Is the S&P 500 way over-priced?

Robert Shiller’s CAPE (Price/10-year simple MA of inflation-adjusted earnings) is at 30.31, the second-highest peak (behind the Dotcom bubble) in 120 years.

S&P 500 CAPE

PEmax (Price/highest prior 12-month earnings) is far lower at 21.04. I prefer this as a more accurate measure of stock pricing than CAPE. But PEmax is still high relative to the peaks of Black Friday in October 1929 and Black Monday in October 1987.

S&P 500 PE of Maximum Prior Earnings

Forecast earnings for the remainder of 2019 may be slightly optimistic, given recent escalation of the US-China trade war, but the forward price-earnings multiple is lower, at 18.62. The sharp difference between forward and historic PE ratios (as in PEmax) is largely attributable to the earnings hiccup in Q4 of 2018 which is excluded from the forward ratio.

S&P 500 Forward Price-Earnings Ratio

Forecast earnings growth, on the chart below, shows a similar anomaly in Q4 of the current year, caused by comparison to the earnings dip in Q4 of 2018. Forecasts assume that earnings will grow between 7.1% and 7.8% for the rest of 2019, rising to above 11% in 2020.

S&P 500 Earnings Growth

Their projections seem optimistic.

Year-on-year sales growth is a modest 5.8% for Q1 of 2019 and is likely to continue between 4.0% and 6.0% for the foreseeable future. The spike in sales growth in 2017 – 2018 is a result of recovery from negative growth in 2015 and is unlikely to be repeated.

S&P 500 Quarterly Sales

Operating margins are just as important. Margins recovered to 11.25% for Q1 2019 (89.9% of stocks reported), after a sharp fall in Q4 2018, but it is questionable whether these are sustainable.

S&P 500 Quarterly Operating Margins


Earnings forecasts seem optimistic. With lower sales growth and downside risk in operating margins, long-term earnings growth of between 4.0% and 6.0% is likely. The 30-year average is 6.17% p.a. but low inflation (and a possible trade war) is likely to see us undershoot this.

Forward Price-Earnings ratio of 18.6 is on the high side for expected low earnings growth. A forward PE of 16.0 or less, however, should be viewed as a buy opportunity.

PEmax and why you should be wary of Robert Shiller’s CAPE

Robert Shiller’s groundbreaking works, Irrational Exuberance and Animal Spirits, led to a Nobel prize in 2013 but we need to be careful of placing too much reliance on his CAPE as an indicator of stock market value.

What is CAPE?

CAPE is the cyclically adjusted price-to-earnings ratio, normally applied to the S&P 500, to assess future performance of equities over the next decade. CAPE is calculated by dividing the S&P 500 index by a moving average of ten years of inflation-adjusted earnings. Higher CAPE values imply poor future returns, while low values signal strong future performance.

Economists John Y. Campbell and Robert Shiller in 1988 concluded that “a long moving average of real earnings helps to forecast future real dividends” which in turn are correlated with returns on stocks. Averaging inflation-adjusted earnings smooths out short-term volatility and medium-term business cycles in the economy and, they argued, was a better reflection of a firm’s long-term earning power.(Campbell & Shiller: Stock Prices, Earnings and Expected Dividends)

Shiller later popularized the 10-year version (CAPE) as a way to value the stock market.

S&P 500 CAPE


CAPE correctly identifies that the S&P 500 was over-priced in the lead-up to Black Friday (October 1929) and ahead of the Dotcom bubble in 2000. It also correctly identifies that stocks were under-valued after the Depression of 1920-21, during the Great Depression of the 1930s, and during the 2008 Global Financial Crisis.


Some CAPE readings are rather odd. The rally of 1936, in the midst of the Great Depression, shows stocks as overvalued. Black Monday, October 1987, which boasts the highest ever single-day percentage fall (22.6%) on the Dow, hardly features. Current CAPE values, close to 30, also appear exaggerated when compared to current earnings.


There are several reasons for these anomalies, two of which relate to the use of a simple moving average to smooth earnings.

The simple moving average (SMA) is calculated as the sum of earnings for 10 periods which is then divided by the number of periods, 10 in our case. While the SMA does a reasonably good job of smoothing it has some unfortunate tendencies.

First, the SMA tends to “bark twice. If unusually high or low data is recorded, the SMA will rise or fall accordingly, as it should. But the SMA will also flag unusual activity, in the opposite direction, 10 years later when the unusual data is dropped from the average.

Second, the SMA is fairly unresponsive. If earnings rise rapidly, the SMA will lag a long way behind current values.

