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.

Is a PE ratio of 12 attractive? A simulation-based view of company valuation

Summary

- The price/earnings (PE) ratio is one of the most widely used measures of company valuation.

- Through a simulation, we show that if growth is expected to slow down, then PE ratios are likely to go down, possibly in a dramatic fashion.

- For example, if earnings are expected to grow only 2% per year, then an attractive PE ratio would be 7.95. This is much lower than the PE ratio of 12, which is generally seen as attractive.

- For a PE ratio of 12 to be attractive, the expected earnings growth has to be at least 10.18% per year.

The PE ratio

The price/earnings (PE) ratio is one of the most widely used measures of company valuation (). It is calculated by dividing a company's share price by its earnings per share. Essentially, the PE ratio reflects a company’s value, as seen by the stock market, divided by its net profits.

What is an attractive PE ratio?

From early 2009 to early 2019 the SPY exchange-traded fund (ETF) has gone up in value approximately 222.72%. The SPY is an index fund, which tracks the S&P 500 index (, ). It had a relatively low net expense ratio of 0.09% at the time of this writing. The SPY has also paid dividends during this period. In early 2019 the dividend was a little less than 2%.

If you bought US$ 10,000 in shares of a company, and had a return comparable to buying and holding the SPY in the 2009-2019 period above, the shares would be valued at approximately US$ 32,272 after 10 years. The spreadsheet section in the figure below shows a simulation where earnings are assumed to grow 2% per year over a period of 20 years. As you can see, the value of US$ 32,272 is reached at year 10. The EP percentages go up because they assume that the share prices remain constant; in reality those prices would go up, keeping the PE ratio somewhat constant. The first EP percentage is the reverse of the PE ratio.

At the top left you see the PE ratio associated with this return. It is a fairly low 7.95. This is much lower than the PE of 12, which is often seen as attractive by investors. That is, if you want to purchase shares of a company whose earnings are expected to grow only 2% per year, and obtain a return for the next 10 years that is comparable to the S&P 500 in the 2009-2019 period, then you should buy shares in a company with a PE ratio of 7.95.

The same simulation-based approach can be used to find out what growth rate would be needed for a PE ratio of 12 to be attractive. This is summarized in the spreadsheet section in the figure below. For a PE ratio of 12 to be attractive, the expected earnings growth has to be at least 10.18% per year.

The PEG ratio

Note that the PEG ratio () in the first spreadsheet section, also shown at the top left, is 3.97. The PEG ratio is the PE ratio divided by the expected annual earnings growth. This PEG ratio is much higher than 1, which is generally perceived as an attractive PEG ratio. And still, the return on the investment in 10 years will no doubt be attractive (the S&P 500 had a remarkable run in the 2009-2019 period), as long as the PE ratio is a low 7.95.

In the second spreadsheet section, the PEG ratio is 1.179, which is much closer to 1. This highlights one interesting property of the relationship between the PEG and the PE ratios - it is a nonlinear relationship. The closer the earnings growth gets to zero, the more warped it becomes, pushing the PEG ratio higher and away from 1 (assuming that the PE ratio is positive).

When growth slows down, the stock market may collapse, even without a recession

The above discussion highlights the fact that, if growth is expected to slow down, then PE ratios are also likely to go down. PE ratios may go down dramatically, leading to a severe stock market correction, even without a recession ().

In fact, as we can see from the discussion above, a severe correction may happen even without earnings going down! In other words, earnings may still keep growing, but at such a slow pace that the market is compelled to adjust PE ratios downward to match the lowered return expectations.

Can 10-year compound annual S&P 500 returns help predict market crashes?

As someone interested in applying data analytics techniques to finance and economics, I tend to look for leading indicators that contribute new insights when compared to existing ones.

It also helps if they are not obvious, and go somewhat against consensus; e.g., in interviews on media covering financial markets issues, frequently experts express the opinion that recent market gains do not influence future performance.

If we put this opinion to the test against data, we find that the opposite is what usually happens, as you can see from the graph below, which shows annualized 10-year compound changes in the S&P 500.

Dividends are not considered in this depiction. The graph is based on monthly data points from January 1910 to March 2022, where the annualized changes are calculated for each month as follows.

SP10(T) = ( SP(T) – SP(T-10y) ) ^ (1/10) – 1

In this equation we have:

SP10(T): the annualized 10-year compound change in the S&P 500 at a given point in time (T).

SP(T): the value of the S&P 500 at a given point in time (T). For this illustration, we used the average value of the S&P 500 for each month.

SP(T-10y): the value of the S&P 500 exactly 10 years prior to the time T.

This is a fairly easy calculation, which relies on a single variable. The graph seems to show that periods in which the SP10 moves quickly above 10% typically precede market crashes.

As a leading indicator (not a cause), the SP10 may not be precise enough to be used alone. Nevertheless, it can be used together with other indicators (e.g., Shiller’s PE10 ratio) in a more complete predictive model.

