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.

Inverse leveraged funds: The destructive effect of sucker rallies

Summary

- One can make money shorting the market using inverse leveraged funds.

- Inverse leveraged funds are not for buy-and-hold investors.

- They are risky bets, which can lead to significant gains or losses.

- One key source of risk are upward rallies. This is demonstrated through spreadsheet-based simulations.

The performance of two inverse leveraged funds

The graph below shows the performance of two popular inverse leveraged funds () during a period of a little less than 20 days in December of 2018. They are available as exchange-traded funds (ETFs). One is the ProShares UltraPro Short S&P500 (SPXU), which tends to replicate the daily performance of the S&P 500 times -3. For example, if the S&P 500 drops 1 percent in one day, the fund goes up 3 percent. The other fund on the graph is the Direxion Daily Small Cap Bear 3X ETF (TZA), which tends to replicate the daily performance of the Russell 2000 index times -3.

I owned shares of these two funds during the time period shown. As you can see from the graph, if you invested in these funds during the period shown, your investment in SPXU would have gone up 31.41 percent. The investment in TZA would have gone up 44.99 percent. This is a period of time in which the S&P 500 had gone down 8.9 percent, and the Russell 2000 had gone down 11.9 percent. So, the SPXU and TZA performed even better than expected during the period. Due to daily compounding, they provided returns over a period of a little less than 20 days that were a bit better than the daily returns; i.e., more than 3 times the drops in the reference indexes.

How one would expect things to go

The screen snapshot below is for a spreadsheet-based simulation that shows how one could expect an investment in an inverse leveraged fund to perform during a period where the S&P 500 is losing value, but with ups and downs. The cells highlighted in yellow contain the settings of the simulation, which are: (a) the initial value invested; (b) the multiplier for the inverse fund; (c) the CBOE Volatility Index (VIX), which represents the expected percentage range of movement in the S&P 500 over the following year; and (d) the bottom range for the percentage variation in the S&P 500.

The “Day % variation” is the simulated daily percentage variation in the S&P 500, calculated based on the VIX value, which was set at 50. This value of VIX suggests a highly volatile market. The “Range (top)” value is calculated based on that daily percentage variation and on the “Range (bottom)” value. Both bottom and top range values define the range of daily variation, in percentage terms, for the S&P 500. Note that the daily variation has a negative bias. This is reflected in the values under “Day % gain”, which tend to lean toward the negative end of the range.

Overall, the S&P 500 goes down 6.61 percent over a period of 20 trading days, with moves up and down throughout that period. As you can see, we are trying to be realistic in our simulation. Neither market indexes nor individual stocks go down or up in a perfectly linear fashion. At the far right we see what happens with the inverse leveraged fund. The overall cumulative percentage gain ends up being 22.08 percent. This would probably be a positive surprise for an investor. This gain is higher than 19.83 percent (3 times 6.61), which one could expect based on the daily multiplier.

The destructive effect of “sucker” rallies

The problem is that often one sees an upward rally during periods where the S&P 500 is losing value. This is the case as well with other indexes and even individual stocks during bear markets. The screen snapshot below is for a simulation where the S&P 500 is losing value over a period of 20 days, but with two 5 percent upward rallies during that period (cells highlighted in yellow). Overall, the S&P 500 goes down one half of a percent over the period. The inverse leveraged fund, instead of going up, also goes down by 4.06 percent.

In this scenario the fund has performed worse than expected. Based on the daily performance of the fund, an investor could have expected a small positive return of about 0.15 percent. The reason for the unexpected poor performance is the counter-compounding effect that the two daily 15 percent drops have on the invested value. Those two daily drops correspond to the two daily 5 percent gains in the S&P 500.

So, you can make money shorting the market using inverse leveraged funds, but the probability that you will be successful doing so is small. This is due to three main reasons: (a) the stock market goes up much more often than it goes down; (b) even during periods when the stock market is going down, there are upward rallies; and (c) once the market moves from bear to bull, it typically stays like that for a while, which can completely wipe out the original investment due to reverse compounding.

Inverse leveraged funds are not for buy-and-hold investors. They are risky bets, which can lead to significant gains or losses. On the positive side, an investor will not lose more than the initial investment with these funds. This could happen if the investor tried to replicate the performance of the fund by shorting an index ETF or trading options borrowing from a margin account.

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.