Shiller's CAPE: A Statistical Fluke

by: John Overstreet

Please, don't get me wrong: I love P/E ratios. Click on my past articles, and you would be hard-pressed to find one that did not put P/E front and center in discussions about inflation, commodities, bonds, geopolitics, you name it. Why I have finally turned on Shiller's P/E10, the Cyclically Adjusted P/E ratio ((NYSEARCA:CAPE)), is simply because a) it adds virtually no value to other measures of P/E, b) the way it has been constructed and applied is highly problematic, and c) it is only effective under a strict set of conditions.

I have talked plenty about why I thought that using trailing twelve-month earnings (TTM) or concurrent earnings and prices is superior to CAPE, but it has taken me a long time to finally realize that CAPE is fundamentally flawed, probably to the point where we might be better off eliminating it altogether. That may be a bit harsh: a ratio is just a ratio, and in any ratio you can find useful information.

But, there is a lot of chatter about how stocks are overpriced because of CAPE, and this is a misappropriation of an already flawed measure.

So, what precisely are the problems?

Having talked about some of my issues with regard to Shiller's use of CAPE in previous articles, in this one, I would like to confront CAPE on its own ground.

In terms of construction, here are the problems with Shiller's P/E10:

1. It is adjusted for inflation.

2. It is backward-looking.

In terms of how it is applied,

1. It is generally compared to "real" returns rather than nominal returns.

2. It does a poor job of predicting future returns.

3. That it has managed to predict any returns is a statistical fluke.

Of course, some of these seem like either necessary evils or outright positive features, particularly those involving the construction of the ratio as well as the comparisons to "real" returns. "Naturally," most readers will probably imagine, "you have to adjust both the ratio and the compared returns for inflation. Everybody knows that. And, of course, it's backward-looking. That's the whole point. We don't know what the future holds, and we use the past to give us a rough guide of what a reasonable level of earnings might be. And, what do you mean it does a poor job of predicting returns? Everybody and their grandmother knows about the relationship between CAPE and future returns."

That is a reasonable point of view, but those adjustments are fatal flaws, not strengths, and the data don't say what people think they say. Let me see if I can shake your confidence a little on these points.

First, look at the chart below. This is a comparison of CAPE with twenty-year annualized nominal returns and inflation. Shiller used ten-year "real returns," of course, and that's the standard we will use in the remainder of the article, but I want to raise some doubts first.

CAPE, inflation, and nominal returns, 20 year

(Note: All data in this article are derived from Robert Shiller's data, unless otherwise stated).

Isn't it odd how well CAPE has predicted inflation? And, isn't it odd how poorly it predicted returns prior to the late 1920s?

That means at least some portion of the negative correlation between CAPE and subsequent returns is a function of CAPE's historically consistent ability to forecast inflation (at least until relatively recently). But, how on Earth did that come about? Since when did CAPE predict inflation? With twenty years of high CAPE ratios, are we due for decades of double-digit inflation?

Well, I can't tell you what inflation will be like in the 2030s, but I am fairly certain that CAPE is not forecasting imminent, relentless inflation.

This is partly a real phenomenon and partly a fluke. Inflation has consistently been inversely correlated with P/E ratios for the last 140 years. That's for real. The fluke is that P/E ratios have moved in Kondratieff-like, regular twenty-year waves, which can be used to create the statistical impression that CAPE somehow predicts inflation.

Rolling correlation P/E vs GDP, Inflation, Commodities, Bond Yields

(Source:, Stephan Pfaffenzeller, Shiller, Roy Jastram's The Golden Constant)

If we are going to consider how CAPE relates to future returns, we should at least consider looking at nominal and real returns separately.

And, then there is the question of construction, particularly whether or not calculation of CAPE should be adjusted for inflation itself, since the stock index would tend to be negatively correlated with inflation and earnings positively correlated, all else being equal. The inverse correlation between P/E ratios and inflation (and especially commodity prices) suggests that P/E ratios either impact inflation or inflation impacts P/E ratios. If it is the first scenario, then rising stocks reduce inflation. To then include inflation as a factor in the returns is essentially double-counting and says nothing about the rationality or lack thereof of investors. If it is the latter scenario, where inflation is impacting P/E ratios, then Shiller's thesis about equity valuations being governed by human emotion rather than economic fundamentals is less certain.

Whatever the case may be, it is clear that the consistent, inverse correlation between P/E ratios and inflation, as well as the supercyclicality of P/E ratios makes comparisons between CAPE and "real" returns problematic at best. Those alone are not grounds to eliminate CAPE, but it makes it necessary to cross-reference nominal P/E measures and nominal returns with CAPE and "real" returns to make sure we are not mixing apples and oranges.

