Is the US stock market still over-priced? Part 1.
The Empiricist approach: enlightenment from numerical evidence
Above: George Berkeley, presumably contemplating the matter not at hand
"I think, therefore I am."
So wrote René Descartes, the famous French philosopher, who thought and thus (presumably) existed between 1596 and 1650.
Descartes was a prominent thinker in the Rationalist school of philosophy. Other notable rationalists included Baruch Spinoza (1632-1677) and Gottfried Leibnitz (1646-1716).
In short - which is a tough thing when it comes to philosophy - rationalism is "the theory that reason rather than experience is the foundation of certainty in knowledge".
(That's according to my physical, printed copy of the Concise Oxford English Dictionary, which is immune to internet editing or censorship.)
Put another way, rationalists reach conclusions by reasoned deduction.
Spinoza was a particularly hardcore proponent of this approach. I studied a bit of philosophy in my first year at university, and still recoil in horror at the memory of trying to wade through his "Ethics" (which you can find here). It starts off by laying out a list of "Definitions", "Axioms" and "Propositions", from which he ultimately derived his conclusions.
[Long story short, and to save you the pain of actually reading Spinoza, his big idea was "Deus sive natura", which translates as "God or nature". In other words, he was a pantheist, believing that god (the creator) and nature (the creation) are the same thing.
Presumably, Spinoza would have been an environmentalist these days. Or, given his proclivity for complexity, perhaps designing impenetrable, high-fee structured derivative products at an investment bank.]
During the same era, another school of philosophy emerged, known as Empiricism. Notable empiricists included Francis Bacon (1561-1626), John Locke (1632-1704), George Berkeley (1685-1753) and David Hume (1711-1776).
Empiricism is defined by the same dictionary as "the theory that all knowledge is derived from sense-experience". Put another way, for an Empiricist there's less rationalist pontificating and more of a "suck-it-and-see" approach.
This led Berkeley to come up with his own "big idea" - the "superfluity of matter". In other words, he concluded that - based on his observable experience - physical matter was superfluous, and may not exist. Sort of like living in the Matrix - or perhaps the Metaverse.
Maybe Berkeley was onto an interesting idea, albeit not that practical. After all, if real things don't exist, then what's the point of worrying about our pension investments?
Anyway, in short, Rationalists relied on pure reason and Empiricists relied on experienced evidence.
The philosophers of both schools were important influences during what's known as the Age of Enlightenment, which ran from about 1688 to 1789. Without it , or something similar, we'd probably all still be peasant farmers with short life expectancies (apart from a few lucky sovereigns and aristocrats).
That period was a necessary precursor to the Industrial Revolutions and subsequent material progress that we’re lucky enough to enjoy today (even if it’s far from perfect).
But what's all this got to do with investing? More specifically, what's it got to do with the valuation of the US stock market, the main subject this article?
Well, I'm going to use something vaguely aligned to these two philosophical approaches to answer the following question:
Is the US stock market still overpriced?
Today I'll start with the empiricists approach. That is, looking at observable evidence. In the next instalment, I'll take a more rationalist approach, based on reason (with the help of some financial theory).
Once we put them together, there's a good chance that we'll get some pretty big clues. So let’s begin.
First of all, it's worth remembering that US stocks fell significantly last year, losing 18.1%, even with dividend income included. That followed a big boom over the prior three years, and in fact ever since 2009, after the crash caused by the Global Financial Crisis. It culminated in a bubble that peaked in December 2021.
The question is whether there are further significant falls to come. After all, multi-year bear (falling) markets aren't exactly unheard of. During the 30 years since I was a fresh-faced graduate trainee at a London investment bank, they've occurred twice: from 2000 to 2002 and 2007 to 2009 (see the following chart).
S&P 500 index - past 30 years
Source: Macrotrends
Of course, the US stock market is hugely important to investors.
Credit Suisse, an investment bank, recently released its annual Global Investment Returns Yearbook 2023, which is an authoritative source of historical market data.
According to the report, the US stock market made up 58% of global stock market value at the end of 2022. That dwarfs second-placed Japan (6%) and the third-placed UK (4%).
Incidentally, the report also contains important historical return data. US stocks made a total (nominal) compound profit of 9.5% a year since 1900. In real terms, after adjusting for inflation, it comes to 6.4% a year.
Keep those empirical figures in mind, as I'll come back to them in part 2.
(By the way, the comparable figures for bonds, in the form of 10-year US treasuries, are 4.7% a year nominal and 1.7% a year real returns. This is a reminder that stocks are a much better place to invest over the long run, for capital preservation and profit.)
The US stock market is gigantic. The chances are, if your investment choices have been left to financial advisors, then you'll have a large amount of money riding on US stocks, much of it via index funds. And a great many independent investors will also have a big allocation to the US market.
Which means that knowing whether US stocks are pricey is a big deal for most investors.
To get to the bottom of this question, I'll take a look at the S&P 500 index, which is the bulk of the US stock market by value. Specifically, I'll look at the following things:
The trend in earnings-per-share (EPS).
The trailing price-to-earnings ratio (P/E), which divides the index level by the EPS reported in the past year.
The cyclically-adjusted P/E ratio or CAPE (also known as the Shiller P/E). It uses the last 10 years of earnings, adjusts them for inflation, and takes an average of the results. This new "E" aims to smooth out the effects of economic cycles, thus giving a valuation ratio that's similar in concept to the P/E, but not as volatile from year to year.
The price-to-sales ratio (P/S), which compares the index level to the top-line revenues of the companies in the index.
