In this series, we have been trying to figure out if there is an equilibrium relationship between stock prices and earnings and, if so, where that equilibrium level lies and how we might make use of it to anticipate future returns. My thesis has been that there likely is an equilibrium level, that we have deviated from that level over the last 30 years or so, and that we will likely see significantly lower returns over the next two decades. Moreover, that period of significantly lower returns has likely already begun.
There is one equilibrium about which we can be pretty sure, represented in Figure 1.
‘P’ represents stock prices, ‘E’ represents earnings per share, and ‘x’ is number of years in the future.
This says that the present PE ratio (P/E) times the inverse of the future growth rate of earnings (E/Eₓ) times future capital gains (Pₓ/P) times the future earnings yield (Eₓ/Pₓ) must equal one.
Most of us are interested in the equation in Figure 2 below, derived from the first equation.
That is, we want to know what the first equation means for future changes in stock prices, especially since dividends have become less and less important over the last century. The Figure 2 equation says that future changes in the prices of stocks are a product of the present earnings yield times future earnings growth times the future PE ratio.
Although this series is not intended to provide a universal summary of all stock investment philosophies, I think some differences in various philosophies can be illustrated in the way they may focus on different aspects of this equation. The key value is ‘x’. If you are looking out 50 or 100 years and thinking about what stocks will do in the ‘long run’, you are likely to focus on earnings growth. Ratios between price and earnings may oscillate, but as (I believe) Peter Lynch said, ‘Long term, the correlation between price and earnings is 1’.
If you base your long-term expectations of future earnings growth on historical earnings growth, you are likely to be in ‘stocks for the long run’. PE ratios have been more or less horizontal while earnings have been vertical (see Chart 1). The best investment strategy would be to simply plow money into the market, with some adjustments for individual needs (e.g., retirement), and expect to catch some segment of long-term returns.
Chart 1. (Source: Robert Shiller data)
Apart from extrapolating from historical earnings growth, the other methods would be some sort of long-term analysis of future growth (based, for example, on demographics or inflation or some transformative technology) or an ideological commitment to futurism or American exceptionalism or, more pessimistically, Spenglerian decline. Certainly, the optimists have the easiest argument to make; after all, good things tend to happen over the long term no matter what happens in the history books (depressions, high inflation, low inflation, skyrocketing debt, wars won and lost, civil unrest, pandemics, Republicans, Democrats). The pessimists have to conjure up some underlying process that would produce some novel crisis that would reverse the trends of the last century, and they have to get the timing right. The pessimists could prove to be right but be off by a decade or a century or two.
In any case, if your investment horizon runs way off into the distance, you are apt to focus on the red in Figure 3 and discount the black.
Most of us do not have 100-year investment horizons, unfortunately. As ‘x’ gets smaller, the way these equations are viewed has to change. Movements in multiples (in this case, the price to earnings ratios) grow in importance, as do changes in rates of growth of earnings.
The PEG ratio, the ratio of price-to-earnings-to-earnings-growth, is one way to deal with this. The PEG ratio is the red portion of the left-hand side of the equation shown in Figure 4.
We can also write it like this:
As we described in previous installments, according to traditional treatments of the PEG ratio, G (measured as a CAGR of earnings growth) should meet or exceed PE (calculated arithmetically) in order for a given stock to be fairly valued, but the problem with this is that this standard is both arbitrary and high. There are very few instances of annualized earnings growth having exceeded PE over any span.
But, there is a logic in setting the standard so high for PEG. If you can find a company where future growth is so high that it meets the initial PE, that growth is very likely to negate any detrimental moves in the PE ratio. So, the patient gurus like Buffett, Bogle, Lynch, and others, using a variety of metrics, search for their diamonds in the rough in the hope of producing adequate returns.
Incidentally, these patient gurus often seem to have a faith in something like American exceptionalism. By this I mean a confidence that America is possessed of a unique economic dynamism and always ‘gets it right’ in the long run. Bogle said, for example, “If you hold the stock market, you will grow with America”, and Buffett said last year, “Never bet against America”. One can imagine that a mixture of nationalistic, progressive idealism and individual pragmatism could produce very high returns, especially if it is imbibed early in an American Century.
Another technique to counter the dangers of a mean reversion in valuations might be to find a handful of companies that have the potential for explosive - even astronomical - growth, then throw as much cash as possible at them with the hope of scoring at least one hit, thereby more than making up for the remaining failures. This was outlined in a recentish episode of the All-In Podcast where they discussed the problem (for individual enterprises) of “over-capitalization”.
And then, at the macro level, one might use Robert Shiller’s CAPE (Cyclically Adjusted PE, or P/E10) ratio, which effectively tries to time multi-decadal shifts in valuations.
This is expressed in the following equation.
