Is the US stock market still over-priced? Part 2.
The Rationalist approach: there's value in valuing things
René Descartes, arch Rationalist, contemplating his stock portfolio
Today I'll return to an important question for all investors: is the US stock market overpriced?
I'm doing that with a bit of help from old philosophers.
There were two main schools of philosophy from the Age of Enlightenment, which ran from about 1688 to 1789. Those were Rationalism and Empiricism.
As a reminder, here are some dictionary definitions:
Rationalism: the theory that reason rather than experience is the foundation of certainty in knowledge.
Empiricism: the theory that all knowledge is derived from sense-experience.
Put another way, Rationalism aims to reach conclusions by reasoned deduction, whereas Empiricism relies on experienced evidence.
In Part 1 (see here) I looked at the empirical evidence. In short, using four observable measures, US stocks appear to remain pricey in relation to the historical track record. That's despite the S&P 500 index falling quite sharply during 2022.
The conclusion was that the market would need to drop in the order of 40% to get back to its longer term trend.
Yes, really.
Importantly, that doesn't mean that it will actually fall off a cliff in the short-term. But it does mean that the risk of such an outcome remains reasonably elevated.
What's more, a high current valuation suppresses the likely future returns for investors, when taking a long-term view (between now and, say, 10+ years into the future).
This is what I'll home in on today more closely, by way of a more Rationalist approach. That's with the help of some standard financial theory and what I believe to be reasonable assumptions.
On which note... math / maths alert!
(Depending on whether you prefer the US or UK abbreviation of mathematics.)
Using formulas is an important part of proper financial analysis. It's unavoidable, but I'll aim to keep it as simple as possible. In any case, for those that are allergic to number crunching, it's the conclusions that really matter (you can jump to the end if you wish).
Also, apologies in advance. This is a bit longer than usual. But if I cut too much out then it won't cover the ground adequately.
Some valuation basics
Valuation of any investment hinges on two central elements.
The first is the amount and timings of cash income expected to be paid to the investor over the life of the investment.
For real estate, this is rental income net of costs. For bonds, it's future coupon interest and repayment of the principal (the amount originally borrowed by the issuer) at maturity. For stocks, it's the stream of future cash distributions per share, in the form of dividends per share (DPS).
(Stock analysis should also take account of stock buybacks, but explaining those is convoluted. A subject for another day.)
Obviously, when it comes to stocks in particular, one of the challenges is projecting those future payments, which are themselves derived from future company earnings.
Even companies with very high current growth and zero dividends are expected to eventually mature, have slower growth, and start to pay out cash. Whereas mature, slower-growing companies will already pay substantial dividends, but tend to be more predictable. This is a large part of the reason why high-growth companies are riskier short-term investments, since there is plenty of scope for them to disappoint.
Secondly, aside from the expected future cash flows from an investment, the other crucial element is the required return of the investors, expressed as an average annual percentage rate of return.
This is variously referred to as the hurdle rate, discount rate or cost of capital. In the specific case of stocks (a.k.a. equities), it's known as the cost of equity.
Higher risk investments should require a higher return to compensate. For this reason, stock investors tend to want a much higher return than bond investors, since stocks are less predictable than bonds. There's also variation between different types of stocks, again according to perceived risk.
It's prudent to want a higher eventual return from a loss-making start-up, that has high promised (but far from guaranteed) growth. On the other hand, investors will tend to accept a lower rate of return from a mature company, with a stable business that already gushes cash (such as multinational producers of branded food products or washing powder).
As for the valuation process, it involves estimating future cash flows, and discounting them using the required rate of return. The discounting process expresses each of those cash flows in terms of today's money, giving each a "present value" (PV). Add up all the individual PVs and you get the total net present value (NPV), which is an estimation of the value today of the individual future cash that will be generated by the investment.
If you haven't come across this discounted cash flow (DCF) concept before, I know it can be confusing. So I'll give a simple example to help explain.
