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Summary

  • Eliminating earnings volatility, as in Shiller's CAPE, reduces the P/E ratio to shadowing deviations from the long-term moving average of stock prices.
  • Stocks behave contra-cyclically during bull markets, becoming inversely correlated with commodities, inflation, interest rates, and earnings, but in this article, we will consider earnings volatility itself, from a few perspectives.
  • Medium-term (five- to ten- year) fluctuations in stock prices seem to be partially predicted by fluctuations in earnings volatility, although it is not especially clear how or why.
  • Based on an extrapolation from the historical relationship between P/E, earnings, and stocks, it appears that a stock market boom will continue until the conclusion of the decade.

Although earnings have tended to grow at a relatively constant rate over the last five or six decades, over the short run, they tend to be relatively volatile. When Shiller's CAPE smooths out earnings, this has two effects. The obvious one is that it eliminates the short-term volatility of earnings. Less obviously, it reduces earnings to playing something like a long-term moving average of share prices. Compare, for example, CAPE with the real S&P 500 index divided by its twenty-year moving average. There is very little difference in the two, and using the deviation from the moving average has only been slightly less predictive of future returns than has CAPE. The question then inevitably arises: when earnings volatility is stripped out, how much value is being added to market analysis?

(click to enlarge)CAPE vs Deviations from moving average of stock prices 1871-2013

(Sources: All charts in this article come from calculations from the data graciously provided by Robert Shiller on his website).

In my previous article, as well as in articles I wrote last year, I pointed out that bull markets are typically contra-cyclical ("counter-cyclical" sounds too much like monetary or fiscal policy), while bear markets are highly cyclical. That is, in a bear market, stocks (SPY,DIA,QQQ) tend to be positively correlated with commodities (GSG,DJP,RJA), inflation, earnings, and interest rates (UST,IEF), but in a bull market, stocks are negatively correlated with these factors.

(click to enlarge)Bull markets vs correlation between stock fluctuations and earnings fluctuations 1871-2013 In this chart, you can see that during bull markets, annual changes in stocks become, not only disengaged from earnings, but inversely correlated with changes in earnings. (In fact, that stock prices become inversely correlated rather than merely indifferent suggests that we cannot simply attribute these rallies to "optimism" as a recent headline suggested, but that is a whole different article).

The interesting thing about the current market is that it appears to have transitioned from a post-crisis bear rally (2009-2011) to a proper bull market (2011-?) in much the same way that the market did in the early 1920s. Ninety years ago, the market shifted from a bear rally in 1922-1924 to a bull market that lasted until the fall of 1929. Those transition years, 2011 and 1924, respectively, also saw the last hurrahs of a commodity boom, as well as political and economic crises abroad. The initial crises of 2009 and 1921 were also experienced as brief but very sharp earnings collapses that manifested themselves, somewhat unusually, as P/E expansions.

Shiller's Cyclically-Adjusted Price/Earnings ratio, just like it says on the tin, denudes the P/E ratio of these cyclical distractions.

(click to enlarge)CAPE vs raw P/E 1871-2013

My hunch is that cycles (i.e., short-term fluctuations) contain important information about the market. The cyclical/contra-cyclical modes in the market already strongly suggest that, but in this article, I wanted to investigate two interrelated questions, one general and one specific:

1. What insights do we lose when we smooth out earnings?

2. What might earnings volatility be saying about the present market?

My answer to the first question is that, over the five- and ten-year ranges, earnings volatility seems to contain important information about future returns. And, in answer to the second question, I believe that the first answer suggests that the parallels with the 1920s are not merely coincidence: earnings volatility would seem to be indicating a strong bull market until the conclusion of the decade. In other words, there seems to be something about a temporary, severe earnings shock that reflects or creates conditions consonant with a raging bull market; that is, a bull market that exhibits all of the contra-cyclical behavior listed above.

All of these observations raise difficult questions, unfortunately. What accounts not only for contra-cyclicality but changes from contra-cyclicality to cyclicality and back? Why would the severity and brevity of an earnings shock appear to result in earnings growth in the short-term but P/E expansion in the medium? Is "earnings volatility" really the right way to frame the phenomenon, or is there something else going on?

Let's not wander into those thickets quite yet, though.

P/E Ratios and Earnings Growth

Instead, let's begin with a more basic question about CAPE and its theoretical underpinnings. Investors buy shares to gain access to future profits. Shiller points out, however, that CAPE and future returns are inversely correlated. The inverse correlation shows that investors have unrealistic expectations about future earnings growth, which is why they should be smoothing out the earnings cycle in the first place.

