Weekly Forecast May 24, 2024: 2-Year and 10-Year Treasury Spread Widens

As explained in Professor Robert Jarrow’s book mentioned below, forward prices contain a risk premium that exceeds the market’s expectation of the 3-month forward price. We document the size of the risk premium in this chart, which shows the zero coupon The yield curve indicated by current Treasury bond prices compared to the compounded annual return on 3-month Treasury bonds that market participants would expect based on the daily movement of government bond yields in 14 countries since 1962. The risk premium, which is the long-term reward of an investment is large and expands over Most of the 30-year vesting period. The graph also shows a sharp downward shift in expected returns in the first few years, and then continues to decline at a slow but steady pace over the entire 30 years. We explain the details below.

For more on this topic, see the analysis of government bond yields in 14 countries through April 30, 2024, provided in the Appendix.

Inverted yields, negative interest rates, and the prospects for US Treasuries for the next 10 years

The negative 2-year/10-year Treasury spread has now lasted for 474 trading days. The spread currently stands at negative 47 basis points, widening 6 basis points from last week. The table below shows that the current line of inverted yield curves is the longest in the US Treasury market since the two-year Treasury yield was first announced on June 1, 1976. The second longest line is 423 trading days beginning on August 18. 1978.

In this week’s forecast, the focus is 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 US Treasury yields over the next decade.

We start from the close of the US Treasury yield curve, published daily by the US Treasury. Using a smooth maximum forward rate approach, the implied forward rate curve on Friday shows a rapid one-month rise in forward prices to an initial peak of 5.51%, versus 5.47% last week. After the initial rise, there is a short decline and rise until interest rates peak again at 4.37%, compared to 4.37% last week. Finally prices peak again at 5.10%, compared to 5.24% last week, and then fall to 3.88%, compared to 3.71% last week, at the end of the 30-year horizon.

Using the methodology described in the Appendix, we simulated 100,000 future paths of the thirty-year U.S. Treasury yield curve. The following three sections summarize our conclusions from those simulations.

Inverted Treasury Yields: Inverted now, 78.3% probability by November 22, 2024

Many economists have concluded that a downward-sloping US Treasury yield curve is an important indicator of a future recession. A recent example of this is this paper by Alex Domash and Lawrence Summers. We measure the probability that the nominal 10-year Treasury yield will be less than the nominal 2-year Treasury yield for each scenario in each of the first 80 quarterly periods in the simulation. (1) The following chart indicates the potential and the inverse return now peaks at 78.3%, compared to 72.2% one week ago, over the 91-day period ending November 22, 2024.

Negative Treasury yields: 12.1% probability by January 25, 2047

The following chart describes the probability of negative interest rates on 3-month Treasury securities for all but the first three months of the next three contracts. The probability of negative interest rates near zero starts at 12.1%, compared to 12.2% a week ago, in the 91-day period ending on January 25, 2047.

Calculate default risk from interest rate maturity mismatch

In light of the failure of Silicon Valley Bank due to interest rate risk on March 10, 2023, we have added a table that applies equally to banks and institutional investors and mismatches individual investors from purchasing long-term Treasuries to borrowers. Short term money. We assume that the only asset is a 10-year Treasury bond purchased at time zero with a face value of $100. We analyze default risk for four different ratios of the initial market value of stocks to the market value of assets: 5%, 10%, 15%, and 20%. For the banking example, we assume that the only class of liabilities are deposits that can be withdrawn at nominal value at any time. In the case of institutional and retail investors, we assume that the commitment is essentially borrowing on margin/repurchase agreement with the possibility of a margin call. For all investors, the liability amount (95, 90, 85 or 80) represents the “strike price” on the call option held by the liability holders. Failure occurs via margin call, bank withdrawal, or regulatory takeover (in the case of banking) when the value of assets falls below the value of liabilities.

The chart below shows the cumulative 10-year probabilities of failure for each of the four possible capital ratios when the asset has a 10-year maturity. For the 5% case, the probability of default is 41.73%, compared to 42.18% last week.

This default probability analysis is updated weekly based on the US Treasury yield simulation described in the next section. The calculation process is the same for any asset portfolio that includes credit risk.