The remainder of the article is going to amplify these themes by digging deeper into the historical data using Shiller's data segments, demonstrating why there is nothing magical at all about CAPE and why its grip on the imagination of the market is a clear and present danger. Built into these comparisons of backward-looking P/E measures with future returns are highly questionable assumptions.

Before pushing ahead, readers should be sure that the problems evident in that first chart are apparent, because those issues are more or less the threads I am going to be pulling at from here on out.

CAPE and Future Earnings

So, now consider a few more charts. The next one is a comparison of CAPE, P/E TTM, and ten-year nominal returns. From the Depression up until the Credit Crisis, these two measures of P/E were quite tightly correlated. Prior to that, the relationship was much weaker, not only between each other, but between each of them and stock returns. It appears that P/E TTM had a tendency to be positively correlated with returns in many instances.

P/E, CAPE, future nominal returns 1871-2011

Why might that be? Forget P/E ratios for a second and think about E/P, the earnings yield. Suppose the stock market was at 1000 and earnings fell from 100 to an unprecedented low of 50 while stocks barely moved, or only move down to 950. That means the P/E would move from 10 to 19. Are stocks overpriced or underpriced? That depends on where earnings are going. If earnings bounce back to 80, the yield on stocks will rise, and P/E will fall. In other words, stock yields may tend to correlate with bond yields, but stocks are not bonds. A very low yield may be a buying opportunity. That's what we saw in 2008-2009, when the P/E TTM ratio shot up into the triple digits. It simply depends on whether earnings mean revert.

That may be a fairly obvious point, but when we combine this simple problem with the other flaws, we get a poisonous brew.

Now forget all that for a moment and consider the following: Shiller's examination of P/E ratios is not expressly designed for predicting stock returns. It is simply that the inverse correlation between P/Es and returns is believed to demonstrate his point about investors being irrational.

The fundamental question is, do investors pay too much for future earnings? One way to check that is to calculate P/Es using forward earnings. In the chart below, I calculate the "P/E F10," which is the stock index divided by a moving average of the subsequent ten-years' worth of earnings, and plot it beside CAPE and returns.

PEF10, CAPE, and future returns

You can see that, like P/E TTM, it correlates quite well with CAPE for long periods of time, especially after World War I. What is really interesting is that it so strongly (negatively) correlates with future returns, almost perfectly so, in fact.

So, a question we can consider is, since Shiller's fundamental concern is whether or not investors pay too much for future earnings, and we have found that this forward-looking P/E ratio (i.e., the P/E F10) is so strongly (negatively) correlated with returns, does that not prove Shiller's thesis even better than CAPE?

At first, I thought that was the case, but once I thought about it again, I realized that it said nothing of the sort. After all, what is the alternative? It is almost (but not quite) the same thing to compare forward-looking earnings with future returns. That is to say, by definition, if you pay too much for future earnings, your future returns will be weak.

Stock returns vs earnings 1871-2013

We will come back to that later. In the meantime, look at the relative levels of CAPE and the P/E F10 before and after the Great Depression in the chart prior to the one immediately above. After the Depression, CAPE remains well above the P/E F10 throughout the entire seventy year-span. The reason is, quite simply, that earnings growth has remained positive over decadal intervals, growing, since the 1960s, at a fairly consistent 6% or so per annum.

Earnings & earnings growth 1871-2013

Things get tricky here. Think about this for a moment. If earnings grow at a relatively constant rate over decade-long periods of time, then shouldn't that alter how we determine where valuations stand relative to their historical averages? In other words, if we are investing in a stock market where earnings are highly variable, using historical earnings may be reasonable, but if we know that profits will now essentially be guaranteed in the long run, using historical earnings would have us consistently underpaying for future earnings, wouldn't it?

Is There A Difference Between Using Past Earnings and Projected Earnings? Not Really

Plenty of smart, prudent people have ripped into analysts for incorporating 2014 or 2015 earnings estimates into their outlooks recently. I think I can only half-agree with that condemnation. Over annual intervals, it seems pretty ridiculous to me to present next year's earnings with a straight face this year. (Then again, what do I know?) On the other hand, for sixty years now, over long enough periods of time, we seem to have a virtual guarantee of 6% earnings growth.

That inevitably raises the question, how reliable is that growth? Is it more prudent to predict earnings for 2024 than 2014? And one has to ask where the growth came from to begin with. It doesn't seem that anybody has a good answer for this.

