Weekly foreign debt yield forecast for April 12, 2024: Foreign debt forward rates have been raised again (EUR: USD) | Private Equity Weekly

Author’s Note

The simulation was conducted in conjunction with a simulation of U.S. Treasury yields, reflecting the correlations between the 12 factors driving yields in each country. For more information about the U.S. Treasury simulation, please contact the authors.These two The simulation of German foreign debt and U.S. government bond yields will affect foreign exchange rates, resulting in the following distribution of the euro-dollar exchange rate one year later:

This week’s foreign debt yield simulation

As explained in Professor Robert Jarrow’s book cited below, forward rates contain a higher risk premium than the market expects for 3-month forward rates.We document the size of this risk premium in the chart below, which shows the zero-coupon yield curve implied by current German bund prices compared to the annualized compound yield on 3-month Treasuries expected by market participants Daily changes in government bond yields for 14 countries since 1962. The chart also shows that yields decline steadily over the first seven years, as discussed below, before gradually rising thereafter.

For more information on this topic, see the analysis of government bond yields for 14 countries as of March 31, 2024 in the appendix.

Yield inversion, negative interest rates and the chances of German Bunds over the next 10 years

In this week’s Eurozone forecast, the focus is on three elements of interest rate behavior: the future probability of an inversion of the yield curve predicting a recession, the probability of negative interest rates, and the probability distribution of German Bund yields over the next ten years.

We start with the German Bund closing yield curve published daily by the Deutsche Bundesbank and other sources. Using the maximum smoothed forward rate method, Friday’s implied forward rate curve showed a rapid rise in 1-month rates to an initial peak of 3.71%, compared with 3.86% last week. After the initial rise, there will be some volatility until rates peak again at 3.06% (from 2.92% last week) before falling to a lower level of 2.43% at the end of the 30-year period, compared to 2.30% last week.

Using the methodology outlined in the appendix, we simulated 100,000 future paths of the German Bund yield curve over 30 years. The next three sections summarize the conclusions we draw from our simulations.

Inverted Bund Yield: Now inverted, the probability by October 11, 2024 is 72.2%

Many economists have concluded that a downward sloping yield curve is an important indicator of a future recession.A recent example is this paper Alex Domarsh and Lawrence H. Summers.

We measure the probability that the 10-year par bond yield is lower than the 2-year par bond yield in each scenario during the first 80 quarters of the simulation.(1) The chart below shows that the chance of a yield inversion reached 72.2% during the 91-day quarter ending October 11, 2024, compared with 65.3% last week.

3-month negative yield: 20.2% chance by December 5, 2053

The chart below depicts the probability of negative bill rates for all 3 months of the next 3 decades except the first 3 months. In the period ending November 28, 2053, the chance of negative interest rates started out close to zero but peaked at 20.2%, compared with 21.7% last week.

Calculate the default risk caused by interest rate maturity mismatch

In light of the interest rate risk-driven collapse of Silicon Valley Bank on March 10, 2023, we have added a table that also applies to mismatches in long-term bond purchases by banks, institutional investors, and individual investors. German Bunds Borrow Short-Term Funds. We assume that the only asset is a 10-year German Bund purchased at time zero with a par value of €100. We analyze default risk for four different ratios of initial market value of equity to market value of assets: 5%, 10%, 15% and 20%. For the banking example, we assume that the only liability category is deposits that can be withdrawn at face value at any time. In the case of institutional and retail investors, we assume the liability is essentially a margin borrowing/repurchase agreement with the potential for margin calls.

For all investors, the liability amount (95, 90, 85, or 80) represents the “strike price” of the put option held by the liability holder. When the value of assets falls below the value of liabilities, insolvency can result through margin calls, bank runs, or regulatory takeovers (in the case of the banking industry).

The chart below shows the 10-year cumulative probability of failure for each of 4 possible capital ratios when the asset maturity is 10 years. For the 5% scenario, the probability of default is 40.77%, up from 44.17% last week.

This default probability analysis is updated weekly based on the German bund yield simulation described in the next section. The calculation process is the same for any portfolio of assets that contains credit risk.