Prospects for the US Treasury in 10 years

In this section, the focus turns to the next decade. This week’s simulation shows that the most likely range for the 3-month US Treasury yield in ten years is 0% to 1%, unchanged from last week. There is a 25.27% probability that the 3-month yield will fall into this range, which is a change from 25.24% one week ago. For the 10-year Treasury yield, the most likely range is 2% to 3%, also unchanged from last week. The probability of being in this range is 22.34%, compared to 22.14% one week ago.

In a recent post on Seeking Alpha, we pointed out that predicting “heads” or “heads” on a coin toss ignores important information. What an experienced bettor needs to know is that on average for a fair coin, the probability of coming heads is 50%. Predicting that the next side of the coin will be “heads” is worth nothing to investors, because the outcome is completely random.

The same applies to interest rates.

In this section, we present the detailed probability distribution of both the 3-month Treasury yield and the 10-year US Treasury yield after 10 years using semiannual time steps. (2) We introduce the probability of rates being at 1 percent each time you enter Rate Groups. The 3-month Treasury yield forecast is shown in this chart:

Three-month US Treasury bond yield data:

SAS3monthUST20240524.xlsx

The probability that the 3-month Treasury bond will return between 1% and 2% in two years is shown in Column 4: 19.16%. 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 0.73% plus 0.02% plus 0.00% = 0.74% (the difference is due to rounding). Blue shaded cells represent positive probabilities of occurrence, but the probability has been rounded to the nearest 0.01%. The shading system works as follows:

• Dark blue: Probability is greater than 0% but less than 1%
• Light blue: 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: Probability greater than or equal to 10% and less than 20%
• Orange: 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 as part of the same simulation.

Ten-year US Treasury bond yield data:

SAS10yearUST20240524.xlsx

Appendix: Treasury Simulation Methodology

Probabilities are derived using the same methodology that SAS Institute Inc. recommends for its KRIS^® and Risk Manager Kamakura^® Client. There is a somewhat technical explanation later in the appendix, but we summarize it in plain English first.

Step 1: We take the US Treasury yield curve at the close as a starting point.

Step 2: We use the number of points on the yield curve that best explains historical yield curve shifts. Using daily government bond yield data from 14 countries from 1962 through April 30, 2024, we conclude that 12 “factors” drive almost all movements in government bond yields. The countries on which the analysis is based are Australia, Canada, France, Germany, Italy, Japan and New Zealand. Russia, Singapore, Spain, Sweden, Thailand, the United Kingdom, and the United States of America. No data from Russia after January 2022 is included.

Step 3: We measure the volatility of changes in those factors and how volatility changes over the same period.

Step 4: Using those measured volatility, we generate 100,000 random shocks at each time step and infer the resulting yield curve.

Step 5: We “validate” the model to ensure that the simulation exactly prices the starting Treasury curve and that it fits history as closely as possible. The methodology for doing this is described below.

Step 6: We take all 100,000 simulated yield curves and calculate the odds that the yield will fall in each of the 1% “bulldozers” displayed in the chart.

Do Treasury yields accurately reflect expected future inflation?

We showed in a recent Seeking Alpha post that investors on average have always done better by buying longer-term bonds than by rolling over short-term Treasuries. This means that market participants were generally (but not always) accurate in forecasting future inflation and adding a risk premium to those forecasts.

The above distribution helps investors estimate the probability of success by making a purchase.

Finally, as noted weekly in Friday’s Corporate Bond Investors Overview, the future expenses (amount and timing) that all investors are trying to cover with their investments is an important part of the investment strategy. The author follows his own advice: cover short-term cash needs first, then move on to cover longer-term cash needs as savings and investment returns accumulate.

Technical details

Daily government bond yields from the above 14 countries constitute the underlying historical data to fit the number of yield curve factors and their volatility. US historical data is provided by the US Department of the Treasury. The use of international bond data increases the number of observations to more than 106,000, and provides a more complete range of experience with both rising rates and negative rates than is provided by the US data set alone.

The modeling process was published in an 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 “HJM” model building works.

The number of factors, 12 for the 14-country model, has remained stable since June 30, 2017.

Footnotes:

(1) After the first 20 years of the simulation, the 10-year Treasury bond cannot be derived from the initial 30-year Treasury yields.

(2) The full simulation uses 91-day time steps for 30 years forward. This note summarizes only the first ten years of the full simulation.