The primary difference between CAPE and the other approaches is that ‘x’, here, has a negative value. Shiller uses a 10-year moving average of (real) historical earnings rather than subsequent earnings, so that x = -10. And then he uses CAPE to anticipate subsequent returns (-10 years + 20 years = +10 years).
In other words, the current earnings yield times the inverse of a historical growth rate (because Eₓ is the historical base value if ‘x’ is negative) produces (the inverse of) CAPE (i.e., P/Eₓ). CAPE could be said to point to high returns, then, especially when the earnings yield is high and earnings growth has been low. If, on the other hand, both PE and the current rate of earnings growth are very high, then CAPE would anticipate very low returns in the future.
Each of these approaches to the mathematical equilibrium expressed in Figure 1 makes certain trade-offs, and these trade-offs are more or less appropriate depending on the timescales involved and the assumptions underpinning them. All three of these approaches (‘earnings for the long run’, the PEG ratio, and CAPE) assume that PEs are mean-reverting, but they are not all equally dependent on this assumption.
‘Earnings for the long run’ is least dependent on fluctuations in PE. Even if PEs were at their historic lows rather than historic highs right now, stocks would still have risen 30x since the 1929 peak, twice the rate of consumer inflation. Over the very long term, if you can get the earnings story right, you will almost certainly get the stock returns right - so long as the relationship between price and earnings remains relatively stable. If, for example, the earnings yield were an outrageous and unprecedented 40% (putting PE at an arithmetic value of 2.5) right now, there would have been no real returns in stocks since 1929, apart from dividends. Even were something like that to occur, it would be hard to imagine it being permanent. Sooner or later, things would stabilize - presumably.
The traditional formulations of the PEG ratio, as we pointed out above, try to negate the problem of PE mean reversion by identifying instances of extraordinary growth, especially at the level of the individual company. At the level of the market index, however, this rarely works; over the last 150 years, the market has risen well above the levels suggested by the claim that a PEG ratio of 1 is fair value, as demonstrated in Part 3 and the chart below.
Chart 2. (Source: Shiller data)
In this series, we have tried something different. We have surveyed the behavior of the four factors in this equation and looked at the relationships between each of them, in search of clues as to what we might expect in the future.
Since the establishment of the Fed, as we have seen in earlier installments, PE ratios appear to be subject to 5-year trough-to-trough cycles, 12.5-year peak-to-peak cycles, and 30-year trough-to-trough cycles. Earnings growth rates, particularly since the establishment of the Fed, appear to be subject to 12.5-year trough-to-trough cycles, and earnings appear to boom, on average, 7.5 years from that trough; earnings growth also experiences peaks about every 30 years. PE ratios are also especially good at predicting 20-year earnings growth rates, especially when PE and unemployment are high and at 12.5-year intervals. Moreover, earnings growth also tends to correlate with the future earnings yield (that is, Eₓ/Pₓ, not the forward earnings yield, Eₓ/P).
The relationship between earnings growth and the earnings yield is perhaps the most fascinating relationship of all, particularly where ‘x’ is set at 7.5 years, as we discussed in Part 4. As we saw, there is quite a bit of overlap in the behavior of the earnings yield (as the inverse of the PE ratio) and the rate of earnings growth. That is, since the establishment of the Federal Reserve, they have both troughed about every 12.5 years, and they have also experienced peaks about every 30 years. Unsurprisingly, then, earnings growth and the earnings yield tend to be correlated with one another.
But the relationship is more complicated than that. Since the establishment of the Fed, bond yields, consumer inflation, and commodity inflation have tended to converge with the earnings yield (Chart 3). This is on top of a tendency for real commodity prices to correlate with the earnings yield perhaps as far back as the 18th Century (Charts 4, 5, and 6). Commodity inflation rates have tended to peak about every 30 years, since the establishment of the Fed, coinciding with the 30-year peaks in the earnings yield and earnings growth described above (Chart 7).
Chart 3. (Source: Shiller data)
Chart 4. (Sources: Please see my “Inflation and Yields” article for list of data sources)
Chart 5. (Sources: Please see “Inflation and Yields”)
Chart 6. (Sources: Shiller and own calculations from World Bank Pink Sheet)
Chart 7. (Sources: Shiller, World Bank Pink Sheet, and Fed)
Earnings growth is unique, however. During the troughs in between the 30-year peaks in the earnings and inflation, there have been one-off bursts in earnings growth. These bursts break the correlation earnings growth usually has with both yields and the rate of commodity inflation, and in these instances, the rate of earnings growth exceeds the level of the earnings yield. Thus, in 1929, the 7.5-year annualized rate of earnings growth was about 25% while the earnings yield was around 5%. About 87.5 years later (12.5 x 7 = 87.5), in 2016, the 7.5-year rate of earnings growth was about 40% per year while the yield was just under 5%. These breakdowns in the relationship between earnings growth and the earnings yield only occur near troughs in the yield (between 1871 and the 1918 peak, there was only one such breakdown) and have always had similar characteristics: a) a breakdown in the correlation, b) the rate of growth rising higher than the yield and inflation of all kinds, c) a subsequent collapse in growth back to the level of the earnings yield or even as low as commodity inflation, and d) 7-14 years of low nominal and real stock market returns. Recall from our outline of the CAPE ratio (Figure 7), that peaks in that ratio are a product of both high earnings growth and a high trailing PE, all then typically followed by 10 years of low returns.
