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The famous Shiller P/E hit 31.1 on Aug. 5, the biggest number in almost two years. So the question naturally arises: How have investors who bought at these what look to be rich prices fared in the past?

In the last few days, Wall Street analysts and business news anchors have been cautioning that stocks are getting pricey—so pricey that they may not have much room to run. More than any other news, it's Apple's spectacular rise that's brought these warnings front and center. On Aug. 5, Bank of America analyst Wamsi Mohan stoked the debate by issuing a rare downgrade on Apple, citing its "rapid multiple expansion." TV hosts and their guests picked up the beat, marveling that the iPhone maker's valuation has more than doubled from $900 billion in June of last year to $1.95 trillion, driven almost entirely by a jump in its price/earnings multiple from 16.9 to 35.

Suddenly, investors are viewing Apple's sudden metamorphosis from a deep value stock to an expensive high-flier as a possible bellwether that the entire big-cap market has zoomed too far, too fast. That's raising fears that if you buy at today's lofty levels, you're likely to garner at best puny gains and, more likely, suffer stiff losses. To assess the probability that investors can pocket strong returns from here—as the vast majority of Wall Street's market strategists still predict, despite the doubts sown by Apple—let's see how the portfolios of the folks and funds who jumped in at today's valuations performed in the years that followed. It's the same question for those who already own U.S. big-caps: Were the people who profited from a run-up like the boom over the past few months wise to keep all of their shares in hopes of more upside to come?

To compare where stocks stand today versus past periods on the continuum from cheap to expensive, we'll use the CAPE, or cyclically adjusted price/earnings ratio developed by Yale economist Robert Shiller. The CAPE methodology restates current profits as a 10-year average of trailing GAAP earnings per share, adjusted for inflation. Thus, the yardstick smooths EPS so that P/Es aren't artificially inflated when a recession, say, drives profits well below their historic norm, or the S&P looks like a bargain because profits bubble to unsustainable highs.

The value of deploying the CAPE has never been clearer than during the pandemic crisis. That's because the collapse in profits is making the S&P 500 appear much more expensive than it actually is. The denominator, projected EPS for 2020, is severely depressed and way understates the underlying earnings power of big-cap stocks in a normal economy that isn't wracked by a once-in-a-century calamity. That big, temporary drop inflates the P/E, making the multiple an unreliable gauge of today's valuations versus past periods.

The CAPE eliminates the distortions caused by lurching swings like the one we're now seeing. It puts today's adjusted P/E at 31.1, based on the S&P 500 price of 3327 on Aug. 5. That's a big number, a peak that the CAPE reached for the first time since September 2018. In fact, the CAPE has only hit 31.1, and stayed there or higher for subsequent periods, during three episodes over the 132 years covered by the Shiller data. The fourth time it reached 31.1 is the day I'm writing this story.

It's instructive to examine how the S&P has performed in the two-, five-, and 10-year periods that following the month when the multiple reached 31.1. Those results may provide clues to where returns will settle over the same interludes starting now.

The results are downbeat, but they don't provide conclusive evidence that purchasing at these prices is anything like a sure loser. It's when you add the challenges posed by two other factors that drive returns—historically slow growth in EPS and the tendency of lofty multiples to drop—that Wall Street's bluebird forecasts look like fantasies.

The first time the P/E reached the current 31.1 was in August 1929, amid the craze preceding the Great Depression. It's hardly surprising that two years later, the S&P had dropped 30%, and after five years the loss had swelled to 54%. By the summer of 1939, the index was still nursing a 42% loss over the past decade. By the way, the S&P's Shiller multiple was over 31 for only two months in 1929.

It didn't reach 31.1 again for 58 years, until June 1997. That month, the S&P 500 hit a record of 876. Amazingly the CAPE ballooned from there. It hovered at 33 or higher for the astounding span of three years, from February 1998 to February 2001. For 21 of those months, the CAPE exceeded 40, a number that it has never recorded before or since. Those gigantic P/Es were driven by the infamous frenzy in tech stocks.

Even from a lofty starting point of 31.1, stocks did great—for a while. After two years, in June 1999, the S&P stood at 1322, registering a gain of 51%. But the bounty didn't last. Five years from reaching a CAPE of 31.1, the index had delivered a total gain of 15.3% or a teeny 3% a year. Three months after that, investors were sitting on a loss as the dotcom bubble exploded.

By June 2007, a decade hence, the total gain was 73%, or a less-than-terrific 5.8% a year. And within a year, by mid-2008, the S&P was back to where we started, at a 31.1 P/E in June 2007. The market had made a complete roundtrip in just over a decade, erasing all the gains along the way.