But, why not ask how well P/E ratios predict earnings growth, rather than just returns? After all, if fluctuations in returns are driven primarily by share price movements (which they are), then wouldn't a negative correlation between CAPE and returns simply indicate that investors are not good at predicting share prices or that they do not care about stock prices as much as we think they do or should?

I was surprised by what I found when I ran the correlations between CAPE and raw P/E (that is, P/E calculated using concurrent earnings) against earnings and returns over three-, five-, ten-, and seventeen-year periods. (I threw the three- and seventeen-year comparisons into the mix randomly). As you can see in the table below, CAPE is negatively correlated with returns over the short-, medium-, and long-term. So is raw P/E, although the relationship is clearly weaker and less uniform. Raw P/E, however, does a fair job of predicting future earnings growth, whereas CAPE does not have any relationship with subsequent earnings.

Subsequent returns and earnings growth (1871-2013)P/E (raw)CAPE (P/E10)

S&P 500 deviation from 20-year moving average (inflation adjusted)

3-year returns-0.09-0.36-0.30
3-year earnings growth+0.54-0.15n/a
5-year returns-0.22-0.42-0.37
5-year earnings growth+0.29-0.13n/a
10-year returns-0.39-0.47-0.45
10-year earnings growth+0.23-0.05n/a
17-year returns-0.30-0.46-0.46
17-year earnings growth+0.38+0.08n/a

The first thing worth noticing is the gap between how well P/E ratios of whatever stripe predict returns and how well they predict earnings. Why might raw P/E be negatively correlated with returns but positively correlated with earnings, for example? I think the second chart in the article already suggests why that might be, but we can compare ten-year returns and ten-year earnings growth to make sure.

(click to enlarge)Ten-year earnings growth and stock returns 1871-2013(click to enlarge)Earnings and return rates at ten-year intervals, 1871-2013

From the late 1950s, returns and earnings tend to both be positive but also inversely correlated with one another, at least until the earnings collapse of 2008-2009. If earnings collapse, stocks tend to be highly correlated with them, but if earnings growth is positive, stocks will inversely correlate with the trend of earnings. It would seem that the stock market fears high profit growth and collapses in profits and thrives on an odd combination of positive but declining earnings growth.

I was even more surprised, however, when I compared raw P/E with earnings growth over the subsequent ten-year period in the chart below. The correlation coefficient in the table above doesn't really seem to tell the whole story.

(click to enlarge)P/E vs subsequent ten-year earnings growth 1871-2023

P/E has predicted earnings growth surprisingly well in the last half-century, except for the earnings growth of the 2000s, when there appears to have been a strong inverse correlation. If you then overlay subsequent stock market returns, it appears that P/E is positively correlated with subsequent earnings growth only during bull markets, and is negatively correlated during bear markets.

(click to enlarge)P/E vs subsequent earnings and returns 1871-2013

In other words, it appears that P/E correlates with subsequent earnings growth only if there is a subsequent bull market. If you take a rolling correlation between P/E and subsequent earnings growth and index returns, it appears to confirm that relationship.

(click to enlarge)Running correlation between P/E and subsequent earnings growth versus subsequent returns 1871-2013(click to enlarge)correlation between P/E and subsequent earnings growth vs subsequent returns at five-year intervals 1871-2013

How on earth could that be?

It might be mere coincidence, but because of the connection represented in the second chart in this article (the relationship between bull markets and cyclicality/contra-cyclicality) and the problem represented in the following two charts, it occurred to me that this relationship between P/E, earnings growth, and returns might mean something.

So, we have to return for a moment to that second chart. Because bull markets are contra-cyclical (share prices and earnings are negatively correlated) and bear markets are cyclical (the two are positively correlated) and, at least over the last century, bull and bear markets coincide with expansion and contraction of the P/E multiple, we can condense this relationship into "earnings beta," which is the product of the correlation between earnings and stock price changes and the relative volatility of earnings (the standard deviation of changes in earnings divided by the same for share prices).

The problem with the relationship between earnings beta and market returns was that, over the very long run, it appeared to be positively correlated with stock market expansions and contractions, but after World War II, it appeared that it might be predicting five-year returns. Because I first observed the relationship as a backward-looking one rather than a predictive one, I opted for the former interpretation, but the latter was troubling, because the extreme levels of the measure indicated either that we had been through a very bad bear market or that we were about to go through one that might be worse than that of the 2000s.