The crash of 1987 happened as the yield curve was steepening

Summary

- It is generally considered a bad sign if the 10y-3mo or the 10y-2y differences in yields fall.

- This is particularly true if the differences in yields fall below zero (a yield curve inversion).

- However, the crash of 1987 happened as the yield curve was steepening, not flattening or inverting.

A crash without an inversion

When talk of a market crash intensifies, many people look for clues from the US Federal debt market to assess the probability of a crash happening soon. There is a widespread belief that the main clues come from Treasury yield differences, or the yields paid by US Federal debt instruments with different maturities.

It is a bad sign if the 10y-3mo or the 10y-2y differences in yields fall below zero (a yield curve inversion). However, as you can see on the figure below, the 1987 stock market crash happened around the time the 10y-3mo and 10y-2y yields peaked.

We show both the 10y-3mo and the 10y-2y differences in yields because some market experts have more confidence in the 10y-3mo signals, whereas others prefer those given by the 10y-2y differences. The reality seems to be that both the 10y-3mo and the 10y-2y differences in yields provide the same overall signals.

But the inversion preceded the recession

Having said that, the 1987 crash was followed by another smaller crash, related to the 1990 recession. This recession was indeed preceded by a yield curve inversion.

So, one could say that the yield curve inversion worked yet again, as it has done repeatedly, as a leading indicator of a recession.

Conclusion

The yield curve inversion phenomenon is a very good predictor of economic recessions, arguably one of the best leading indicators available to investors. And market crashes usually happen around recessions. But a market crash may happen without an economic recession.

In fact, the crash of 1987 happened as the yield curve was steepening, which is essentially the opposite of flattening – and arguably a bullish signal.

Fed rate cuts and the two recent recessions

Summary

- The last two recessions were preceded by Fed rate cuts.

- Stock market reactions were somewhat different in the two recessions.

- In the early 2000s recession (March 2001 to November 2001) the stock market was already going down by the time the Fed started cutting rates, and continued going down.

- In the Great Recession (December 2007 to June 2009) the stock market reaction to the Fed cutting rates was more optimistic, with a three-month rally that saw the S&P 500 go up by a little less than 10 percent.

- After that initial rally, the stock market dropped by more than 50 percent (in early 2009), with several “sucker rallies” in between.

- Generally speaking, a Fed rate cut at a period when the signs of an upcoming recession are pilling up should be a source of concern for stock market investors.

The last two recessions were preceded by Fed rate cuts

The graphs below are for the period from January 1999 to June 2019, and were generated using Yahoo Finance and the US Federal Reserve Economic Data (FRED) (, ). The graph at the top shows the weekly variation in the S&P 500 index together with its 50-month simple moving average. The graph at the bottom shows the effective federal funds rate.

As you can see, the last two recessions were preceded by Fed rate cuts. The dashed lines suggest that stock market reactions were somewhat different in the two recessions. In the early 2000s recession (March 2001 to November 2001) the stock market was already going down by the time the Fed started cutting rates, and continued going down.

In the Great Recession (December 2007 to June 2009) the stock market reaction to the Fed cutting rates was more optimistic, with a three-month approximately 10 percent rally in the S&P 500. After that, the stock market dropped more than 50 percent, with several “sucker rallies” () in between. Those rallies are common in recessions, including the early 2000s recession.

We want the debt that we do not need

Since there have been many previous recessions before the last two, some business commentators refer back to several of those other recessions to predict the future, and to frame Fed rate cuts in a positive light. Lower rates stimulate economic activity by making credit more easily and widely available, which could in theory prevent a recession.

The problem is that it is human nature to buy more than we can afford, or need, if we can fund those purchases through debt. Most people will want to buy a more expensive car on credit than they can afford either paying cash or with higher interest rates; the latter increase monthly payments. The same goes for homes.

This is all about perceived status, and extends to corporations. Other things being equal, a CEO of a larger and more dominant company will have a higher status among peer CEOs. As a result, companies tend to take on more debt, if it is easily available at low rates, to fund acquisitions or “buy” market share prior to recessions. Conservative use of funds goes out the window if credit is easily available.

As noted above, many business commentators refer back to recessions other than the last two to predict the future. The problem is that the farther back you go, the more different the socio-economic environments tend to be from today. This is why it is probably a good idea to look at what happened more recently when trying to extrapolate to now and the near future.

A Fed rate cut prior to a recession is not a good sign

Should a Fed rate cut at a period when the signs of an upcoming recession are pilling up be a source of concern for stock market investors? Any way you look at it, the answer is “yes”.

Human nature does not change that easily, and greed will not be checked unless things go really bad. When things go really bad, behavior changes. Individuals and organizations become more conservative regarding their finances.

Very likely a Fed rate cut prior to a recession will sustain or even exacerbate the types of behavior that are at the source of the recession.

Having said that, Fed rate cuts are important for the economic recovery and renewal that are normally seen after recessions.