Kamakura Weekly Forecast, May 6, 2022: Forward Rates Rise Again

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Inverted yields, negative rates and 10-year US Treasury probabilities

Forward rates underlying the US Treasury yield curve jumped again this week after the Fed hiked rates 50 basis points. In this week’s forecast, the focus is based on three components of interest rate behavior: the future probability of the inverted yield curve predicting recession, the probability of negative rates, and the probability distribution of US Treasury yields over the next decade.

We start from 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 a maximum smoothing forward rate approach, Friday’s implied forward rate curve shows a rapid rise in 1-month rates to an initial high of 3.46% from 3.32% last week. After the initial rise, there is some volatility before rates peak again at 3.32% from 3.00% previously. Rates eventually peak again at 4.25%, down from 3.87% previously, then drop to a lower plateau at the end of the 30-year horizon.


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Using the methodology described in the appendix, we simulate 500,000 future paths for the 30-year US Treasury yield curve. The following three sections summarize our conclusions from this simulation.

Inverted Treasury yield: 35.4% probability by May 2023

Many economists have concluded that a downward sloping US Treasury yield curve is an important indicator of future recessions. A recent example is this article by Alex Domash and Lawrence H. Summers. We measure the probability that the 10-year nominal coupon Treasury yield will be lower than the 2-year nominal coupon Treasury yield for each scenario in each of the first 80 quarterly periods of the simulation. 1

The following chart shows that the probability of an inverted return remains elevated, peaking at 35.4%, from 48.4% last week, in the 91-day quarterly period ending May 5, 2023.


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Negative treasury yields: 7.7% probability by spring 2028

The following graph depicts the probability of negative 3-month Treasury bill rates for all the last 3 months of the next 3 decades. The probability of negative rates starts near zero but then increases steadily to peak at 7.7%, up from 8.4% last week, in the period ending April 2030:


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10-year US Treasury probabilities

In this section, the focus is on the coming decade. This week’s simulation shows that the most likely range for the yield on 3-month US Treasuries ten years from now is 0% to 1%. There is a 27.64% chance that the 3-month yield will fall within this range, a change from 29.00% last week. For the 10-year Treasury yield, the most likely range is 2% to 3%. The probability of being in this range is 25.12%, compared to 26.45% last week.

In a recent article on Seeking Alpha, we pointed out that a “heads” or “heads” prediction in a draw misses critical information. What a knowledgeable bettor should know is that on average, for a fair coin, the probability of heads is 50%. A prediction that the next coin toss will be heads is literally worthless to investors because the outcome is purely random.

The same is true for interest rates.

In this section, we present the detailed probability distribution for the 3-month Treasury bill rate and the 10-year US 10-year Treasury bill yield using semi-annual time steps. We present the probability of where rates will be at each time step in 1% “rate buckets”. The forecasts are presented in this graph:


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US 3-Month Treasury Yield Data:


The probability that the yield on 3-month Treasury bills will be between 1% and 2% in 2 years is shown in column 4: 31.63%. The probability that the 3-month Treasury yield will be negative (as has often been the case in Europe and Japan) in 2 years is 1.19% plus 0.01% plus 0.00% = 1, 20%. Cells shaded blue represent positive probabilities of occurrence, but the probability has been rounded to the nearest 0.01%. The shading scheme works like this:

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

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

Light yellow: the probability is 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 derived under the same simulation.

10 years

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US 10-Year Treasury Yield Data:


Annex: Cash simulation methodology

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

Step 1: We take the closing of the US Treasury yield curve as a starting point. For today’s forecast, it’s May 6, 2022.

Step 2: We use the number of points on the yield curve that best explain historical shifts in the yield curve. Using daily data from 1962 through March 31, 2022, we conclude that 10 “factors” determine almost all movements in US Treasury yields.

Step 3: We measure the volatility of changes in these factors and its evolution over the same period.

Step 4: Using these measured volatilities, we generate 500,000 random shocks at each time step and derive the resulting yield curve.

Step 5: We “validate” the model to ensure that the simulation EXACTLY assesses the starting Treasury curve and that it matches the story as closely as possible. The methodology for doing this is described below.

Step 6: We take the 500,000 simulated yield curves and calculate the probabilities of yields falling in each of the 1% “buckets” shown in the chart.

Do Treasury yields accurately reflect expected future inflation?

We showed in a recent article on Seeking Alpha that, on average, investors have almost always done better buying long-dated bonds than rolling over short-dated Treasuries. This means that market participants have generally (but not always) been accurate in their forecasts of future inflation and in adding a risk premium to those forecasts.

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

Finally, as mentioned each week in The Corporate Bond Investor Friday preview, the future expenses (both amount and timing) that all investors try to cover with their investments are an important part of the investment strategy. . The author follows his own advice: cover short-term cash needs first, then cover more distant cash needs as savings and investment returns accumulate.

Technical details

Daily treasury bill returns are the basic historical data for adjusting the number of yield curve factors and their volatility. Historical data is provided by the US Department of Treasury.

An example of the modeling process using data up to March 31, 2022 is available at this link.

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



For technically inclined readers, we recommend Professor Jarrow’s book Modeling fixed income securities and interest rate options for those who want to know exactly how the construction of the “HJM” model works.

The number of factors (10 for the US) has been stable for some time, but the volatilities for each factor are updated monthly.

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