If you were given a choice between receiving $100 today or the promise of receiving $100 a year from now, which would you prefer?
The answer should be to get the money today, given that a bird in the hand is worth two in the bush. And that you could use the money straight away, instead of having to wait.
But let's say you think a return of 5% a year would make up for receiving the money in a year's time. That should take account of things like the loss of buying power of each dollar over a year (inflation), and how much you trust the person making the promise to pay you.
On that basis, we can place a value today on that future $100. It would be $95.24, being $100 divided by 105%. That's the price you should be prepared to pay today to buy that promise of $100 in future, at a 5% annual return.
If the $100 was due in two years we can do a similar thing. In that case the value today would be $90.70, being 100 divided twice by 105%. So that's what you should pay today for the promise of $100 in two years. Note how the cash amount two years out is divided by 105% twice, being once for each intervening year.
Of course, most investments have much more complex streams of cash flows than a single bullet payment at one point in future. But the same principles apply. Each individual cash flow should be divided once by 100% plus the required return (5% in the example), for each year between now and when you'll get it.
Add up the resulting present values (future amounts, discounted for the required return over each time period) and you get a valuation, or estimate of the fair price that you should pay.
In certain situations, the above principles can be simplified into handy formulae that get us there quickly, without having to calculate the present value of each individual cash flow.
The simplest valuation formula of them all is the perpetuity. A perpetuity is an investment that pays exactly the same amount of cash to the investor every year. The investment never matures and the cash payments never grow.
This is the formula for a perpetuity: P = c / r
Where P= price, c = annual cash flow and r = required annual rate of return (discount rate).
So if the perpetuity paid a fixed $10 a year forever, and you wanted a 5% annual return on investment, you should be prepared to pay $200 to own that income stream ($10 divided by 5%). Note that in the long-run, over more than 20 years, you will actually receive back more than $200.
However, in many cases, the expected future cash payments from an investment might be expected to grow over time. For example, net rental income from a building, after deducting maintenance costs, property taxes and any other costs. Over the long haul, that's probably going to grow roughly in line with general consumer price inflation, or something such as average household incomes.
Assuming the payments still go on forever (in perpetuity), but now with growth baked in, the investment would be what's known as a growth perpetuity.
So how do we factor the growth into the valuation? Fortunately, we can stand on the shoulders of giants. The formula has already been worked out.
This is the formula to value a growth perpetuity: P = c / (r - g)
Where P = price, c = initial annual cash flow, r = required rate of return and g = annual growth rate of cash flows.
(If you really want to get into the weeds of how this formula is derived, take a look at this video or this document.)
Extending the previous example, let's say the first payment is still $10, the required return is still 5% a year, and that the payments grow at 2% a year (instead of being fixed). The appropriate price would now be $333.33, which is $10 divided by 3% (being 5% less 2%).
Note how the valuation is now much higher than the $200 for a fixed-payment (non-growth) perpetuity. That's because the denominator (lower part) of the fraction in the formula is smaller, since it has changed from "r" to "r minus g".
This should make intuitive sense. Owning a stream of growing cash flows should be worth more than owning a stream of fixed cash flows.
Also note that the higher the growth rate, the higher the valuation. If we change g to 3%, then the value comes out at $500. That's $10 divided by 2% (5% required return less 3% growth rate).
With that bit of financial wizardry out of the way, let's consider how it can be applied to stocks.
Valuing a stock index as a growing perpetuity
Individual companies come and go, as do the constituents of a stock index. Some thrive for decades, or even centuries. Others have their moment in the sun and then wither away over time.
But, for practical purposes, we can assume that a stock index itself will be around forever, or at least exist so far into the future that the valuation difference is minimal. Companies will drop out of the index, but new ones will be added when they are. The only exceptions tend to be when countries are at the wrong end of a major war, or when governments seize private assets.
For example, investors lost everything in both Russia and China in the aftermath of their respective Communist revolutions, when private property was banned. My assumption is that this isn't going to happen in the US any time soon. In any case, if it does, we'll all have much bigger problems to worry about than our investments.