(click to enlarge)earnings beta vs concurrent stock market performance 1871-2013(click to enlarge)Earnings beta vs subsequent stock returns 1946-2013But, since P/E predicts earnings growth only when a bull market follows, it occurred to me that the correlation coefficient and relative volatility might be talking about different if related things.

Earnings Volatility and Earnings Growth

Think about the collapse of earnings in 2009 and what subsequent ten-year earnings will look like. Earnings fell something like 85% year-on-year, but they quickly reverted to their post-World War II trajectory. If earnings remain perfectly flat over the next five years (that is, until the spring of 2019), it is mathematically inevitable that the ten-year growth rate in earnings will peak in March 2019 at 30% annualized growth, which is double the historic peak. Or, imagine that earnings fall immediately from their December 2013 $100.2 level to the December 2003 level of $48.74 and remain there until 2019. Ten-year earnings growth will still peak at 20% per annum, comfortably above every other ten-year period's growth rate.

(click to enlarge)what earnings growth will look like if they revert to 2003 levels from 2014-2023(click to enlarge)projecting earnings growth rate if earnings remain flat from 2013-2023

Unless earnings achieve an exceptionally pitiable level precisely in the Spring of 2019 or achieve absolutely otherworldly growth before then, there is a very high probability that the P/E ratio of the 2000s will be highly correlated with subsequent earnings growth for the current decade. If that is the case, based on historical extrapolation, we can infer that the 2010s will be a period of exceptional stock returns.

Really? Is that a remotely rational conclusion? There are only two possible explanations for why this connection between P/E, subsequent earnings growth, and stock returns could make any sense: either it is pure coincidence or earnings volatility bears information about the future direction of the market not captured by CAPE.

A slightly less hocus-pocus demonstration of this relationship between P/E and earnings is represented in the two charts below. Rather than comparing the correlation between P/E and future earnings growth with future returns, they compare the correlation between P/E and concurrent earnings growth with future returns. And, in this instance, the relationship is the opposite: a negative correlation between P/E and historical earnings growth over the five- and ten-year spans does a fair job of predicting subsequent returns. The correlations between P/E and earnings growth, whether subsequent or concurrent tend to be a little above 0.4 or below -0.4, respectively. Earnings volatility appears to be communicating something.

(click to enlarge)Correlation between concurrent P/E and earnings growth vs subsequent stock returns 1871-2013

A connection between volatility and subsequent returns would leave us with some knotty problems. First, it implies that the level of earnings volatility is more important than the direction of that volatility. That is, it does not matter whether earnings shocks are positive or negative; as long as they are volatile, it would seem to be good for stocks in the not too distant future. (An earnings shock such as the one in 2009 would be disastrous in the short run but wonderful in the medium for stocks). Second, whether there is a positive or negative shock to earnings, if we can assume that stocks will go into bull mode in relatively short order, we can also assume (again, especially since 1913) that P/E will expand and stock fluctuations will inversely correlate with earnings fluctuations (again, see the second chart in the article). In other words, a rebound from a negative shock to earnings (as in 2009) will primarily redound to the greater glory of stocks, not earnings.

In the following charts, you can see the relationship between the log of the relative volatility of earnings to subsequent five- and ten-year returns. The correlations are positive but very weak (just shy of 0.2), but I think our eyes do not mislead us by suggesting that earnings volatility plays some sort of role.

(click to enlarge)relative earnings volatility vs subsequent five year returns 1871-2013(click to enlarge)relative earnings volatility vs subsequent ten-year returnsIf we compare the relative volatility of earnings with the rolling correlation between P/E and subsequent earnings growth, there is a relationship, but there is something else going on, too. There is a breakdown of some kind as earnings have become more and more volatile over the last four or five decades.

(click to enlarge)relative earnings volatility versus P/E correlation with subsequent earnings growth

Volatility certainly cannot explain everything, then. I suspect, however, that there is a relationship between volatility and the progression of the correlation between earnings and share price fluctuations (the relationship in the first chart and the earnings beta measure) that I am not fully grasping, perhaps due to my feeble mathematical imagination. Perhaps the P/E ratio itself contains information that is not captured by either earnings volatility or CAPE contains individually.

Skipping the Math

Instead of reducing all of this to a single mathematical variable, then, perhaps we can try a narrative approach. I am imagining a process such as the following one, with each stage lasting something like five to ten years:

1. A bear market. Stocks are increasingly correlated with earnings; earnings are also becoming more and more volatile.

2. A bull in bear's clothing. Earnings become extremely volatile due to the inevitable crisis, stocks decouple from earnings (as well as interest rates, inflation, and commodities).

