Using CAPE To Predict Stock Market Returns

Our portfolios have giddily ridden a bull market that’s entering its ninth year. Which means we’re lots richer and this old bull is getting up there in age. As in, probably too leathered and weathered even to be eaten after the toreador has sullied his sword.

But it’s true that, just as in the bullring, toros don’t die of old age. They get killed. And, just as in Hemingway’s favorite metaphor, the death follows a prescribed pattern.

The pattern of this bull’s death will go like this: 1) Equity valuation multiples will rise to unusually high levels; 2) Statistical gravity will kick in, and long-term valuation indicators will mean revert; and 3) Valuation multiples will stumble into the dirt and be slowly dragged out of the ring.

As predictable as the mean reversion pattern is, however, the particulars of timing and trajectory are never knowable in advance. Just because we observe high valuation multiples for U.S. equities doesn’t mean we know when or how those valuation multiples (and/or equity prices) will revert to a more “normal” level.

But we can draw some pretty good conclusions about long-run returns performance on the basis of CAPE and a couple other predictive indicators.

We previously ran through a little scenario planning exercise here on FL where we dissected how U.S. equities might behave over the next several years. And the analysis remains pertinent, so it’s worth a look. But for all its glory, the exercise doesn’t provide numerical guidance. It just describes reasoned possibilities.

And so we’re gonna prance into the bullring and wave our CAPE at the old bull and explore U.S. equities valuation slightly more numerically. And we’ll see what kind of long-run returns we might reasonably anticipate in U.S. stocks.

This post is the first installment of at least three articles where we’ll look at some statistics and make some long-run forecasts of equities returns. And we’ll talk about the kinds of equity allocations that likely make sense. And that’s no bull.

Using CAPE
Using CAPE

Cape of Good Hope

There are (arguably) several relevant metrics useful for examining stock market valuations on an historical basis and predicting future equities returns. The most well known is Shiller’s CAPE, which is pretty good if you’re impressed by Nobel prizes.

CAPE is an equity market’s price-to-cyclically-adjusted-earnings ratio. And it’s a lot like the more widely used PE ratio, but with a twist.

PE reflects the market’s current valuation multiple relative to underlying earnings: That is, if a company earns profit of $1 per share each year, and each share of that company’s stock trades on the market at $14, then you’d say the company trades at a PE of 14. (Mathematically: P of 14 is divided by E of 1.)

And PE is great for lots of types of analysis. But, particularly when considering a market as a whole over time, PE suffers from a cyclicality effect brought on as an artifact of the usual business cycle. Company earnings per share fluctuate in accordance with the underlying economic conditions of expansion and contraction. Which can make PE ratios volatile and weak for forecasting.

To correct for this, Shiller took a page right out of Benjamin Graham’s book(s) and decided to “cyclically adjust” PEs so that business cycle effects would get smoothed out. Mechanically this entails dividing current-market P by a smoothed or averaged E observed over the last 10 years, rather than just dividing current-market P by E observed over the last 1 year.

All of which is about as exciting as sand. Until we get to the exciting part: When applied to entire stock markets, CAPE is purty durn good at forecasting future stock market performance over the next 10 to 15 years.

The forecasts work like this: When the current CAPE is low, you’d anticipate greater future returns than when current CAPE is high. And vice versa.

(Technical note: There are some arguments about CAPE. First, there’s an argument about “payout ratio” changes over time and whether, given changes to companies’ dividend policies, CAPE comparisons can be useful over time. Zero points are awarded here. “Adjusted CAPE” can be easily calculated (as Shiller has done), and nothing important changes. Second, there’s an argument from Siegel that CAPE comparisons over time are screwed up because of accounting rule changes. This argument is trickier and may have some merits at the margins, but there are strong counterarguments, and on net, it’s not something that warrants attention for our purposes because we really only care about the broad strokes – the finer points can be left to the academics; we’ll busy ourselves with making money instead.)


How good is CAPE at forecasting, exactly?

Well, the answer kinda depends.

If we look at CAPE measured on the S&P going back to 1881 (as originally done by Shiller), CAPE at any single point can explain roughly 46% of annual stock market returns over the following 10 to 15 years. (And if we go back to 1926, the explanation is 43%.) Which is pretty okay. Better than Miss Cleo. But just okay. As in: More variation in returns remains unexplained by CAPE than explained. And a decade-plus is a helluvalong time to be wrong.

However, if we look at CAPE going back only to 1979 (or when we’d arguably be in the “modern era”), CAPE can maybe explain about 82% of subsequent returns in U.S. equities (whether we’re looking at the S&P 500 or at the overall public equities market).

And the correlation between CAPE and returns over the next 10 to 15 years is -0.96 in the modern era. Which is nosebleed high. And which tells us numerically that a low CAPE = high future returns, and a high CAPE = low future returns, in terms that are anything but uncertain.

Note that these post-1979 figures are reflective of some possibly dubious quantitative methods, so take them with a grain of bath salts. It’s tough to have lots of confidence in the results because of a relatively small number of observations. Despite this, the fact remains that more recent CAPE readings seem to do a better mathematical job of explaining the future than older CAPE readings, and the overall pattern can’t be dismissed. This recency effect could be anomalous, but it could also be reflective of other factors that lead to CAPE being more powerful now than before, including better raw data for input into the model (no offense to Shiller) and a more settled structural mix in the underlying economy.

Cape Fear

Anyway, at present, CAPE is weighing in at right about 27.7. Which, for context, is a reading exceeded in only two moments since 1881: First, right around Black Tuesday; and second, in the leadup to the Mortgage Crisis Crash. (Graph from Data as of Dec. 30, 2016.)

