## Inverse Yields, Negative Rates, and the Probability of US Treasuries Over the Next 10 Years

Friday marked the eighth day of inversion in U.S. Treasury yields, which are highly likely to remain inverted even in January 2023. In this week’s forecast, Focus on three elements of interest rate behavior: the future probability of an inverted yield curve predicting a recession, the probability of negative interest rates, and the probability distribution of U.S. Treasury yields over the next ten years.

We start with the closing US Treasury yield curve and interest rate swap quotes based on the guaranteed overnight funding rate published daily by the Federal Reserve Bank of New York. Using the maximum smoothed forward rate method, Friday’s implied forward rate curve showed a rapid rise in the 1-month rate to an initial peak of 3.64%, compared to 3.63% last week. After the initial rise, there was some volatility before interest rates peaked again at 3.28%, compared to 3.51% previously. Rates eventually peaked again at 4.51%, compared to the previous 4.71%, before falling to a lower plateau at the end of the 30-year period.

Using the methodology outlined in the appendix, we simulated 500,000 future paths of the 30-year US Treasury yield curve. The next three sections summarize our conclusions from this simulation.

## Inverted Treasury Yield: Invert now, 59.1% probability by January 6, 2023

A number of economists have concluded that the downward-sloping U.S. Treasury yield curve is an important indicator of future recessions. A recent example is this paper by Alex Domash and Lawrence H. Summers. The US Treasury 2Y/10Y spread has been negative (inverted) for the past 8 sessions and is currently at -0.20%. We measure the probability that the 10-year par Treasury yield is lower than the 2-year par Treasury yield in each case in each of the first 80 quarters of the simulation.[1] The chart below shows that during the 91-day quarter ending January 13, 2023, the probability of a yield inversion remains high, peaking at 72.4%, compared to 59.1% last week.

## Negative Treasury yields: 8.4% probability by September 28, 2029

The chart below depicts the probability of negative 3-month Treasury bill rates for all countries except the last 3 months over the next 3 decades. The probability of negative rates starts near zero, but then steadily rises to a peak of 8.4%, compared to 8.1% last week through July 5, 2030:

## Probability of U.S. Treasury Bonds in the Next 10 Years

In this section, the focus turns to the next decade. This week’s simulations show the most likely range for 3-month Treasury yields over 10 years is 0% to 1%. The probability of the 3-month yield falling into this range is 28.89%, a change from last week’s 27.74%. For the 10-year Treasury yield, the most likely range is 2% to 3%. The probability of being in this range is 24.97%, compared to 23.96% last week.

In a recent article on Seeking Alpha, we pointed out that the prediction of “heads” or “tails” in a coin toss misses critical information. What a seasoned bettor needs to know is that for a fair coin, the probability of heads is an average of 50%. Predicting that the next coin flip will be “heads” is worthless to investors because the outcome is completely random.

The same goes for interest rates.

In this section, we present detailed probability distributions for the 3-month Treasury bill rate and the 10-year US Treasury 10-year yield using semiannual time steps. We present the probability of interest rates at each time step in 1% “rate buckets”. The prediction is shown in the figure below:

3-Month U.S. Treasury Yield Data:

Kamakura March UST20220715_.xlsx

The probability that the 3-month Treasury bill yield will be between 1% and 2% in 2 years is shown in column 4: 25.85%. The probability that the 3-month Treasury bill yield will be negative in 2 years (often seen in Europe and Japan) is 1.49% + 0.01% + 0.00% = 1.50%. Cells shaded in blue represent a positive probability of occurrence, but the probability has been rounded to the nearest 0.01%. The shadow scheme works as follows:

Dark blue: probability greater than 0% but less than 1%

Light blue: The probability is greater than or equal to 1% and less than 5%

Light yellow: probability greater than or equal to 5% and 10%

Medium Yellow: The probability is greater than or equal to 10% and less than 20%

Orange: The probability is greater than or equal to 20% and less than 25%

Red: The probability is greater than 25%

The chart below shows the same probabilities for the 10-year US Treasury yield as part of the same simulation.

10-Year U.S. Treasury Yield Data:

Kamakura 10 years UST20220715_.xlsx

## Appendix: Treasury Simulation Methodology

These probabilities are derived using the same methodology Kamakura recommends to its risk management clients, who currently hold over $38 trillion in assets or assets under management. A modest technical explanation is given later in the appendix, but we first summarize it in plain English.

Step 1: We start with the closing US Treasury yield curve.

Step 2: We use the number of points on the yield curve that best explains the historical yield curve shift. Using daily data from 1962 to June 30, 2022, we conclude that 10 “factors” drive nearly all moves in Treasury yields.

Step 3: We measure the volatility of changes in these factors and how it has changed over the same period.

Step 4: Using these measured volatility, we generate 500,000 stochastic shocks at each time step and derive the final yield curve.

Step 5: We “validate” the model to ensure that the simulation is pricing the starting Treasury curve accurately and that it matches history as closely as possible. The way to do this is described below.

Step 6: We take all 500,000 simulated yield curves and calculate the probability that the yield will fall within each 1% “bucket” shown in the graph.

## Do Treasury yields accurately reflect expected future inflation?

We showed in a recent article on Seeking Alpha that, on average, investors almost always do better by buying long-term bonds than by rolling over short-term Treasury bills. This means that market participants often (but not always) accurately forecast future inflation and add a risk premium to that forecast.

The above distribution helps investors estimate the probability of a successful long position.

Finally, as mentioned weekly in Corporate Bond Investor Friday at a Glance, the future fees (amount and timing) that all investors are trying to cover with their investments are an important part of an investment strategy. The authors follow their own advice: meet short-term cash needs first, then gradually meet longer-distance cash needs as savings and investment returns accumulate.

## technical details

Daily Treasury yields form the underlying historical data on the number of factors fitting the yield curve and their volatility. Historical data provided by the U.S. Treasury Department.

This link provides an example of the modeling process using data as of March 31, 2022.

The modeling process was published in a very important paper by David Heath, Robert Jarrow and Andrew Morton in 1992:

For the technically inclined reader, we recommend Professor Jarrow’s book Modeling Fixed Income Securities and Interest Rate Options for those who want to see exactly how “HJM” model building works.

The number of factors (10 in the US) has been stable for some time.

footnote

[1] After the first 20 years of the simulation, the 10-year Treasury cannot be derived from the initial 30-year Treasury yield.