The third anomaly relates to the use of a moving average of earnings to reflect future earnings potential. Companies may incur losses at the low-point in the business cycle, especially in a severe down-turn like 1929 or 2008, but the impact on future earnings capacity is marginal.

Take a simplistic example, where earnings are $1 per year for 9 years but a loss of $5 is incurred in the following year.  When the business cycle recovers, potential earnings are likely to be $1, not $0.50 (the 10-year SMA).


All of these flaws are evident in the CAPE chart above.

Problem 1

Expect a fall in CAPE next quarter (Q1 2019) when losses from Q4 2008 are dropped from the SMA period.

Problem 2

Earnings multiples in the lead-up to Black Friday (1929) and the DotCom bubble (2000) are both overstated because of the lag in the SMA caused by rapidly rising earnings.

Problem 3

Potential earnings in 1936 are understated because of the sharp fall in earnings during the Great Depression, resulting in an overstated earnings multiple. The same situation occurs 2009-2018 when losses from 2008 inflate CAPE values.

Proposed Solution

I tried a number of different moving averages in order to avoid the above anomalies but all, to some extent, presented the same problems.

Eventually, I tried dropping the moving average altogether, instead using the highest previous four consecutive quarter’s earnings to reflect future earnings potential. I call this PEmax © (price over maximum historic earnings). PEmax matches normal historic price-earnings ratio (PE) most of the time, when earnings are growing, but eliminates the distortion caused by sharp falls in earnings near the bottom of the business cycle.

S&P 500 PEmax

PEmax overcomes distortions associated with the 1936 bear market rally, Black Monday in 1987 and our current situation in 2018.

Compare how the two perform on a single chart below.

S&P 500 PEmax compared to CAPE

The spikes on Black Friday and the Dotcom bubble are more muted on PEmax but still warn that stocks are over-priced relative to future earnings potential. The 1936 bear market rally is restored to its proper perspective. As is the 1987 Black Monday spike, by removing the distortion caused by declining earnings in the early 90s. The same happens after the Dotcom bubble. And again in 2009 -2018.

Potential Uses

The historic average (1900 – 2018) for PEmax is 12.79. For what it’s worth, standard deviation is 5.32 but this is not a normal distribution.

S&P 500 PEmax distribution

The median (middle) value is slightly below the mean, at 12.23.

Visual inspection of the data suggests that low values are skewed towards the first half of the 20th century. The average over the last 50 years (1969-2018) is 15.85 but, again, this may be distorted by the Dotcom era.

Based on visual inspection, we suggest using a PEmax of 15.0 as the watershed:

  • PEmax greater than 15.0 indicates that stocks are over-priced; while
  • PEmax below 15.0 presents buying opportunities.

Potential Weaknesses

PEmax has one potential weakness. If S&P 500 earnings are ever exaggerated by an unusual event, to a level that is unlikely to be repeated, potential earnings will be overstated and PEmax understated. Fortunately, that is likely to be a rare occurrence, where earnings for the entire index spike above actual earnings capacity.


PEmax ©, an earnings multiple based on the highest previous four consecutive quarter’s earnings, is a useful comparison of price to future earnings potential. It eliminates many of the distortions traditionally associated with price-earnings multiples, including CAPE. High PEmax values (above 15) suggest poor future performance, while low PEmax values (below 15) correspond with greater investment opportunity.

PEMAX second highest peak in 100 years

I published a chart of PEMAX for the last 30 years on Saturday. PEMAX eliminates the distortion caused by cyclical earnings fluctuations, using the highest earnings to-date rather than current earnings. The idea being that cyclical declines in earnings reflect a fall in capacity utilization rather than a long-term drop in earnings potential.

Since then I have obtained long-term data dating back to 1900 for the S&P 500 and its predecessors, from

PEMAX for November 2017 is 24.34, suggesting that stocks are over-valued.


Outside of the Dotcom bubble, at 32.88, the current value is higher than at any other time in the past century. PEMAX at 24.34 is higher than the peak of 20.19 prior to the 1929 Black Tuesday crash, and higher than the 19.8 peak before Black Monday in 1987.

This does not mean that a crash is imminent but it does warn that investors are paying top-dollar for stocks. And at some point values are going to fall to the point that sanity is restored.

Robert Shiller’s CAPE ratio

Here is Robert Shiller’s CAPE ratio for comparison. CAPE attempts to eliminate distortion from cyclical earnings fluctuations by comparing current index values to the 10-year average of inflation-adjusted earnings.

Shiller CAPE 10 Ratio

While this works reasonably well most of the time, average earnings may be distorted by the severity of losses in the prior 10 years.

