The 3-Month T-Bill Rate: Average Of 100,000 Scenarios Up 0.23% To 3.46% In 2025

by: Donald van Deventer


We update our June 12 simulation in the wake of new highs for the 30-year Treasury set on Friday afternoon.

We generate 100,000 scenarios using 9 factors driving the yield curve and interest rate volatility benchmarked in U.S. Treasury history from January 1962 through March 2015.

The average simulated value for the 3-month T-bill rate in 2025 was up 0.23% over the June 12 simulation as low rate scenarios shifted to higher levels.

We use 100,000 scenarios for the U.S. Treasury (NYSEARCA:TLT) yield curve this week to examine the outlook for Treasuries and the magnitude of the term premium (or risk premium) above and beyond expected rate levels that are embedded in the yield curve. We do this standard scenario analysis for the same reason it's been standard practice among sophisticated financial institutions for more than 40 years: not to make a point forecast of interest rates, but instead, to understand more completely the range of interest rate risk that we are facing. The U.S. Treasury yield curve from which simulations are initiated is the June 26, 2015 yield curve as reported by the U.S. Department of the Treasury. Please see the full Kamakura interest rate update for a detailed description of the methodology.

Current Yield Curve and Recent Yield Movements

The chart below lists current U.S. Treasury yields, recent changes, and recent highs and lows since January 1, 2015. We also list the all-time highs and lows, and the most recent dates on which those highs and lows have occurred.

Overall, rate movements for the week were mixed and modest. The movements in 1-month and 6-month U.S. Treasury yields since January 1, 2015 are shown here:

The movements in the curve can be summarized this way, where "recent" refers to changes since January 1, 2015:

  1. The biggest yield change of the week was 0.23%, which occurred for the ten-year Treasury yield.
  2. The smallest yield change of the week was 0.00%, which took place at the 1-month and 3-month maturities.
  3. The 1-month Treasury yield finished the week at 0%, the tenth day in a row at the zero point. This compares to the recent high and low values of 0.05% and 0%. The all-time high in the 1-month yield was 5.27% recorded on February 21, 2007. The all-time low was 0% on June 26, 2015.
  4. The 1-year Treasury yield finished the week at 0.29% - a change of 0.04% since last week. This compares to the recent high and low values of 0.3% and 0.16%. The all-time high in the 1-year yield was 17.31% recorded on September 3, 1981. The all-time low was 0.08% as on September 19, 2011.
  5. The 10-year Treasury yield finished the week at 2.49% - a change of 0.23% since last week. This compares to the recent high and low values of 2.5% and 1.68%. The all-time high in the 10-year yield was 15.84% recorded on September 30, 1981. The all-time low was 1.43% on July 25, 2012.
  6. The 30-year Treasury yield completed the week at 3.25%, a change of 0.20% since last week and a new high for 2015. This compares to the recent low value of 2.25%. The all-time high in the 30-year yield was 15.21% recorded on October 26, 1981. The all-time low was 2.25% as on February 2, 2015.

Recent movements in 1-year, 10-year, and 30-year Treasury yields are shown in this graph:

The long-term history of rate movements from 1962 shows a large rise in rates followed by a large fall in rates - a caution to all who are supremely confident about their forecast for rates:

History is interesting, but what lies ahead? We turn to that now. We reach these conclusions from our simulation:

  1. This week's simulation shows the risk-neutral 3-month U.S. Treasury bill rate rising to a mean risk-neutral level of 0.613% in one year, compared to the 0.613% quarterly forward rate implied by current yields.
  2. The mean risk-neutral 3-month U.S. Treasury bill rate in ten years rises to 3.459%, compared to the forward rate at that time of 3.139%. This is an increase of 0.23% from our simulation, using data from June 12, 2015.
  3. The simulated mean empirical expected 3-month T-bill rate at the 1- and 10-year horizons was 0.628% and 4.009%, respectively. A change in assumptions (and therefore parameters) would change these estimates.
  4. The probability of a negative risk-neutral 3-month Treasury bill rate is 0.815% in one year and 17.500% in ten years.
  5. The simulations first show the risk-neutral 3-month Treasury bill rate hitting 10% in a few scenarios in quarter 9. By the ten-year point, the 39th quarter, the probability that the 3-month Treasury bill rate is over 10% rises to 4.627%.
  6. At ten years, the empirical expected zero coupon bond yield is 2.939%. The actual U.S. Treasury zero yield is 2.540%.
  7. The term premium at ten years is -0.399%.
  8. By the 30-year maturity, the empirical expected zero yield is 4.550%, compared to the actual 3.456% 30-year U.S. Treasury zero yield.
  9. At 30 years, the term premium on a zero coupon bond basis is -1.093%, given the parameter assumptions we have made.

The next graph shows the difference in simulations for the current yield curve versus the most recent prior simulation results. We show the distribution of the risk-neutral values of the three-month Treasury bill rate in quarter 39, the ending quarter at a 10-year horizon. The current simulation (in black) has many fewer scenarios than the prior one (in brown) at low and negative rates, and slightly more scenarios for the higher rate levels. This results in the 0.23% rise in the average simulated 3-month Treasury bill rate:

In coming weeks, we will be adding some risk management summary statistics to illustrate how to use these conclusions for portfolio strategy.


Frequently Asked Questions

Over the last few years of publishing U.S. Treasury forward rates and interest rate simulations, a few questions are asked regularly by both retail and institutions investors. We answer a selected subset of them in this appendix.

Why is an interest rate forecast necessary?

For large institutional investors, a forward-looking simulation of interest rates and macro factors is the standard first step in optimizing their equity and fixed-income portfolios. This is standard best practice in both theory and practice. For many retail investors, this may be a new concept to some, even though it's obvious that one should refinance a floating rate mortgage if one expects rates to rise. Another clear conclusion from a forward-looking simulation is this: One shouldn't own the stock of one's employer, because the stock price is likely to be low in the scenario where the investor gets laid off from work. These two examples are just common sense, but careful investors know that there are no $20 bills to be found on Wall Street, and that understanding the full range of scenarios that might come about leads to better investment strategy. If one believes that bank stocks rise with high interest rates, what is the probability of that happening? We answer that question in this note. These quantitative simulations are essential for realistic risk management of assets and liabilities ("ALM").

What is the term premium, and why is it important?

Former Fed Chairman Ben Bernanke had an insightful post April 13, 2015 on the term premium embedded in the U.S. Treasury curve and how that premium has changed over time. In the post, he very appropriately cites some careful analysis done at the New York Fed by Adrian, Crump and Moench. How big is the potential model risk in estimating the term premium in the U.S. Treasury curve? Prof. John Cochrane at the University of Chicago recently posted a thoughtful piece on the difficulties of extracting the market's expected future interest rates from the current yield curve. Modeling assumptions are very important in the measured levels of the term premium.

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 original source of the U.S. Treasury yield information on the H15 statistical release is the U.S. Department of the Treasury. 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). The original publication, Adams and van Deventer (1994), was modified in van Deventer and Imai (1996).

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: I/we 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.