German Bund Yield Probability in the Next 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 bill yield in the Bund market in ten years is 0% to 1%, which is the same as last week. The chance of the 3-month yield falling within this range is 29.68%, compared with 26.39% a week ago. Note the downward shift in the second and third half-year periods. The most likely range for the 10-year German Bund yield is 1% to 2%, also unchanged from last week. The chance of being in this range is 24.41%, compared with 22.26% a week ago.

In a recent article on Seeking Alpha, we pointed out that predicting “heads” or “tails” when flipping a coin misses critical information. What experienced bettors need to know is that on average, for a fair coin, the chance of heads is 50%. For investors, the prediction that the next coin toss will be “heads” is effectively worthless because the outcome is purely random.

The same goes for interest rates.

In this section, we use a half-year time step to present the detailed probability distributions of the 3-month bill rate and the 10-year foreign debt yield.(2). We give the probability of each time step rate in the form of 1% “rate buckets”. The forecast for the return on the 3-month note is shown below:

3-month bill yield data:

SASDEU3m20240412.xlsx

Column 4 shows the probability that the 3-month note will yield between 1% and 2% in 2 years: 32.72. The probability that the 3-month yield will be negative within 2 years (which is often the case in Europe and Japan) is 9.35% plus 0.73% plus 0.03% plus 0.00% = 10.10% (difference due to rounding). Cells shaded blue represent a positive chance of occurrence, but the chance has been rounded to the nearest 0.01%. The shading scheme works as follows:

• 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% or 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 odds for the 10-year German Bund yield derived as part of the same simulation.

German ten-year government bond yield data:

SASDEU10y20240412.xlsx

Appendix: Bund rate of return simulation method

The probabilities are derived using the same method recommended by SAS Institute Inc. to its KRIS® and Kamakura Risk Manager® clients. A moderate technical explanation is given later in the appendix, but we first summarize it briefly.

Step one: we take Foreign debt closing yield curve as our starting point.

Step 2: We use the point on the yield curve that best explains the changes in the historical yield curve. We notice in the chart below that the span of foreign debt yields (in terms of interest rate levels and maturities) is only 40.69% of the historical experience of 14 countries:

In order to achieve the highest degree of realism for forward-looking simulations, the use of international databases is crucial. Using daily government bond yield data for 14 countries from 1962 to March 31, 2024, we concluded that 12 “factors” drive nearly all changes in government bond yields. The countries on which the analysis is based include Australia, Canada, France, Germany, Italy, Japan and New Zealand. Russia, Singapore, Spain, Sweden, Thailand, United Kingdom and United States of America. Data from Russia is not included after January 2022.

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

Step 4: Using these measured volatilities, we generate 100,000 random shocks at each time step and derive the final yield curve.

Step 5: We “validate” the model to ensure that the simulation accurately prices the starting Bund curve and is as historically consistent as possible. The method for doing this is described below.

Step 6: We take all 100,000 simulated yield curves and calculate the probability that the yield falls in each 1% “bucket” shown on the chart.

Do nominal yields accurately reflect expected future inflation?

A recent article we published on Seeking Alpha showed that, on average, investors buying long-term bonds almost always perform better than rolling over short-term U.S. Treasuries. This means that market participants usually, but not always, accurately predict future inflation and add a risk premium based on that prediction. The study will be updated in the coming weeks using the 14-country data set.

technical details

The daily government bond yields of the above 14 countries form the basic historical data for the number of factors and their volatility in the fitted yield curve. Bund historical information provided by Deutsche Bundesbank. The use of the international bond data increases the number of observations to more than 106,000 and provides a more complete experience of high and negative interest rates than using the Bund data set alone.

The modeling process is published in important Paper By David Heath, Robert Jarrow and Andrew Morton, 1992:

The arbitrage-free foreign exchange rate simulation is based on this famous paper by Amin and Jarrow:

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 is built.

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

Footnote:

(1) After the first 20 years of the simulation, the 10-year yield cannot be derived from the original 30-year yield structure.

(2) The actual simulation used a time step of 91 days, spanning a time horizon of 30 years.

Editor’s note: This article covers one or more micro-cap stocks. Please be aware of the risks associated with these stocks.