You are neither right nor wrong because the crowd disagrees with you. You are right because your data and reasoning are right.

~ Warren Buffett

CAPE v PEMAX: How hot are market valuations?

Robert Shiller’s CAPE ratio is currently at 32.17, the second-highest peak in recorded history. According to, prior to the Black Tuesday crash of 1929 CAPE had a reading of 30. The only peak with a higher reading is the Dotcom bubble at 44.

Shiller CAPE - click to enlarge

Click here to view at

Shiller’s CAPE, or Cyclically Adjusted PE Ratio to give it its full name, compares the current S&P 500 index value to the 10-year average of inflation-adjusted earnings. The aim is to smooth out the earnings cycle and provide a stable assessment of long-term potential earnings.

But earnings have fluctuated wildly in the past 10 years, and a 10-year average which includes severe losses from 2009 may not be an accurate reflection of current earnings potential.

S&P 500 Earnings

The dark line plotted on the above chart reflects the highest earnings to-date, or maximum EPS. The market often references this as the current, long-term earnings potential, in place of cyclical earnings.

The chart below compares maximum EPS (the highest earnings to-date) to the S&P 500 index. The horizontal periods on max EPS reflect when cyclical earnings are falling.

S&P 500 and Peak Earnings

It is clear that the index falls in response to cyclical fluctuations in earnings (the flat periods on EPS max). But it is also clear that earnings quickly recover to new highs after the index has bottomed. In Q1 of 2004 after the Dotcom crash and in Q3 of 2011 after the 2008 global financial crisis.

The next chart plots the current index price divided by maximum earnings to-date. I call it PEMAX. When earnings are making new highs, as at present, PEMAX will reflect the same ratio as for trailing 12-month PE. When earnings are below the previous high, PEMAX is lower than the trailing PE.


What the chart shows is that, outside of the Dotcom bubble, prices are highest in the last 30 years relative to current earnings potential. The current value of 22.56 is higher than at any time other than the surge leading into the Dotcom crash.

The peak value during the Dotcom bubble was 30.19 in Q2 of 1999. The highest value in the lead-up to the GFC was 20.23 in Q4 of 2003.

Does the current value of 22.56 mean that the market is about to crash?

No. The Dotcom bubble went on for two more years after reaching 22.80 in Q3 of 1997. The present run may continue for a while longer.

But it does serve as a reminder to investors that they are paying top-dollar for stocks. And at some point values are going to fall to the point that sanity is restored.

The four most expensive words in the English language are “this time it’s different.”

~ Sir John Templeton

Robert Shiller’s CAPE

I have long held the view that using Robert Shiller’s CAPE to determine whether stocks are under- or over-priced is misleading. Average levels for CAPE have shifted over time, and one cannot rely solely on historic highs and lows as a measure of whether the market is over-bought or over-sold.

So I was interested to learn that Robert Shiller currently maintains 50% of his investment portfolio in stocks. From an interview with Jason Zweig at WSJ:

Today’s level “might be high relative to history,” Prof. Shiller says, “but how do we know that history hasn’t changed?” So, he says, CAPE “has more probability of predicting actual declines or dramatic increases” when the measure is at an “extreme high or extreme low.” ….Today’s level, Prof. Shiller argues, isn’t extreme enough to justify a strong conclusion. So, he says, he and his wife still have about 50% of their portfolio in stocks.

Robert Shiller maintains exposure to stocks | WSJ

Jason Zweig writes:

Many analysts have warned lately that Prof. Shiller’s long-term stock-pricing indicator [CAPE] is dangerously high by historical standards…..If only things were that simple, Prof. Shiller says. “The market is supposed to estimate the value of earnings,” he explains, “but the value of the earnings depends on people’s perception of what they can sell it again for” to other investors. So the long-term average is “highly psychological,” he says. “You can’t derive what it should be.” Even though the CAPE measure looks back to 1871, using data that predates the S&P 500, it is unstable. Over the 30 years ending in 1910, CAPE averaged 17; over the next three decades, 12.7; over the 30 years after that, 15.7. For the past three decades it has averaged 23.4. Today’s level “might be high relative to history,” Prof. Shiller says, “but how do we know that history hasn’t changed?” So, he says, CAPE “has more probability of predicting actual declines or dramatic increases” when the measure is at an “extreme high or extreme low.” …..Today’s level, Prof. Shiller argues, isn’t extreme enough to justify a strong conclusion. So, he says, he and his wife still have about 50% of their portfolio in stocks.

Read more at Robert Shiller on What to Watch in This Wild Market – MoneyBeat – WSJ.