Thus, we can value the US stock market as a growth perpetuity.
The underlying cash flows paid to investors will vary from year to year, due to the usual economic cycles and what share of company profits are paid out to investors. But, over the very long run, we can make pretty good estimates of likely outcomes, and use those averages.
In terms of the long run growth rate of profits (g), and thus growth of cash payments to shareholders (c), we should assume it's about the same as expected economic growth. That's in nominal terms, before adjusting for inflation (real terms).
After all, as a group, companies can't grow faster than the economy forever. Otherwise they'd soon become bigger than the whole economy, which is obviously impossible.
When it comes to the required return (r) for investors, in financial parlance this is known as the "cost of equity" when applied to stocks.
There's much theorising about how much the cost of equity should be. But as good a place to start as any is to look at the historical record. In other words, to look at what stock investors actually made in the past, over the very long haul.
In Part 1, using figures from the Credit Suisse Global Investment Returns Yearbook 2023, I wrote the following:
"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."
Given that information, a good starting point for the cost of equity (required return or discount rate) is 9.5% a year.
Also, using those figures, we can work out that inflation averaged 2.9% a year between 1900 and 2022 (since 109.5% divided by 106.4% equals 102.9%). I think that's a fair, long-term inflation assumption for the future as well (even though current inflation rates are higher).
Part of that total return of 9.5% a year is the cash income from dividends paid to investors. Using another data set, I've estimated that the average dividend yield came to around 4% over the same time period. Which means that capital gains (price rises) averaged out at 5.5% a year between 1900 and 2022.
Finally, we need to modify the growth perpetuity formula a little to move from calculating a fair price (P) to calculating a fair price-to-earnings ratio (P/E). In this case for the S&P 500 index.
We do this by dividing both sides of the formula by "E", the index earnings per share. Then we get this:
P/E = (c / E) / (r - g)
Remember, c is the starting cash flow per share received by shareholders. Put another way, it's the dividend per share.
(Technically speaking, it also includes an element of stock buybacks, which have increasingly replaced dividends since the 1980s. I've taken that into account also, but the details would take too long to explain here.)
c / E represents the cash distributions per share divided by earnings per share (EPS). This is what's known as the pay-out ratio. It's the percentage of profits that companies distribute in cash form, via dividends and/or stock buybacks. Therefore...
P/E = Pay-out ratio / (r - g)
I estimate that the average pay-out ratio for US stocks has been about 68% since 1900, and is running at a similar level recently.
In any case, we can't be certain about precise outcomes for the pay-out ratio or the future growth rate of GDP, and thus US corporate profits. But the data shows the following:
Long-term returns on US stocks have been 9.5% a year, or 6.4% in real terms (after adjusting for inflation).
About 5.5% a year came from capital gains, driven by growth in earnings-per-share (EPS).
About 4% a year came from cash distributions (mainly dividends).
The pay-out ratio averaged about 68%.
It's fair to assume that future inflation, over the long run, will be similar to the average since 1900 of about 2.9% a year (or 3% among friends).
Applying the P/E formula above, we can then see what the appropriate P/E level should be under various scenarios that are close to those figures.
Note that the current P/E ratio for the S&P 500 is 21.0, and for the period 1871 to now the mean (average) P/E was 16.0 and median (mid-point) was 14.9.
The following table shows a range of scenarios needed to achieve a 9.5% a year long-term return, with the pay-out ratio set at 50%, 60% or 70% and future profit growth set at 4%, 5% or 6%.
P/E ratio scenarios assuming a required rate of return of 9.5% a year
Source: OfWealth
I've highlighted the P/E figure of 15.6 in bold, since it lies between the long-term, historical mean and median P/E levels. To achieve that requires 5% a year future growth and a 70% pay-out ratio.
It isn't a coincidence that those figures are also close to the historical averages (5.5% and 68% respectively).
