Projected one month Treasury bill rates showed a sharp twist this week, with rates in 2019 down by as much as 0.15% and rates in 2024 up by 0.12%. Forward 1 month T-bill rates are now projected to peak in the second quarter of 2022 at 3.77%, postponed by a year relative to last week, but at the same peak level. This is the seventh consecutive implied peak in one month bill rates, something not seen for a few years. The impact of the peak can be seen in the three dimensional graph of Treasury yield movements (below) and Treasury forward rates. The forecast shows projected 10 year U.S. Treasury yields rising steadily to 3.97% in 2024, up 0.05% 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:
- The 10 year U.S. Treasury yield is projected to rise from 2.61% at Thursday’s close (down 0.02% from last week) to 2.99% (down 0.05% from last week) in one year.
- The 10 year U.S. Treasury yield in ten years is forecast to reach 3.97%, 0.05% higher than last week.
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 (TLT) (TBT), bond funds (BOND)(BND), municipal bonds (NUV) and exchange traded mortgage funds (REM) to assess likely total returns over the next 120 months.
Today’s forecast for U.S. Treasury yields is based on the May 8, 2014 constant maturity Treasury yields that were reported by the Department of the Treasury via the Federal Reserve H15 statistical release at 4 p.m. Eastern Daylight Time May 9, 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 week’s projections for the 1 month Treasury bill rate (investment basis) show their implied peak at 3.77% in the second quarter of 2022, only the seventh projected peak in a number of years.
The 10 year U.S. Treasury yield is projected to rise steadily to reach 3.97% on April 30, 2024, 0.05% higher than last week.
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 2015 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 drop in August 2016 (in yellow), except for the very short end of the curve. By August 2017 (in red), the U.S. Treasury curve is lower in short and intermediate maturities by as much as 1.75% from the 2015 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 6.00%.
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 makes a sharp twist upward with short rates leading the charge. By August 2016 (in yellow), short rates stay high and long term rates fall, plunging by more than 1.00%. The 2017 yield curve (in red) shifts downward, leaving rates much lower than they are today. 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).
The numerical values for 360 months of zero coupon bond prices and yields are available by subscription to the KRIS U.S. Treasury Yield Service via info@kamakuraco.com. For comments, questions, or more information about the yield curve smoothing and simulation capabilities in Kamakura Risk Manager, please contact us at info@kamakuraco.com. Kamakura interest rate data are available in electronic form in both general and Kamakura Risk Manager database format.
Donald R. van Deventer and Martin Zorn
Kamakura Corporation
Honolulu, May 8, 2014
Copyright © Kamakura Corporation, 2014. All Rights Reserved.