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.

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.

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.

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.

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.

The big difference between today and the 1980s: Valuations

The figure below shows two main graphs. The graph at the top shows the Fed funds rate from 1978 to 1987, approximately the period in which Paul Volcker served as Chair of the Federal Reserve. Rate hikes preceded the 1980 recession. Rates were raised again around 1981, then reduced, and then raised again; leading to the 1981-1982 recession.

The graph at the bottom shows the U.S. 10 Year Treasury yield, the CPI inflation rate (left scale), and the value of the S&P 500 index (right scale). Note that the U.S. 10 Year Treasury yield generally followed the Fed funds rate in the period, and that both were high while CPI inflation was still within approximately two-thirds of its previous peak. Interestingly, the S&P 500 was mostly flat during this period of major turmoil.

Could one conclude that the Fed’s current hiking cycle to combat inflation may have a similar outcome – i.e., a period where the S&P 500 is mostly range-bound? While it is possible that the answer to this question is “yes”, there is a big difference between today and the 1980s, namely valuations. The figures below show the valuations in the 1980s and now.

As you can see, valuations in the 1980s during the two recessions were largely below 10, whether we look at the S&P 500 PE ratio or the corresponding inflation-adjusted Shiller PE10 ratio. Today they are slightly above 20 (PE ratio) and 27 (PE10 ratio). The video linked below discusses these and related issues, as well as some recent developments.

A simulation-based valuation of the S&P 500: February 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 4.70% from the previous year, and the 10-year U.S. Treasury yield is at 3.73%. The numbers on the right refer to a less positive scenario: S&P 500 earnings are up by 4.70%, and the 10-year U.S. Treasury yield is at 4.30%.

The second scenario takes us to a fair price for the S&P 500 of 2,537.50, which is 47.34% 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: January 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 rather benign scenario: S&P 500 earnings in 2023 are up by 4.70% from the previous year, and the 10-year U.S. Treasury yield is at 3.49%. The numbers on the right refer to a more likely scenario: S&P 500 earnings are up by 4.70%, and the 10-year U.S. Treasury yield is at 4.22%.

The second scenario takes us to a fair price for the S&P 500 of 2,667.12, which is 44.65% 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 options.

A simulation-based valuation of the S&P 500: December 2022

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 rather benign scenario: S&P 500 earnings in 2022 are up by 5.60% from the previous year, and the 10-year U.S. Treasury yield is at 3.75%. The numbers on the right refer to a more likely scenario: S&P 500 earnings are up by 3.10%, and the 10-year U.S. Treasury yield is at 4.00%.

The second scenario takes us to a fair price for the S&P 500 of 2,644.39, which is 45.12% 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 options.

A simulation-based valuation of the S&P 500: October 2022

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 rather benign scenario: S&P 500 earnings in 2022 are up by 10% from the previous year, and the 10-year U.S. Treasury yield is at 3.00%. The numbers on the right refer to a more likely scenario: S&P 500 earnings are up by 5%, and the 10-year U.S. Treasury yield is at 4.00%.

The second scenario takes us to a fair price for the S&P 500 of 2,693.12, which is 44.11% 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 options.

A simulation-based valuation of the S&P 500: August 2022

A simulation-based valuation of the S&P 500: July 2022

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 rather benign scenario: S&P 500 earnings in 2022 are up by 10% from the previous year, and the 10-year U.S. Treasury yield is at 2.50%. The numbers on the right refer to a more likely scenario: S&P 500 earnings are down by 10%, and the 10-year U.S. Treasury yield is at 3.50%.

The second scenario takes us to a fair price for the S&P 500 of 2,638.16, which is 45.25% down from the most recent high. A sobering thought, given the rally that we are in right now, which many believe to be nothing more than another bear market rally.

Interest rates and PE ratio expansion: S&P 500 going above 4100 before the end of 2020?

Summary

- Most professional investors see price/earnings (PE) ratios as inversely proportional to interest rates.

- Mathematically, this would be expressed as: PE = k / IR.

- Assuming that the interest rate on 10-year Treasuries could rise to 1%, and the k multiplier to rise to the pre-COVID level of 0.39, the expected S&P 500 PE ratio would then be 38.66.

- This would bring the S&P 500 up to 4,148. Still, not as expensive, in PE ratio terms, as in either the 2000s dot-com bubble or the Great Recession.

Interest rates and PE ratios

Most professional investors, including the late Benjamin Graham (), see PE ratios as inversely proportional to interest rates for Treasuries. Mathematically, this would be expressed as follows, where PE = the PE ratio of an equity security, IR = a relevant interest rate, and k = a multiplier.

PE = k / IR

There are a couple of key reasons for this relationship. One is that Treasuries become less attractive as an investment when interest rates go down. Since the Treasuries market is very large, a little over $21 trillion at the time of this writing, even a fraction of it moving to equities would push their PE ratios up significant.

Another key reason for the relationship above is that investing in Treasuries when interest rates are low becomes risky in terms of principal preservation. Treasury prices are inversely related to the interest they pay, or their yields. When yields are very low, the tendency is for them to go up.

