Yield curve inversions, un-inversions, and US recessions

The figure below (source: Federal Reserve Bank of St. Louis) displays the spread between the 10-year and 3-month U.S. Treasury yields from the early 1980s through 2025. This yield spread is a closely watched indicator in financial markets, as it reflects investor expectations about future economic conditions. A yield curve inversion—occurring when the spread falls below zero, meaning short-term interest rates exceed long-term rates—has historically been associated with upcoming recessions. Economists and policymakers often regard this inversion as a reliable leading indicator, given its strong track record in signaling economic downturns with a lead time of several months to over a year. As shown in the graph, each sustained inversion over the past four decades has typically preceded a recession, underscoring its continued relevance in macroeconomic forecasting.

It is important to note that the yield curve typically un-inverts, or returns to a positive slope, before a recession actually begins. In the graph, recessions are represented by the shaded areas, and a close examination reveals that the un-inversion often precedes the onset of these downturns. However, the time gap between the un-inversion and the start of a recession can vary significantly, ranging from a few months to over a year. This variability highlights the complexity of using the yield curve as a precise timing tool, even though it remains a valuable early warning signal. For a brief discussion on this pattern, along with a few other related topics, please refer to the video linked below.

A simulation-based valuation of the S&P 500: April 2025

The figure below shows two simulation-based valuations of the S&P 500. They assume a fair price-to-earnings (PE) ratio for the S&P 500 that is the inverse of half of the 10-year U.S. Treasury yield. The price (at the top) is the most recent top value of the S&P 500.

The numbers on the left consider a more benign scenario: S&P 500 earnings in 2025 are up by 13% from the previous year, and the 10-year U.S. Treasury yield is at 3.61%. The numbers on the right refer to a less positive scenario: S&P 500 earnings are up by 6%, and the 10-year U.S. Treasury yield is at 4.17%.

The second scenario takes us to a fair price for the S&P 500 of 2,673.79, which is 56.48% down from the most recent high. The video linked below discusses these simulations, some of the most recent values for the simulation inputs, and a few other things.

How far are we from a recession according to the Sahm Rule in August 2024?

The figure below shows the adjusted three-month moving average of the national unemployment rate in the U.S. for the past 12 months, with the minimum and current values indicated at the bottom-left and top-right areas. This is known as the Sahm Recession Indicator, which signals the start of a recession when the it rises by 0.50 percentage points or more relative to its minimum value in the previous 12 months. The Sahm Recession Indicator has been named after economist Claudia Sahm.

If the adjusted three-month moving average of the national unemployment rate, or the the Sahm Recession Indicator, continues rising at the same rate, we should either be in recession right now in August 2024, or enter a recession within the next few months – according to the Sahm Rule, which is based on the Indicator. The video linked below provides a brief discussion on this a few other related issues.

A simulation-based valuation of the S&P 500: July 2024

The figure below shows two simulation-based valuations of the S&P 500. They assume a fair price-to-earnings (PE) ratio for the S&P 500 that is the inverse of half of the 10-year U.S. Treasury yield. The price (at the top) is the most recent top value of the S&P 500.

The numbers on the left consider a more benign scenario: S&P 500 earnings in 2024 are up by 12.10% from the previous year, and the 10-year U.S. Treasury yield is at 4.28%. The numbers on the right refer to a less positive scenario: S&P 500 earnings are up by 9.90%, and the 10-year U.S. Treasury yield is at 4.28%.

The second scenario takes us to a fair price for the S&P 500 of 2,843.17, which is 49.37% down from the most recent high. The video linked below discusses these simulations, some of the most recent values for the simulation inputs, and a few other things.

Where is the yield curve un-inversion?

The figures below show the graphs of the 10y-3m Treasury yields and 10y-2y Treasury yields. The inversion in the 10y-3m graph is the best indication of an impending recession, and that graph typically un-inverts immediately prior to a recession.

While the first graph does not show an un-inversion, the second (i.e., 10y-2y) does. And the second tends to predict the first, because the 2y yields tend to predict the 3m yields. That is where the yield curve un-inversion is, at the moment. The video linked below discusses this in a bit more detail.