The third bell-ringer came in November 2017, when the CAPE reached our mark for the first time in almost 17 years. The P/E, in fact, stayed over 31 for 11 months but never exceeded 33.3. Over the following two years, the S&P waxed by 20%. Of course, we won't reach the five-year test until late 2022. But as of today, the S&P's increase since hitting 31.1 in late 2017 is 28%, or 8.5% annualized.

The fourth time the CAPE made 31.1 was Aug. 5, 2020.

So what do the past returns from the same starting point tell us about what to expect? We can draw the following conclusions from those episodes.

First, short-term gains can be fabulous after starting at a 30-plus CAPE, but over a longer horizon, those returns tend to reverse. Five years after our P/E reached 31.1 in 1997, the index had barely beaten inflation. After 10 years, the annual increase was under 6%, and less than 12 months after that, went negative in the financial crisis.

The 8.5% returns we've seen since November 2017 are good, but it's too early to conclude that they'll last. Strong evidence suggests that they won't.

Second, the short-term jumps arise mainly when the CAPE hits 31 and runs higher, as it did for many months in the build-up to the 2000–2001 tech bubble. But the span from late 1999 to 2002 is the only episode in which the CAPE rose well above 31.1 and stayed there for an extended period. In other words, the S&P got a big boost only from a CAPE that kept notching new heights on one occasion. We can conclude that getting more juice from an even higher multiple, though possible, is unlikely.

Third, when the CAPE reaches 31.1, and especially when it keeps climbing from there, it topples from the mountaintop. It was the CAPE's never-before-witnessed flights into the 40s that triggered the panic selloff and sent the S&P below where it first hit our benchmark three years before.

In the Great Depression, the CAPE dropped from 30-plus to single digits. In 2002, it slid by one-third to 21. Even after hitting 31.1 in late 2017, the CAPE shrank to 25 in the April selloff. It appears that a CAPE of over 30 is much more likely to revert to the mid-20s or lower than to go higher, except in a short-lived spike.

Fourth, since an even higher CAPE is unlikely when starting at 31.1, investors face two problems. First, the multiple is a lot more likely to contract than even to remain steady, potentially hammering future returns. Second, even if the CAPE stays at 31.1, all future gains will depend on earnings growth. Indeed, expanding profits have been a big contributor to capital gains in recent years. As the U.S. emerged from the financial crisis in early 2010 through 2019, EPS increased at an 8% annual pace.

That record, however, is extremely unusual. Over the 55 years from 1965 to 2019, EPS advanced at 2.1%, adjusted for inflation. That's around one point slower than growth in national income. Although total earnings track the overall economy over long periods, earnings per share lag because companies issue new stock to expand, spreading profits over larger numbers of shares. And new competitors enter the market, issuing their own shares, or if they remain private, grabbing part of the profit pool and leaving less for the old guard.

Fifth, the CAPE tends to go in the opposite direction from interest rates. At most times, the lower the 10-year Treasury yield, the higher the CAPE, and vice versa. Rising rates pounded stocks in the early 1980s, and yields at record lows appear to be buoying the S&P now. But the best time to buy equities is when rates are high or average, and the CAPE is low, periods such as 1980 and 2008. The worst time is when the opposite conditions prevail, as in 1966 and 2000. People who bought then got terrible returns over the succeeding years, simply because the world returned to normal at higher rates—and falling CAPEs that shrank prices. Today's high-CAPE, low-rate climate resembles both of those heady periods.

Conclusion: A 31.1 CAPE is a dangerously high starting point for buying stocks. The price investors are willing to pay for each dollar of earnings will probably shrink from here. And EPS is already getting pounded by the COVID-19 lockdown, and the idea profits will soar in the recovery to compensate for the fall in multiples, and then some, is far-fetched.

A CAPE of 25, still extremely high by historical standards, would put the S&P around 2950, 11% lower than today. A better bet is a CAPE of 20, and that's scary. A drop to that benchmark would push the S&P under 2500 for a decline of 25%. All the bulls' rationalizations can't get past this basic truth: Companies have to practically perform miracles to give you big returns when their stocks are pricey, and can reward you richly if they just muddle along if they're cheap. Keep in mind that in 2017, Apple was selling at an 11 P/E. Would you rather buy it there, or at the current 35? One's a no-brainer, the other's a gamble. The story of Apple epitomizes the course of the whole market. You've got to "believe" a story to be a buyer here—and you wouldn't need a story if either were a bargain.