecast. In this section of the report we use Monte Carlo simulation in the Heath Jarrow and Morton framework using Kamakura Risk Manager. We project 13 quarters, consistent with the CCAR program, but we generate a large number of scenarios randomly. We select 3 that we hope will be of interest to readers. In the first scenario, the initial U.S. Treasury yield curve is shown in dark blue. In the first scenario, by August, 2014, the curve shifts up moderately to the light blue curve shown below. Then yields shift dramatically upward in August 2015 (in green) and then shifts upward again in August 2016 (in yellow. By August 2017 (in red), the U.S. Treasury curve is lower in short and intermediate maturities by as much as 2.00% from the 2016 peak.
Scenario B: Extended Pain and Suffering
In the second scenario, the U.S. Treasury curve powers up consistently, with steady increases in nearly parallel shifts in August 2014 (light blue), August 2014 (in green), August 2016 (in yellow) and August 2017 (in red). In the Monte Carlo simulation of potential rate paths done for this note, most of the scenarios were similar to this one.
There is no respite for long term bond holders in this scenario, with the long end of the U.S. Treasury yield curve settling above 9.00%.
Scenario C: Long Rates Controlled by a Spike in Short Term Rates
In scenario 3, the U.S. Treasury curve shifts upward during 2014. In 2015, shown in green, the yield curve rise halts, and yields decline a bit. By August 2016 (in yellow), short rates jump sharply and long term rates fall, plunging by more than 1.00%. The 2017 yield curve (in red) shifts upward on the short end, with long rates unchanged versus 2016. This scenario was a rare one in the Monte Carlo simulation.
A Reminder to Readers about These Three Scenarios
All of these scenarios are plausible in that (a) they begin with the current U.S. Treasury curve and they are (b) simulated forward in a no arbitrage fashion (c) using historical U.S. Treasury volatilities. That being said, there are an infinite number of possible forward curve shapes and paths, and these three have been selected more for their drama than anything else. If one were to select only one scenario to focus on, it would be the forward rate implied forecast explained in more detail below.
Today's Kamakura U.S. Treasury Yield Forecast
The Kamakura 10 year monthly forecast of U.S. Treasury yields is based on this data from the Federal Reserve H15 statistical release:
The graph below shows in 3 dimensions the 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, forecasts for the first 60 months of U.S. Treasury yield curves are as follows:
The forecasted 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 interest rate forecasting, and the maximum smoothness forward rate approach to yield curve smoothing is detailed in Chapter 5 of van Deventer, Imai and Mesler (2013).
Disclosure: I have no positions in any stocks mentioned, and no plans to initiate any positions within the next 72 hours. I wrote this article myself, and it expresses my own opinions. I am not receiving compensation for it (other than from Seeking Alpha). I have no business relationship with any company whose stock is mentioned in this article.