Earnings-per-share (EPS)
US corporate EPS has been on a tear in recent years. But, like most things in markets, it tends to mean revert at some point. Earnings can't grow at fast rates forever, and certainly not at rates that exceed overall economic growth. Otherwise, in due course, companies would earn more than GDP, which is clearly impossible.
The following is a chart of annual EPS going all the way back to 1871. It uses a logarithmic vertical scale, which means that the same percentage change up or down always looks the same size. Put another way, if EPS increased by exactly the same percentage each year then the chart would show a straight line, rising from the bottom left to the top right.
S&P 500 EPS (log scale)
Source: multpl
The final figure of $187 only runs up to September 2022 in this data set, presumably because not all companies have reported their end of year results yet.
Even so, using some unscientific eyeballing, and imagining the straight trend line if EPS grew at a constant rate, I'd say that it looks well above that trend. My guess is that the trend figure is somewhere around $150, which is 20% lower.
To get another view, I found another chart. This one is on a linear vertical scale, meaning that if earnings grew by the same percentage every year it would appear as a smooth exponential curve. This time the data is adjusted for inflation, meaning expressed in today’s money.
Since the trend curves upwards over time, it provides a reminder of how corporate earnings beat inflation in the long run, which is a crucial part of how stocks deliver real profits to investors (as well as the stream of growing dividend payments).
You can find that chart here. Once again, the latest data looks well above trend, and the trend level appears once more to be around $150, or maybe a tad higher.
My conclusion is that recent EPS is meaningfully above trend and likely to mean-revert to the lower trend level at some point.
This is especially true if a recession sets in this year, which is highly likely to cause corporate earnings to fall as sales drop. Also, US interest rates are still rising, which will add to companies' interest expenses when they have to renegotiate debts or borrow more funds.
Trailing price-to-earnings ratio (P/E)
Over the long run, since 1871, US stocks have had a mean (average) P/E ratio of 16 and a median (mid-point) P/E ratio of 14.9.
(Note: I believe the median is more meaningful here, since P/E ratios can rocket when earnings collapse, even if the market drops sharply. This happened in the wake of the Global Financial Crisis, as the "E" fell much more than the "P". Such outlier readings tend to skew the mean / average to a higher level, whereas the median / mid-point is relatively unaffected.)
The current P/E reading is 21.4. That would need to fall by 30% just to reach the historical median level.
You can see the historical chart here.
Cyclically-adjusted P/E ratio (CAPE, or Shiller P/E)
Remember, the CAPE smooths out short-term swings in earnings. As such it's a good reference point for where things stand relative to likely long-term earnings power through economic cycles, or something approaching that.
Since 1881, the mean CAPE ratio has been 17 and the median is 15.9.
Currently it stands at 29.1, after falling 25% from a recent bubble peak of 38.6 in November 2021, as the market fell. However, it would need to drop another 42% to match the historical mean and 55% to match the median level.
You can see the historical CAPE chart here. Something to note is that it remains well above the already-elevated level prior to the global financial crisis, which started in 2007.
Price-to-sales ratio (P/S)
Finally, let's look a price-to-sales. The data here only goes back as far December 2000, which was part way through the bursting of the technology bubble that peaked in March 2000.
Even though the timescale is shorter, the data is still interesting.
The current P/S reading is 2.34, which is well above the 1.77 level of December 2000. This is perhaps relevant, since US stocks dropped a lot last year from bubble levels. But, given the still-elevated P/E and CAPE ratios, there may be more of a fall to come. Just as happened between 2000 and 2002, as that bubble burst.
Since December 2000, the P/S had an average (mean) of 1.68 and (mid-point) median of 1.54. Put another way, the market would have to fall by 28% to reach an average P/S level, and by 34% to reach the historical mid-point.
You can see the historical P/S chart here.
Summary and conclusion
I've taken a look at some empirical evidence to help us answer the question of whether the US stock market is still overpriced.
All measures assessed look like they are inflated when compared with the historical record.
1.   EPS may need to drop around 20% to get back on trend.
2.   P/E would need to drop 30% to reach its historical median level.
3.   CAPE would have to fall 42% to reach its historical mean and 55% to reach the median level.
4.   P/S would have to drop 34% to reach its median (albeit recorded over a much shorter period).
Incidentally, note what would happen if both EPS and P/E dropped as outlined above. That would imply a market fall of 44% (due to EPS at 80% of the current level multiplied by P/E at 70% of the current level).
That's very similar to the sort of fall required for the CAPE to get close to its historical mean or median levels.
My conclusion is that there's plenty of empirical evidence that the US stock market remains overpriced, despite falling sharply last year.
This does not necessarily mean that US stocks are about to plunge off a cliff again. Although that's certainly a significant possibility, especially if corporate earnings disappoint during 2023.
But even if US stocks don't plunge, it's not great news for investors. The implication of high market prices today is lower future returns, over the long run.
I'll return to that topic within Part 2: The Rationalist approach.
(Stand by for a bit of maths. But I promise it to explain it as clearly as I can.)
In the meantime, who better to have something to say about philosophers than Monty Python?
By which I mean, The Philosopher's Song and the Philosophy football match (Germany vs. Greece). Would Descartes or Berkeley approve? (I doubt it.)
Please remember to write to me with your comments or questions (email address below). It's always good to hear from you.
Until next time,
Rob Marstrand
ofwealth@substack.com
The editorial content of OfWealth is for general information only and does not constitute investment advice. It is not intended to be relied upon by individual readers in making (or not making) specific investment decisions. Appropriate independent advice should be obtained before making any such decision.