Fortune favors the bold, and so does misfortune

The figure below illustrates a truth that most investors know, but tend to forget. Taking high levels of risk in the financial markets increases the tail probabilities, which are associated with massive gains and massive losses. The lure of high-risk decisions and related investment instruments often acts as a sort of tax on the statistically illiterate.

But investors can reduce the chances that they will end up at the left tail end of the probability distribution. When it comes to stock investing, paying attention to two events can help. The first is the percentage difference between 10-year and 3-month U.S. Treasury yields falling below zero, because a U.S. recession tends to occur within the next 18 months.

The second is the stock market, measured by an index such as the S&P 500, reaching a double-top within that that period of 18 months after the percentage difference between 10-year and 3-month U.S. Treasury yields falls below zero. This combination is extremely bearish. And this is where we are about now. The video linked below discusses this in a bit more detail.

A simulation-based valuation of the S&P 500: October 2023

The figure below shows two simulation-based valuations of the S&P 500. They assume a fair price-to-earnings (PE) ratio for the S&P 500 that is the inverse of half of the 10-year U.S. Treasury yield. The price (at the top) is the most recent top value of the S&P 500.

The numbers on the left consider a more benign scenario: S&P 500 earnings in 2023 are up by 3.20% from the previous year, and the 10-year U.S. Treasury yield is at 4.91%. The numbers on the right refer to a less positive scenario: S&P 500 earnings are up by 1.10%, and the 10-year U.S. Treasury yield is at 5.47%.

The second scenario takes us to a fair price for the S&P 500 of 2,015.07, which is 58.18% down from the most recent high. The video linked below discusses these simulations, some of the most recent values for the simulation inputs, and a few other things.

A simulation-based valuation of the S&P 500: September 2023

The figure below shows two simulation-based valuations of the S&P 500. They assume a fair price-to-earnings (PE) ratio for the S&P 500 that is the inverse of half of the 10-year U.S. Treasury yield. The price (at the top) is the most recent top value of the S&P 500.

The numbers on the left consider a more benign scenario: S&P 500 earnings in 2023 are up by 3.20% from the previous year, and the 10-year U.S. Treasury yield is at 4.62%. The numbers on the right refer to a less positive scenario: S&P 500 earnings are up by 1.20%, and the 10-year U.S. Treasury yield is at 5.48%.

The second scenario takes us to a fair price for the S&P 500 of 2,012.28, which is 58.24% down from the most recent high. The video linked below discusses these simulations, some of the most recent values for the simulation inputs, and a few other things.

How many times until a coincidence becomes a pattern? The case of yield curve inversions preceding recessions and the magical number 7

Let us say that a coincidence involving two events, where one seems to predict the other, happens a number of times. How many times until it can be considered not only a coincidence, but a statistically significant pattern? We propose a framework to answer this question. Using the framework, we find that the number of times required is 7. We illustrate the practical application of our framework in the context of a very important phenomenon: When the percentage difference between 10-year and 3-month U.S. Treasury yields falls below zero, a U.S. recession appears to occur within the next 18 months.

All of this is laid out in much more detail in the article linked below. In this article, we have established the minimum number of times required for the inversion-recession phenomenon to be deemed more than a coincidence, and rather a statistically significant pattern. That number is 7. Therefore, given that since 1970 we have observed 8 instances of the inversion-recession phenomenon, we can conclude that this not a coincidence, and that it is in fact a statistically significant pattern.

https://www.tandfonline.com/doi/full/10.1080/03610926.2023.2232908

The video below complements this post, by briefly addressing some of the issues discussed in the post.

Do equity indices bottom before recessions?

An interesting debate taking place right now (November 2022) relates to whether the equities market has already priced in a recession, and is now moving up into what could be a new bull market. This could mean that the forward-looking equities market, represented by equity indices (e.g., Wilshire 5000, S&P 500), has bottomed before a recession.

I have conducted a rather extensive review of various equity indices to see if there is a historical precedent, prior to November 2022, for an index that has bottomed before a recession. I could not find any. The figure below (source: Federal Reserve Bank of St. Louis) shows the Wilshire 5000, which covers all American stocks.

The figure shows two areas where the index bottomed after a recession and during a recession. These are only illustrations of a broader pattern - I could find no instance in which a bottom occurred before a recession, in any index (including the S&P 500). So, do equity indices bottom before recessions? Apparently not. The video linked below discusses this and other cases in more detail.