Under What Circumstances Should You Worry That the Stock Market Is “too High”? | Brad DeLong

Brad DeLong discusses Robert Shiller’s CAPE ratio, a stock-price measure he helped develop:

….on average, at a ten-year horizon, for any CAPE ratio below 35 the S&P has delivered average real asset returns pretty much outclassing all other major asset classes…..

Thus you can see why I am relatively unsatisfied with Shiller’s writing:

“In the last century, the CAPE has fluctuated greatly, yet it has consistently reverted to its historical mean–sometimes taking a while to do so….”

Shiller’s rhetoric leads us to focus on graphs like this one of the Campbell-Shiller CAPE, and to think that what goes up must–someday–come down:


But is there any reason to think that the central tendency of the CAPE today is the same as what it was in the 1880s or the 1950s? There is no unchanging machine buried in the earth for the past 120 years throwing dice to determine the CAPE. It would be much better to say that extreme values of the CAPE are followed by reversion not to but toward the previous historical mean. And dividends and earnings shift too. A much better graph than the CAPE graph is the cumulative reinvested return graph [on a log scale]:

Cumulative Reinvested Returns

It goes way up, and way down, but the dominant feature is not mean reversion but rather exponential growth…..

Read more at Under What Circumstances Should You Worry That the Stock Market Is "too High"? | Brad DeLong.

SHILLER: The Market Is At One Of Its Most Expensive Levels Of All Time…| Business Insider

Joe Weisenthal on Yale Professor Robert Shiller’s CAPE pricing model:

So while it’s true that the market is very expensive right now, based on his measure, [Shiller] notes that it’s difficult to use this information to actually time the market. Just because it’s expensive, doesn’t mean it will go down. Furthermore, the market has been expensive based on his measure for the past 20 years excluding the period of the recent crash, which raises the question of whether there’s been some fundamental change to the economy or markets that would warrant higher valuations.

Read more at SHILLER: The Market Is At One Of Its Most Expensive Levels Of All Time, And There's One Thing Can Take It Down | Business Insider.

Robert Shiller: CAPE should not be used for market timing

From an interview with Robert Shiller in January 2013:

Blodget: ….one frustration a lot of people have with the cyclically adjusted P/E and others is that it’s not particularly helpful for the timing mechanism, do you think it’s good to use as a sort of projected 10-year return, where when P/Es are high the return tends to be low, and vice versa?

Shiller: John Campbell, who’s now a professor at Harvard, and I presented our findings first to the Federal Reserve Board in 1996, and we had a regression, showing how the P/E ratio predicts returns. And we had scatter diagrams, showing 10-year subsequent returns against the CAPE, what we call the cyclically adjusted price earnings ratio. And that had a pretty good fit. So I think the bottom line that we were giving – and maybe we didn’t stress or emphasize it enough – was that it’s continual. It’s not a timing mechanism, it doesn’t tell you — and I had the same mistake in my mind, to some extent — Wait until it goes all the way down to a P/E of 7, or something.

Blodget: Right, perfectly safe, so then you can buy.

Shiller: But actually, the lesson there is that if you combine that with a good market diversification algorithm, the important thing is that you never get completely in or completely out of stocks. The lower CAPE is, as it gradually gets lower, you gradually move more and more in. So taking that lesson now, CAPE is high, but it’s not super high. I think it looks like stocks should be a substantial part of a portfolio.

Read more at Robert Shiller On Stocks – Business Insider.

Is the market overpriced? Episode V

In my last post I concluded that the same factors driving rising inequality — new technologies and access to cheap labor through increased globalization — may also be driving a sustainable increase in corporate profits. While we may be understandably wary of “this time is different”, consider the following:

The rise of China as a trading partner over the last two decades.

US Imports from China

Corporate profits at 11% of GNP suggest a new paradigm when compared to the historic (normal) range of 5% to 7%.

Corporate Profits/GNP

The decline in employee compensation as a percentage of corporate value added mirrors the rise in corporate profits.

Employee Compensation/Value Added

And Robert Shiller’s CAPE, normally used to argue that the market is currently overpriced. If we stood in 1994 and looked at the range of CAPE values for the past century, we would no doubt have concluded that a CAPE value greater than 20 indicates the market is overpriced. In the last two decades, the CAPE only briefly dipped below 20 at the height of the global financial crisis. Now pundits argue that a CAPE value greater than 25 indicates the market is overpriced. Something has definitely changed.

Shiller CAPE

Whether the change is sustainable, only time will tell. But one thing is clear. Of the 466 corporations who have so far reported earnings for the first quarter 2014, 77% have either beaten (68%) or met (9%) their estimates. Corporate profits are not in imminent danger of collapse.