Which directionally suggests that A) CAPE is currently very high; and B) we’d expect CAPE to mean revert sometime in the next decade, taking stock returns down with it.

But now we’ve gotta think about what, exactly, we mean when we say that CAPE will “mean revert.” Specifically: what “mean”?

At a high level, it’s possible that CAPE readings from way, way back are less comparable to current CAPEs than more recent readings are. In part, this is because of the social science part of economics: There’s general attitude towards stocks (i.e., secular investor sentiment) that can change over time and lead to something like “CAPE inflation,” and so it’s possible we’ve just entered a period of lotsa human love for equities. Hence, higher CAPEs that’ll stay high.

There are also changes in the underlying economic structure of the economy that could slowly alter the numerical relationship between P and Cyclically-Adjusted E. Which is a topic for another time, but suffice it to say that it’s likely tougher to compare equities valuations from the year 1892 with the year 2012 than it is to compare 1985 with 2005.

All of which is important because the U.S. S&P median CAPE dating back to 1881 is way different from the median dating back only to the start of our adopted “modern era” as of 1979.

Going back to 1881, mean and median CAPE are in the range of 16. From 1979 forward, mean and median CAPE are around 21. So if our current CAPE of 28 is measured against the “old” CAPE, we’re looking at the possibility of a 40% drop to achieve the mean. But the possible drop is only 25% looking at younger, spryer CAPE from 1979.

I’ll now suggest once more you check out the earlier FL post on this stuff – there are lots of ways CAPE can “correct” or “mean revert” that don’t involve a nasty decline in market prices.

For additional context, consider this: Although a CAPE of ~28 is up there, it’s still way, way below the maximum ever observed in the U.S., which is around 44.

And the 75th percentile for CAPE distribution in U.S. history since 1979 is 26, meaning that, yes, we’ve only spent about 25% of our time with CAPEs above 26. But we’ve also spent a full one-fourth of our time with CAPEs above 26…as in 9 full years since 1979.

For completeness of the descriptive statistics post-1979: the 25th percentile value is 15, and the minimum observed is a little above 6. A table below summarizes.

So, yeah, we’re in rarefied air. But we’re also not above a sort of critical threshold of 30, which is where valuations start to look really nasty.

You’re Standing On My Cape

So what does a CAPE of nearly 28 imply for performance of the S&P 500 over the next 10 to 15 years?

We can expect average real returns (i.e., returns after inflation) in the range of 3% to 4% annually for the next decade or so according to CAPE-only forecasts.*

Which really isn’t so bad. Yes, it’s way below the real returns “normally” observed in U.S. equities. But it isn’t curl-into-the-fetal-position awful. It’s real growth, after all.

But it’s worth noting that, in instances when U.S. CAPE has exceeded 30 (which we’re darn close to right now), average annual returns over the subsequent 10 to 15 years have been slightly negative (in the range of -0.4% to 0.5%).

And so, if we’re thinking about using history as a guide to form a qualitatively-textured forecast, then you’d maybe say something like this:

“Okay, long-run average real returns in U.S. equities are around 8%, and now we’re probably looking at returns under half that, with some real downside risk of even lower or negative average returns over a decade.”

How those averages become realized over time is trickier than lassoing a bull, though, so bear in mind the issue of volatility. Yes, over a decade-plus horizon, we can be reasonably confident U.S. equities returns are gonna be relatively weak on average. But that doesn’t mean the next two years won’t show gains of 10%+ each, followed only then by sideways piddling while earnings catch up. Or gains next year of 80% followed by a 50% crash the year after. If Shiller’s figured out this shorter-term part of the equation, he’s keeping his notes to himself.

Also consider: Assuming a constant Cyclically-Adjusted E, U.S. equities prices could increase 40% and still result in a CAPE below the maximum observed in U.S. history. So there’s the possibility of upside.

On the other hand, if CAPE were to revert to post-1979 median levels at constant earnings values, then you’d expect a 25% decline in equity prices. Which would be tantamount to a hungry bear coming out of hibernation and eating you for lunch. (We won’t discuss what a drop of CAPE to 25th percentile levels would do to your portfolio.)

The Great Gain Caper

Where’s all this leave us?

Statistically, the likelihood of CAPE going up is less than the likelihood of some sort of downward reversion over the next several years.

The likelihood of below-trend real returns in U.S. equities over the next decade-plus is quite high. And around 3% to 4% on average seems fair.

Here’s a table from Meb Faber citing Shiller that summarizes the sorts of returns different CAPE levels predict. (The table’s a few years old, but the results are still valid and, although data back to 1881 are used, similar results would show if data were limited to 1979 and later.)

But CAPE, for all its usefulness, remains very general in its predictions, and our confidence in what it implies has to be limited. And so, while we may have reached a tentative conclusion here that U.S. equities’ futures are looking a little roughed up by all the bull action from the last eight-plus years, there are two other predictive variables we need to look at to really wrap our arms around this bull.

Which is where we’ll turn next. As we’ll see, one of our predictive variables is at least as powerful as CAPE. And it’ll help us refine our forecast. A couple other predictors are interesting as well because they help fill out the analysis and improve confidence.

Until then, Luchadores, stay well, stay strong, avoid hungry bears, and don’t take no bull from nobody.

Luchadores, what are your thoughts on CAPE? Do you care about CAPE, or will your investment strategy remain intact regardless of CAPE levels?

*(Technical notes: Some of this discussion reflects empirical work published by Vanguard and an investment group out of Germany. Both rely in part on Shiller’s compilation of U.S. equities data and on Shiller’s CAPE computations. But neither report’s approach can be fully endorsed by old FL because both suffer from different limitations. Nevertheless, the findings remain useful – provided we think about things the right way. We just can’t put as much stock in them as might be tempting.)


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