To put this another way, the equilibrium of the equation in Figure 1 appears to be more than the product of its factors. When we multiply two of the factors - for example, PE and the inverse of G (i.e., the inverse of Eₓ/E) to form the PEG ratio, or the current rate of earnings growth and PE to form CAPE - we certainly increase our ability to model or anticipate stock price performance (Pₓ/P), because we are inexorably brought closer to the equilibrium value of 1, but we lose some of the information that is contained in looking at the way each factor relates to one another. The problem with this ‘information’ is that it is not perfectly reliable. Earnings and employment consistently collapsed every 12.5 years from as early as 1921, until 1996, when they boomed instead, and then resumed the pattern in 2008 and 2020. Every breakdown in the correlation between the earnings yield and earnings growth since 1871 has resulted in a more or less immediate peak in stock prices until 2017, after which stock prices continued to rise until the present. Whether or not the breakdown in that correlation is ‘correctly’ anticipating a crash by 2024 and low returns to 2030 remains to be seen.
There is also no way to be absolutely sure that the earnings yield acts as a limit on long-term inflation (including earnings growth) and yields. And, even if it does serve as a limit, we cannot be sure that it acts as a limit to the 7.5-year rate of growth and not some other rate, or that violations of such a limit will inevitably be followed by bear markets, just as we cannot be sure that CAPE or PEG will be as good at predicting 10-year returns as they have been over the last century, nor that one century of skyrocketing earnings will be followed by another. In the end, we rummage through history trying to piece together the past in such a way as to make sense, hopefully without upsetting our most cherished prejudices too much and hope that if we are wrong everybody else was wrong too by a percentage point or two more.
The conventional wisdom seems to be ‘stocks for the long run, but be mindful of valuations and mean reversions along the way; but don’t fight the Fed, yet inflation matters too, and watch real interest rates, and keep an eye on China, and also the debt ceiling, and of course don’t forget the coronavirus, but the metaverse/crypto/web3 might change everything…’. Investors then must weigh each of these differently at different times and frame a narrative that holds it all together. Successful investors like the ‘patient gurus’ above have historically pruned these considerations way back. They have focused on a few key patterns that, whether through skill or luck or a combination of the two, landed them on the right side of history for long enough to make their long-term returns outperform everyone else’s.
What if earnings are not destined to simply grow exponentially? What level of earnings growth is necessary to overcome a mean reversion? Is there a way to anticipate growth? When do mean reversions tend to occur? Under what conditions do they tend to occur? This series has attempted to answer some of these questions, primarily through looking at the historical relationship that PEG has with stock returns.
We found that the equilibrium relationship between the two has shifted over the last 30 years. Although the PEG ratio has not been that low (‘low’ implying that the market has been ‘cheap’ or ‘undervalued’), stock prices have risen quite impressively. In other words, stocks are rising at a rate higher than previous history (1871-1980) would have suggested.
From the equation at the center of this installment, we now know that the equilibrium relationship between the PEG ratio and returns is determined by the future PE ratio (Pₓ/Eₓ).
If the ratio over the remainder of the decade should remain roughly where it is now (something like 25), the equilibrium level of the PEG ratio will be where it has been since the end of the Cold War. If the PE ratio doesn’t materially change, the correlation between stock prices and earnings must approach 1.
What are the chances that PE will be roughly where it is today? As we discussed above, PE tends to trough every 30 years. The following chart shows how well PE correlates with itself over spans running from 0 to 720 months (60 years). Especially since 1914, the PE ratio tends to correlate at 360-month intervals (30 years) but inversely correlate at 240-month intervals (20 years) and at 600-month intervals (30 years + 20 years = 50 years).
Chart 8. (Source: Shiller)
Incidentally, readers may notice that at intervals at multiples of 90 months (7.5 years) and 150 months (12.5 years) (that is, 90, 150, 180, 270, 300 months…) the correlations seem to jump. I am not quite sure why, but it seems to be linked to the 7.5-year and 12.5-year patterns described above and in earlier installments.