Let's step back again. The real question has always been how much should we pay for future earnings. When we look at the numbers from that point of view, it suggests that, since the Depression, forward-looking P/E ratios have fallen fairly steadily, while backwards-looking ones like CAPE have tended to rise. If we project median rates of earnings growth over the last 140 years onto the next ten, it suggests that forward-looking P/E ratios are about right, although it is somewhat strange that those ratios have been so stubbornly high over the last twenty years.


PEF10 scenarios

So, how ludicrous is it to calculate P/E ratios from ten-year forecasted earnings based on nothing more than a blind historical extrapolation? Wouldn't a backward-looking ratio like CAPE be more prudent? Isn't that what the question boils down to? Doesn't it seem imprudent to count chickens before they've hatched?

It may seem like we are playing with fire by taking ten-year forecasts of earnings seriously, but I have to point out that those earnings forecasts are based on projecting historical performance out into the future, and here's the rub: the period in which earnings have consistently been positive over decade-long intervals also happens to be the only period in which CAPE did a good job of predicting future returns.

In other words, there is a very strong correlation between rising earnings and CAPE's ability to forecast returns. Why is that? Perhaps it is obvious to others, but it was not obvious to me at first: there is virtually no difference between using a moving average of the previous ten years' earnings as a proxy for normal earnings and projecting the average historical rate of growth into the future. It changes the long-term absolute levels, but it does not change the cyclicality, since the cyclicality for the last century has come almost entirely from the stock index, not earnings.

To put it yet another way, for people who may think that it is ridiculous to make projections of future earnings growth based on historical earnings growth, that is precisely what Shiller's CAPE does. He certainly does not present it that way. When he presents the correlation between CAPE and subsequent returns, he uses a scatter-plot for the entire post-1871 market, which masks the degree to which CAPE is dependent on stable earnings growth. When you separate the steady-growth scenarios from the unpredictable growth scenarios, the problem becomes manifest.

CAPE vs Real returns 1871-1913 CAPE vs real returns 1930-2003

To sum up, there is only a slight difference between using past earnings and using forward earnings projections extrapolated from historical growth. If you use CAPE, this has a tendency to raise equity valuations above long-term averages, but it is possible that the markets have "known" that earnings are backstopped and have been willing to pay accordingly, which is reflected in the gap between CAPE and the P/E F10.

In any case, I have to reiterate that the CAPE has really only managed to predict future returns when earnings have risen over the long term. Look at the following table. I have used a variety of P/E measures, including not only those calculated from ten-year trailing earnings, one-year trailing earnings, and forward earnings, but a ten-year centered moving average and a twenty-year centered moving average. Smoothed out averages, particularly those, which incorporate future earnings, do a better job of predicting future returns.

P/E ratios Correlation w/ real returns Correlation w/ nominal returns over/under historical average Last period for under/over
CAPE -0.45 -0.47 +53% Dec '13
P/E 10* -0.35 -0.31 +52% Dec '13
P/E -0.37 -0.40 +15% Sept '13
P/E TTM -0.37 -0.40 +20% Dec '13
P/E TTM* -0.37 -0.39 +17% Dec '13
P/E F10 -0.59 -0.66 +38% Dec '13 (est)
P/E F10* -0.43 -0.68 +25% Dec '13 (est)
P/E C10 -0.49 -0.53 n/a Dec '03
P/E C10* -0.45 -0.53 n/a Dec '03
P/E C20 -0.54 -0.59 n/a Dec '03
P/E C20* -0.45 -0.57 n/a Dec '03

(The asterisks refer to P/E measures calculated from nominal values).

In the chart below, you can see how the increasingly negative 50-year rolling correlations between P/E measures and subsequent returns have strengthened when earnings have strengthened and weakened when earnings have weakened.

correlations btwn P/Es and returns vs earnings behavior 1871-2013Using ten-year rolling correlations produces much the same effect. CAPE is no better at predicting future returns than other measures, since its effectiveness is contingent upon a constant growth in earnings.

10y rolling correlations btwn P/Es and returns vs earnings stabilization 1871-2013

Correlation btwn CAPE PEF10 & returns vs Earnings

That leaves CAPE with two fundamental, interrelated weaknesses:

a) it effectively assumes a positive rate of earnings growth (masked as a moving average), leaving it exposed in a market where earnings are volatile--and having assumed that positive rate of growth,

b) it nevertheless routinely overestimates the amount the market is valuing equities by using backwards-looking earnings.

It's the worst of both worlds.