Interest rates on 10-year Treasuries

The figure below shows the interest rates for the 10-year Treasury notes from January 2007 to July 2020. Those rates, which influence a number of other consumer-relevant rates (e.g., those for mortgages), go from 4.76% to 0.55% during the period.

While the interest rates have been going down over the years, they went up significantly during the recovery from the Great Recession. The same may happen during the recovery from the COVID recession. A move from 0.55% to 1% would be significant.

S&P 500 PE ratios

The figure below shows the PE ratios for the S&P 500 from January 2007 to July 2020. Note that the PE ratio for July 2020 is nowhere near the peak during the Great Recession.

The k multipliers

Finally, the figure below shows the k multipliers for the relationship between the S&P 500 PE ratios and interest rates on 10-year Treasuries from January 2007 to July 2020. An all-time low was reached for the multiplier in July 2020.

In a low interest rate environment, a high k multiplier would typically be associated with a high PE ratio. The multiplier increase, if it happens, should lag the interest rate reduction. Investors need time to be convinced that interest rates will remain subdued. 

S&P 500 above 4,100 soon?

Assuming that the interest rate on 10-year Treasuries could rise to 1%, and the k multiplier to rise to the pre-COVID level of 0.39 (which is below its historical average), the expected S&P 500 PE ratio would then be 38.66. This would bring the S&P 500 up to 4,148. Still, not as expensive, in PE ratio terms, as in either the 2000s dot-com bubble or the Great Recession.

This PE ratio expansion for the S&P 500 is already happening at the time of this writing, with the S&P 500 hitting an all-time high. Our main point in this post is that, if interest rates on Treasuries remain low, we may see more of that - even with bankruptcies among small businesses, significant  unemployment, and high volatility (including downward corrections).

How could the March-June 2020 stock market rally have happened if $1T moved to the sidelines?

Summary

- As the rally in the S&P 500 happened, approximately $1T of money moved to the “sidelines”; that is, into money market funds.

- Of that $1T, about 20% was from retail investors and 80% from institutional investors.

- This is not what we have seen in previous recessions. Normally when money moves to the sidelines the S&P 500 goes down.

- One could argue that the money that is on the sidelines would be coming in to take advantage of pullbacks, as the new money that came in earlier is taken out to fuel consumption. Some of these pullbacks could be severe.

The March-June 2020 rally in the S&P 500

The figure below shows the rally in the S&P 500 during the March-June 2020 period. The index has gone from approximately 2,237 to 3,055; up about 36%.

We used the charting feature of Yahoo Finance (). The slow-moving line is the 52-day moving average.

About $1T moved to the sidelines

As the rally in the S&P 500 happened, approximately $1T of money moved to the “sidelines”; that is, into money market funds. This is illustrated by the figure below, with charts from FRED (). Of that $1T, about 20% was from retail investors and 80% from institutional investors.

The top chart shows the growth in money market funds from retail investors. For example, if an individual investor with an account on E-Trade (i.e., a “retail” investor) sells a stock position, that money typically will go into a sweep account tied to a money market fund. The bottom chart shows the growth in money market funds from institutional investors.

So, both retail and institutional investors moved a lot of money to the sidelines. This is not what we have seen in previous recessions. Normally when money moves to the sidelines the S&P 500 goes down.

Many people would interpret this as money leaving the financial markets, in absolute terms. This is not what happened. For each stock sale there must be a corresponding purchase. If investors on the sidelines are buying, and sellers are moving to the sidelines, there should be no significant change the in the total amount held by money market funds.

If investors are selling to raise cash, and stock prices are going up, there must be “new” money coming into the stock market at a higher rate than the rate at which investors are selling.

The Fed’s balance sheet grew by $2T during the rally

As you can see in the figure below, the Fed’s balance sheet grew by about $2T during the rally. It grew $3T from February. That is partly what fueled the rally.

This new money that has been “created” by the Fed takes some time to make its way into the hands of people who can buy stocks. So, what we are seeing here is the beginning of something interesting; a rather rare occurrence.

What does this mean? The bull case

One could argue that the money that is on the sidelines would be coming in to take advantage of pullbacks, as the new money that came in earlier is taken out to fuel consumption. Some of these pullbacks could be severe, because newcomers may be parking money in stocks as they would with a bank account - with money that they need to pay for recurring expenses.

This should propel the stock market higher after each pullback. The increase in consumption caused by the money coming out of the stock market may give the impression that the economy is recovering by itself. The ensuing optimism would push stocks even higher.

But the impression that the economy is recovering would be a mirage, at least early on. This highly volatile bull market would be largely driven by the liquidity injected by the Fed. The volatility would be triggered by mixed headlines; e.g., consumer confidence is up, but so is the government deficit.

We could see something like the S&P 500 reaching 4,000 amid a wave of bankruptcies! Not all companies will go bankrupt, of course. For each local “Supa Burger” that goes bankrupt, there will be a bit more market share for the local McDonald’s and Burger King competitors.

Active investing may shine brighter than passive (index funds) in this scenario. Active investors have to think about a number of issues, such as how failures in one industry can benefit leaders in another. As a Hertz goes bankrupt, Uber may benefit. (Disclosure: the author owns shares of UBER at the time of this writing; and also of MCD and QSR, for the references above.)