Note also how the highest P/E ratio shown (20.0, in the bottom right of the table) requires 6% growth and a 70% pay-out ratio. Those are both above the historical average levels, yet a P/E of 20 is still below the current level of 21.
It's unlikely that such a high pay-out / high growth combination could be achieved over a long stretch of time. That's not just because companies can't grow faster than nominal GDP over the very long run. It's also because a higher pay-out ratio means that companies are keeping less of their profits to invest in future growth.
On a linked question, is it even reasonable to think that future US economic growth can be as fast as it was since 1900? I doubt it, since an important element of economic growth is population growth, and that's slowing down.
The US population grew from 76 million in the year 1900 to 332 million in 2022, which works out as an average compound growth rate of 1.21% a year. But the population forecast for 2040 is about 379 million, giving a future growth rate of a little over 0.74% a year.
Put another way, the part of economic growth driven by population expansion should be about half a percentage point lower in future than during the 1900 to 2022 period. In turn, it's reasonable to assume that the long-term trajectory of corporate profit growth will also be lower by a similar amount.
This adds further weight to the argument that the right-hand side of the table above, with a growth rate of 6%, is unlikely to happen. A long-term growth rate of 5% or below is a more reasonable expectation.
We can also turn the formula around, and work out what sort of average annual return would justify the current P/E ratio of 21. This is summarised in the following table, using the same scenarios for pay-out ratios and growth rates.
Implied return scenarios using a current P/E of 21
Source: OfWealth
The implication here is that, starting from the current P/E level, investors in the S&P 500 index should expect lower future returns than the long-run historical average of 9.5% a year. That's especially true if we rule out the right-hand column as being an unlikely scenario (higher profit growth than in the past, despite slower US population growth).
Total average returns, including capital gains and dividends, of between 7% and 8% a year seem more likely.
If we assume inflation averages about 3% a year in future, that points to real (above-inflation) returns of 4% to 5% a year.
Summary and conclusions
I've now looked at US stocks using both an Empiricist's approach (comparing observable evidence against the historical track record) and a Rationalist's approach (using financial theory to value the index, under different scenarios).
To get back to historical valuation averages, Part 1 pointed to a necessary drop of around 40%, and perhaps more.
To achieve the same sort of returns in future that long-term investors have enjoyed in the past, today's Part 2 points to a drop in the region of about a quarter (P/E from 21 to around 15.6), and perhaps more.
In summary, both approaches point to the same conclusion: US stocks remain pricey, despite last year's falls.
How did we get to this position? I suspect there's a whole younger generation of professional investors that's become too used to ultra-easy and cheap money, meaning low interest rates. They've ignored, forgotten - or never learned - the principles of valuation, such as those set out above.
Eventually, things will have to come back into balance.
Long-term investors in the S&P 500 index will most likely find this manifests itself in one of two main ways:
Another significant market fall this year or soon thereafter. This isn't too hard to imagine given rising interest rates and recessionary business conditions, which could hit corporate earnings for a time. It would then take a number of years for the market to climb back again, as earnings resumed growth. The net effect would be relatively weak long-term investor profits.
No significant market drop, but relatively poor long-term returns from this starting point. This is not least since a relatively high current P/E implies a lower cash distribution yield for investors (from dividends and stock buybacks). To clarify, if we flip P/E on its head it becomes E/P, or earnings divided by price, which is also known as the earnings yield (when expressed as a percentage). A higher P/E gives a lower earnings yield, and cash distributions have to come from those earnings over time.
As you can see, I'm not predicting an imminent US stock market crash, although I wouldn't be surprised to see one. It's a mugs' game to make predictions about the short-term direction of markets.
I'm just saying that US stocks as a whole still look overpriced, based on both observable evidence and financial theory.
Put another way, the US is a stock pickers' market. For investors to have a hope of making decent returns, they most likely need to be selective, rather than owning an index-tracking fund.
Sorry it's been longer than usual, and I know it's been number heavy. But I hope you agree that this huge market deserves some time to pick over.
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.