Readers of previous installments might also recall that PE ratios were best at anticipating 20-year rates of earnings growth whereas this chart shows that PE is inversely correlated with 20-year future PEs. So, if PEs are high now, more likely than not, they will be low in 20 years’ time and earnings growth will be high. That would fit rather well with the notion that earnings growth tends to positively correlate with the earnings yield. In 2040, therefore, we might imagine that growth will have been high and PEs low.
In Part 4, we discussed how these 30-year patterns in the earnings yield, commodity prices, and consumer inflation appear to be neo-Kondratiev waves linked to Schumpeterian technology supercycles that intensified after the establishment of the Fed. The paleo-Kondratiev waves tended to peak every 50 or 60 years. The former also appears to be somewhat more oriented towards consumer durables (cars and radios in the 1920s, TVs in the 1950s, PCs in the 1980s, smartphones in the 2010s) than industrial goods (steam power, railroads) prior to the Fed.
In any case, under the Fed, the earnings yield has tended to peak every 30 years, with peaks seeming to have occurred circa 1920, 1950, 1980, and 2010, and thus 2040 would seem the likeliest time for the next peak, all else being equal. And because these peaks tend to coincide with higher levels of consumer and commodity inflation, stock returns both real and nominal tend to be lower. Even with a relatively weak supercyclical rise in the earnings yield in 2000-2010, stocks were flat from 2000 to 2014.
It is possible, however, that some vestige of the old 50-60 year Kondratiev waves remain. Consumer inflation and Treasury bond yields seem to have been more subdued in the 1940s and 2000s than they were in the 1910s and 2000s.
Chart 9. (Source: Shiller)
In any case, assuming an extension of these Fedworld patterns, yields appear to be most likely to rise in the 2030s. And earnings and inflation will likely help push them higher.
Let’s piece this together. First, as we saw in the previous installments and as suggested in the simple equations above, earnings must grow at a rate above some equilibrium level set by the initial PE ratio in order for stocks to rise or hold their current level. That is suggested by the history of the PEG ratio and its relationship with returns. Up until about 30 years ago, the PEG ratio appeared to have had a relatively stable equilibrium level which has since risen considerably.
What has changed the equilibrium level of PEG? In a word, the secular decline in yields and inflation. More precisely, a falling earnings yield (i.e., a rising PE), as spelled out in Figure 1.
But, there is a problem in the relationship between PE ratios and earnings growth. PE ratios - especially high PE ratios - historically tell us at least two things. First, long-term earnings growth (G) is likely to be high, and second, G will have to be high if stocks are going to rise.
But, G tends to be suppressed by a low future earnings yield (that is, a high future PE). When G exceeds the future earnings yield, this results in very high returns (e.g., 1920s, 1990s, 2010s) and very high CAPE ratios, but this has been consistently followed by a collapse in long-term earnings growth and returns.
The present PE ratio ‘promises’ a very high rate of growth over the next 20 years. The peak in the PE ratio in 2020 is probably even more reliable, in light of historical patterns discussed above. A projected high level of earnings growth in 2040 would also coincide with 30-year Fedworld patterns in earnings, inflation, and yields.
Chances are, therefore, that PE in 2040 will be considerably lower than it is today. A falling PE does not have to result in a fall in stock prices (especially nominal prices). After all, PE ratios in 1949 were much lower than they had been in 1933, but stocks rose about 50% over that period (you can eyeball this in Chart 1). But, it got there largely because of the collapse in earnings in 1929-1933. That is, PE in 1929 was about the same as it was in 1933. There is very little evidence, in other words, of a long-term rise in stock prices in combination with a collapsing PE, except in the wake of a severe earnings crisis. It is unlikely, then, that stocks over the next two decades will likely be able to make much ground in a falling PE environment, unless stock prices were to be first knocked down to much lower levels.
Chart 10. (Source: Shiller)
We have had a century of convergence in yields and inflation and growth. This has raised the level of things like CAPE and the equilibrium level of the PEG ratio in recent decades and increased the frequency of long-term imbalances (Chart 10). The imbalance of the 1990s resulted in a series of sharp, cyclical crises (2000-2002, 2008-2009) embedded within a long-term bear market (2000-2014). Perhaps the imbalance between growth and yield in the 2010s will not be followed by a similar bear market in the 2020s. But, as I will argue in the final installment, Part 6, much of what is needed for a bear market is already in place.
Part 6 will look at four investment horizons (2070, 2040, 2030, and 2024) using what I think we have found thus far and imagine how investors might best position for them.
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Disclosure: I/we have no stock, option or similar derivative position in any of the companies mentioned, and no plans to initiate any such positions within the next 72 hours. I wrote this article myself, and it expresses my own opinions. I am not receiving compensation for it. I have no business relationship with any company whose stock is mentioned in this article.
Additional disclosure: I am short the tech sector, long Treasuries, and short commodities.