The Problem of Supercycles

That is not all. All of these ratios suffer from another fatal flaw when used as predictors of ten-year returns. They all depend on the supercyclicality of the market. If you look back at the chart near the beginning of the article that shows CAPE "predicting" the level of inflation, you will see that both inflation and returns have deviated from the cycle. In the rolling correlations above, we can also see that these (negative) correlations between P/E ratios and returns appear to be weakening over the last twenty to thirty years.

Part of that is due to the increased volatility of earnings, but part of that is also due to an upward bias in stock valuations over the same period of time. Stocks are moving up higher and for longer periods of time, which is breaking the regularity of the old Kondratieff cycle in markets and undermining the once-reliable link between P/Es and returns.

Before considering this latest variation on trends in stocks and earnings further, let's take stock again of where we are:

1. It is, at best, problematic to use inflation-adjusted ratios or returns. It is probably not fatal to do so, but it is anachronistic and unnecessary, and to do so prejudicially rejects the possibility that P/E ratios are driven by fundamentals rather than emotion.

2. Using P/E ratios to estimate multi-year returns depends on one's ability to predict earnings over that same period. The notion that CAPE has any ability to predict future returns rests on the idea that future earnings will look like past earnings. The only difference between this and projecting earnings into the future is in the absolute level of P/E ratios. It only varies the degree to which stocks are made to appear over- or undervalued.

3. Using P/Es to predict future returns depends not only on an accurate prediction of future earnings but on the consistency of the supercycles. The dramatic expansion of P/E multiples in the late 1990s, the relatively high levels that were maintained during the 2000s, and the relentless rise in P/E ratios since 2011 all seem to point to a break in that once reliable cyclicality.

CAPE is completely dependent on these factors. Without regular supercycles and without relatively predictable earnings, the ability of CAPE to 'telegraph' future returns is approximately zilch!

As I said, the regularity of supercycles has apparently broken down since the mid-1990s. That is reflected in virtually every chart we have examined so far.

The Earnings Conundrum

No matter which measure we use, we are therefore forced to come to grips with the "problem" of constant earnings growth. To repeat, if an analyst insists on using backward-looking ratios like CAPE to forecast future returns with the handy-dandy correlations that Shiller used and analysts continue to use today, he/she is already taking it for granted that future earnings growth will approximate past earnings growth. But, if that is the case, why not just project that growth outright?

Why hide behind CAPE?

I am not saying it is intellectually dishonest to use CAPE. Rather, I would say it is intellectually self-deception. It is speculation with a veneer of historical studiousness.

If we do project something like 5-6% earnings growth over the next ten years, then P/E ratios are not nearly as expensive as CAPE suggests. But, once the implicit assumption of earnings growth within CAPE is brought out from the shadows, how many analysts really feel comfortable predicting earnings over the next decade? Do people seriously attempt this? Perhaps someone does somewhere, but really, all I see and hear are arguments over whether we should use CAPE, TTM, or short-term earnings forecasts, a discussion that is useful only if you know how to use each ratio.

Why have earnings grown so consistently since the 1930s and especially since the middle of the last century? Could it have anything to do with the profound revolutions we have experienced in monetary matters since 1914? Or are there endogenous forces within the real economy having this profound impact? If it is due to political and institutional factors (e.g., the establishment of a central bank and the transition to a fiat currency system), is there any reason to think that the backstopping of profits will not be sustainable over the next decade? If the rise in profits has been natural rather than artificial, can we expect that cause to continue to work its magic in the 2010s and 2020s?

Profits, Inflation, and the Yield Curve 1871-2012

As far as I know, nobody knows the answers to those questions, but if investors, after careful consideration, should regard continued growth of profits as more likely than not over the long term, then why bother with CAPE at all? Why not rely on forward-looking estimates and dispense with the charade?

CAPE is Useless

I worry that I have failed to adequately demonstrate these issues, but this is probably the best I can do for now. And, it would be prudent for me to stop here, since the data, to my mind, is fairly conclusive: CAPE has only managed to predict returns when earnings growth is constant, and if future earnings growth is constant, you don't really need CAPE.

In conclusion, my analysis in previous articles suggested that this market is in a period of secular P/E expansion (SPY, DIA, QQQ) and weakness in commodities (NYSEARCA:GSC) and emerging markets (BIK, FRN). The worrisome thing about American stocks is not the otherworldly performance of the last two years but rather the otherworldly performance of stocks over the last sixty to eighty years. If we cannot come up with a convincing account for this sea change in the markets and why it may or may not continue in the future, we are forced to devise more creative ways of looking at markets.

P/E F10, CAPE, and stock/bond relative performance 1871-2013

Disclosure: I have no positions in any stocks mentioned, and no plans to initiate any 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.

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