What does this mean? The bear case

It is hard to see a scenario where this new money printed by the Fed, the portion available for stock purchases, will all go to the sidelines due to pessimism. Money market accounts are paying very little, because Treasury yields are so low. Investors are compelled to put the money somewhere. The stock market is one of the only options.

It is not hard to see a scenario where inflation will grow due to an increase in money supply, even as GDP contracts. Inflation is bad for fixed-income investing, making Treasuries even less attractive, but inflation is not necessarily bad for stock investing. At least not while inflation is growing but is still relatively low (e.g., low single digits).

This creates a positive feedback loop for stocks!

However, this is a bad scenario if maintained for too long, which could bring about severe economic strain, and another major drop in the stock market. High inflation would eventually prompt the Fed to increase interest rates, without a robust economy to compensate for that tightening if GDP is contracting.

But this bad scenario may take a few years to materialize.

Can the stock market collapse without a recession?

Summary

- A “recession” is usually defined as two consecutive quarters of gross domestic product (GDP) contraction.

- Stock market collapses are generally believed to be associated with economic recessions.

- We show that this is not the case, based on data from Australia.

- Even though Australia has experienced uninterrupted GDP growth from 1992 to 2018, its stock market dropped by around 67 percent from late 2007 to early 2009.

The case of Australia

The picture below shows two charts prepared with data from Tradingeconomics.com (). The top chart shows the growth in gross domestic product (GDP) in Australia from 1992 to 2018. The bottom chart plots the S&P/ASX 200 index during the same period. This index is maintained by Standard & Poor's and is seen as the benchmark for Australian equity performance; much like the S&P 500 in the U.S.A.

Note that the index fell by approximately 67 percent from late 2007 to early 2009. This stock market collapse was more severe than the one experienced in the U.S.A. around the same time.

The period from late 2007 to early 2009 broadly coincides with the period widely known as the Great Recession ().

Yet, there was no economic recession in Australia during that period. What happened was a decrease in the rate of GDP growth; from between 4 and 5 percent, down to between 1 and 2 percent.

If GDP growth slows down, earnings growth is also likely to slow down

When GDP growth decreases but does not turn negative, GDP continues growing – but at a slower pace. The growth in company earnings tends to also decrease during such times, even though earnings may continue growing.

Because of various amplification factors – such as impaired consumer confidence, aggressive competition, and higher interest expenses – earnings growth may decrease much more than GDP growth.

A decrease in GDP growth from 4 to 2 percent may lead to a much wider decrease in average earnings growth for a subset of the market (e.g., from 20 to 2 percent), causing a widespread panic about valuations for the entire market.

PE-based valuation

Let us illustrate this through a plausible scenario. An investment of $10,000 will generate a 100 percent return (i.e., approximately double in size) in 9 years if made in shares of a company whose price-earnings (PE) ratio is 26, and whose yearly earnings growth is 20 percent. If yearly earnings growth drops to 2 percent, which is essentially no real growth at a 2 percent rate of inflation, the same investment will double in size in 9 years only if the PE ratio drops down to 12.

In the scenario above, a PE of 26 would have to go down to 12 for a comparable PE-based valuation of the company to be achieved. That is, at a PE of 26, the company would suddenly look very expensive.

The PE drop from 26 to 12 is of approximately 54 percent. That would typically translate into a big short-term decrease in market capitalization, and a big loss to investors, even with mitigating actions such as share buybacks and dividends.

Next S&P 500 bottom? Maybe 1468

Summary

- The S&P 500 index (SP500) has been recently dropping.

- The Shiller (PE10) has also been dropping.

- We can estimate the bottom of the SP500 based on historical PE10 values.

- This estimated SP500 bottom is 1468.94.

Faster moving averages chase slower ones

The picture below shows two charts prepared with Yahoo Finance (). The top chart shows the SP500 together with its 5-month moving average. The bottom chart also includes the 10-month moving average.

This picture illustrates one import point: faster moving averages usually “chase” slower ones. This is, of course, a figure of speech.

The fastest moving average of all is the index itself; e.g., the 1-month moving average of the index measured on a 1-month basis.

The corresponding 5-month moving average is slower, and the 10-month is even slower.

The slowest moving average of all is the average (or mean) of the index over its entire history.

History tells us that, as the gap between the fastest and slowest moving averages increases, so does the likelihood that they will converge with a “vengeance” – at a wide angle.

The Shiller PE ratio

The Shiller PE ratio (PE10) () is based on average inflation-adjusted earnings from the previous 10 years. As such it removes the “contamination” of inflation and other factors that artificially influence the denominator of the standard PE ratio. This is why we use it here.

In October 2018 the PE10 reached 33.01, the second highest peak in its history. Since then it has been going down, presumably chasing a moving average. If it were to bottom, history suggests that it would go down to around the slowest moving average: its historical average of 16.58 (approximately, in October 2018).

The SP500 bottom

The PE10 going from 33.01 to 16.58 would be a drop of 49.77 percent.

The SP500 was 2924.59 in October 2018. A drop of 49.77 percent would take it to 1468.94.