U.S. Treasury Simulations Show 3-Month Treasury Bill Rate Rising From 0.05% To An Average Of 2.78% In 10 Years

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by: Donald van Deventer

Summary

Starting with the March 31 U.S. Treasury curve, we use rate-dependent interest rate volatility and a 9 factor Heath, Jarrow and Morton model to generate 1,000 scenarios.

The average risk neutral rate simulated for the 3 month U.S. Treasury bill rate was 0.48% in 4 quarters and 2.78% ten years from now.

The range of 3 month bill rates simulated went from a low of minus 1.35% (consistent with events in Europe) and a high of 16.43.

In the wake of the news from the Federal Reserve Open Market Committee March 18, we have again updated our interest rate outlook, using the March 31, 2015 closing U.S. Treasury curve and simulating forward from that starting point. The simulations are based on historical movements in the U.S. Treasury curve from 1962 to the present. We simulate U.S. Treasury yields in two closely related ways. The first method is the so-called "risk neutral" yields that are used to value any securities that are tied to the U.S. Treasury curve. The 1,000 scenarios we generate price today's Treasuries at their exact market prices. Since these risk neutral scenarios contain a risk premium, over very long time horizons they are higher than the actual rates that market participants expect to come about, the so-called expected "empirical rates."

This week's simulation shows the 3 month U.S. Treasury bill rate rising from an initial 0.05% to a mean risk neutral level of 0.479% in one year, just below the forward rate of 0.489%. The mean risk neutral 3 month U.S. Treasury bill rate in ten years rises to 2.776%, compared to the forward rate at that time of 2.422%. The highest 3 month rate simulated ten years forward was 16.431% and the lowest was -1.346%, consistent with recent events in Europe.

For a historical perspective and summary of the actual distribution of one year rates in the U.S. and Japan, see our interest rate analysis of March 11, 2015.

Current U.S. Treasury Zero Coupon Bond Yields and Forward Rates

The current zero coupon bond yields and forward rates implied by today's U.S. Treasury curve are given in this graph:

This week's 1 month forward rates for the first ten years are compared to forward rates in last week's analysis in this graph:

This Week's 1,000 Scenario Simulation

Today's analysis is based on a simulation of 1,000 scenarios using a 9 factor term structure model based on the analysis of Heath, Jarrow and Morton ("HJM"). The HJM model allow us to readily use multiple factors to drive the yield curve and allows us to use realistic assumptions about the volatility of interest rates along the 30 year length of the U.S. Treasury curve. We use 9 points on the yield curve as the risk factors driving the entire curve. These factors have maturities from 3 months to 30 years. We use a separate econometric relationship for each quarterly segment of the yield curve. The econometrics are done using quarterly data from the U.S. Department of the Treasury from 1962 through the end of 2014. We use a rate-dependent volatility function for the 9 risk factors. The simulation is done in such a way that all current Treasury bonds are priced correctly by our 1,000 scenario Monte Carlo simulation.

The Probability Distribution of U.S. Treasury Yields for the Next 10 Years

In this section, we report 40 quarters of simulated results for U.S. Treasury zero coupon bond yields at these maturities:

  1. 3 months
  2. 1 year
  3. 5 years

For each maturity, we report the following statistics for the simulated "risk neutral" yields in the 1,000 scenarios:

  1. The matched maturity forward rate at each maturity
  2. The lowest rate simulated
  3. The 1st percentile yield
  4. The 10th percentile yield
  5. The 25th percentile yield
  6. The 50th percentile yield
  7. The average yield
  8. The 75th percentile yield
  9. The 90th percentile yield
  10. The 99th percentile yield
  11. The highest yield simulated
  12. The average "empirical" or expected actual yield

The 10 Year Outlook for the 3 Month U.S. Treasury Yield

The simulated results for 3 month U.S. Treasury zero coupon yields are given here:

The 10 Year Outlook for the 1 Year U.S. Treasury Yield

The simulated results for 1 year U.S. Treasury zero coupon yields are given here:

The 10 Year Outlook for the 5 Year U.S. Treasury Yield

The simulated results for 5 year U.S. Treasury zero coupon yields are given here:

A 30 Year View of Rate Movements

In this section, we present the same percentiles graphically for the 3 month, 1 year, and 5 year U.S. Treasury zero coupon bond yields.

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.