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.

Long treasuries as no expiration puts on the S&P 500

The table below shows the variation in the price of the Vanguard Long-Term Treasury Index Fund ETF (VGLT) from May 2019 to April 2020, which was a period where the Fed reduced its federal funds rate from 2.39% to 0.05%. The S&P 500 crashed during this period.

As you can see, an investment in the VGLT early in that period would have appreciated about 31% at the end of the period. The VGLT is one of the lowest cost ETFs investing in long treasuries. This would have made purchasing VGLT shares analogous to buying “no expiration puts” on the S&P 500, with an extra advantage – the VGLT shares paid an interest.

The video linked below provides a brief discussion on these a few other related issues. Disclosure: the author owns VGLT shares at the time of this writing.

PE-based valuation of companies: A five-minute strategy

The table below shows the simulation-based fair value of the price-to-earnings (PE) and price-to-earnings-to-growth (PEG) ratios associated with various annual earnings growth rates. It uses an approach discussed in this blog (). The lowest growth rate shown is minus 50 percent, which would refer to a company whose net profits are going down by 50 percent every year. The highest growth rate shown is 100 percent, for a company whose net profits are doubling every year.

Generally speaking, a PE of 12 is considered indicative of fair value, and so is a PEG of 1. As you can see, these are gross simplifications that would apply only to a company whose annual earnings growth rate is about 10 percent. By contrast, a company whose earnings are contracting at a 2 percent annual rate would be fairly valued with a PE of 6.51 and a PEG of -3.25. At the other end of the growth rate scale, a company whose earnings are growing at an annual 75 percent rate would be fairly valued with a PE of 260.47 and a PEG of 3.47.

As we can see, the relationship between the PE and PEG ratios is nonlinear. This is why valuations sometimes look odd to those thinking in terms of a PE of 12 and a PEG of 1. High growth companies, often in cutting-edge technology areas, may be fairly valued at PEs that look astronomical and PEGs that are significantly greater than 1. The video linked below discusses this in a bit more detail.

The yield curve uninversion is here

The figure below shows the graph of the 10y-3m Treasury yields for the period going from the early 1980s to 2025. The inversion in the 10y-3m graph is the best indication of an impending economic recession in the US, and that graph uninverts immediately prior to a recession.

As you can see, the uninversion of the 10y-3m Treasury yield curve is here, and universions always happen before recessions. Interestingly, this is happening at a time when many aspects of the US economy look strong. The video linked below provides a brief discussion on this a few other related issues.

How inflation widens the wealth gap

The figure below shows the pay of two individuals, L (lower pay) and H (higher pay). Their pay starts respectively at $50K and $100K in year 1, and is then adjusted by the official rate of inflation, until year 20. We assume two rates of inflation, 0.5% and 5%, which leads to the values on the left and right tables. We also assume that individual L has no savings (i.e., earns only enough to live paycheck by paycheck), and that individual H saves the difference and invests it in a financial instrument that pays the official rate of inflation (e.g., a specialized money market fund).

Looking at these gaps, one could conclude that the rate of inflation does not make any difference in either the pay or wealth gap between individuals L and H. H’s pay is twice L’s pay regardless of inflation rate. And the amount saved by H in year 20 at 5% inflation is worth the same as the amount saved in the same year at 0.5% inflation, in terms of purchasing power. These conclusions may make sense, until we consider two facts that are illustrated in the figure below from FRED, which shows the rate of inflation for IT products and services.

The first fact we should consider is that the rate of inflation is not the same for all items. We can see that, for IT products and services, the rate of inflation is negative most of the time in the graph. Given this, individual H can buy significantly more IT items in year 20 at 5% inflation, and certainly way more than individual L at 0.5% inflation. The second fact we should consider is that the rate of inflation becomes very negative near or during recessions (see left part of the graph, near 2008). This places individual H at an advantage at 5% inflation, because as prices go down, H’s higher absolute savings will buy more.

As you can see, the wealth gap widens more at higher inflation rates. It is noteworthy that more and more of people’s expenses, even large ones, are related to IT products and services. But inflation for these has been typically negative in modern times. So, someone whose pay is adjusted for inflation at a higher rate will be able to buy more and more of these products and services as time goes by. Moreover, that person will also be in a better position to take advantage of economic downturns that lead to sharp downward corrections in prices, which happen regularly. The video linked below provides a brief discussion on this a few other related issues.

How to beat the S&P 500 without much effort: A one-year moving average strategy

Summary

- One of the most successful strategies for long-term investment returns is to buy and hold a broad-coverage index fund.

- The SPY is an exchange-traded fund (ETF) that tracks the S&P 500, and is a good example of broad-coverage index fund.

- A simple strategy can be devised to obtain even better than buy-and-hold long-term returns, employing fast- and slow-moving averages.

- We explain and test a one-year moving average strategy that in the long term performs significantly better than buying and holding SPY.

The one-year moving average for SPY from 1995 to 2018

The graph below has been created with Yahoo Finance (). It shows the variation of the SPY exchange-traded fund (ETF) from 1995 to 2018 (in red), plus the one-year moving average during that period (in blue). The SPY tracks the S&P 500 index, and had a net expense ratio of 0.09% at the time of this writing. One of the advantages of index funds is that they have a low expense ratio compared with actively-managed mutual funds.

Note that there are two moving averages in the graph: (a) the SPY “share” price (or net asset value per share) at any given time, which is the fastest moving average possible for the fund; and (b) the SPY’s one-year moving average, which is a slow-moving simple average of the fund’s share prices. (see ).

Simple inspection would suggest that, after an initial purchase, one would do better than holding SPY by employing a simple two-step strategy: (1) sell when the SPY crosses below its one-year moving average; and (2) buy back when SPY crosses above its one-year moving average.

A test of the strategy

While on the graph the simple strategy above may look appealing, the strategy must be tested with real data and under realistic assumptions. The figure below shows part of a screen snapshot of a test of the strategy, with multiple trades on a spreadsheet. Each row of the spreadsheet corresponds to one trade. The first row corresponds to the initial buy. A conservative fee of US$ 40 per trade is assumed, in part to account for bid-ask spread losses.

The figure below shows the final rows of the simulation, the result of a comparison buy-and-hold baseline strategy, and the percentage difference. Starting with an investment of US$ 100,000 made in January 1, 1995, the simple one-year moving average strategy gets us to US$ $980,558 on January 1, 2018. The buy-and-hold baseline strategy gets us to US $611,714. That is, the simple one-year moving average strategy performs about 60 percent better.

The simulation disregards dividends and sweep account gains (whereby cash earns interest). At the time of this writing, one could easily get money market yields in sweep accounts that were comparable in value to the SPY dividend.

Is the 365 days used for the moving average optimal? Probably not, but our simulation suggests that this number is effective at limiting false positives while at the same time capturing major drops of the index (e.g., those in the two recessions in the period considered). False positives would be much more frequent with a faster moving average, such as a 50-day moving average. If too frequent, false positives can significantly increase trading-related losses, to the point of negating the benefit of the strategy.