3. Raging bull. Stocks are now strongly inversely correlated with earnings (and interest rates, inflation, and commodities). Earnings volatility falls relative to stocks.

At the very end of the third stage, a switch occurs: earnings accelerate, but so do stocks. That is essentially the end of low earnings volatility and the contra-cyclical relationships. Back to stage one.

In this narrative guise, I think my summary of the unfolding of stock market supercycles is not all that different from Shiller's description of particular episodes of market history in Irrational Exuberance. He notes, for example, the eerily steady earnings growth of the late 1990s. But, there are also important qualitative differences between the interpretations implied by an approach which focuses on earnings volatility and one that excludes that volatility.

For one, the first approach deemphasizes the absolute level of the P/E ratio, whereas the relationship between CAPE and returns is entirely a function of the absolute level of the ratio. I think the former approach, although still theoretically and mathematically embryonic, allows greater flexibility in terms of market analysis and goes some way towards explaining why P/E has bottomed at a relatively high level in the current cycle and may give us some indication of gauging when this market will peak.

Intermediate corrections aside, this market looks set to be bullish over the remainder of the decade. The extreme market volatility that only ended in 2011 suggests that there are at least a few more years to go, and the low correlation between stock fluctuations and earnings fluctuations also suggests that this bull market has not fully matured as of yet.

So, how should we think about the relationship between earnings and the market? There are so many ways to look at the relationships discussed here. Let me see if I can recast these relationships somewhat with a single chart. It will not be especially simple, but perhaps it will put the relationship between earnings growth, volatility, and returns in a more straightforward way.

A Bird's Eye View of Earnings and the Market Since 1871

In the following chart, we will take a look again at the relationship between P/E, concurrent earnings growth, and concurrent stock market performance. I have also inverted P/E and stock returns to highlight the critical relationships. Above, we noted that an inverse correlation between concurrent earnings growth and P/E implied a bull market in the following five to ten years, but I want to shift the focus a little.

There are a few features that should be immediately recognizable from the beginning of the discussion. First, that P/E tends to be highly correlated with returns only after World War II (as well as in 1924-1930, but not 2008-2011), reflective of the market's modern tendency for P/E to be driven by multiple expansion rather than changes in earnings. At the same time, we can see that earnings growth has increasingly tended to be inversely correlated with both stock prices and the P/E multiple (note: because the scale for stock returns and P/E is inverted, this will appear as a positive correlation), although earnings since World War II are more consistently positive over the long term (at least until the 2000s).

(click to enlarge)Earnings growth, stock market performance, and P/E 1871-2013

Beyond that, however, is the relationship between peaks in earnings growth and changes in stock market performance. You might notice that peaks in earnings growth often roughly coincide with changes in the direction of the stock market, especially stock market peaks, even though annualized changes in stocks and earnings tend to be inversely correlated, especially during bull markets!

Earnings peaked in 1906, roughly around the same time as stocks. Late in the Roaring '20s, earnings growth spiked upwards again, peaking in 1931 (due to the 1921 collapse in earnings). The 1959 peak in stock return growth was led by the peak in earnings growth a few months earlier. In 1997, earnings growth peaked again, a few years before the top in the market.

As discussed in a previous section of the article, we already know (as much as anything can be known about the future) that earnings growth will peak in 2019 at a historically high level, probably twice the 1950s peak.

What is less noticeable perhaps is that earnings growth also peaks after the conclusion of bear markets, however. Stocks bottomed in 2009 but earnings topped out in 2012. In 1974, stocks bottomed; earnings peaked in 1981. In 1939, stocks bottomed, and earnings peaked in 1943. Stocks bottomed in 1921, earnings peaked in 1924. With the exception of the 1981 peak, most earnings peaks were due to violent earnings recoveries.

If you look at the 10% line on the earnings growth axis, you can see that peaks in earnings growth seem to be tied more to changes in long-term stock market direction than either the peaks or troughs of the stock market itself. The difference seems to be one of a difference in timing and volatility.

What about the market of the current decade of the 2010s? CAPE is too blunt an instrument to say anything especially reliable about such a specific time frame, but the timing and volatility of changes in earnings and share prices suggests that a significant P/E expansion during a stock market collapse is the formula for exceptional medium-term (five- to ten-year) gains. Perhaps the single most interesting thing about this chart is that market bottoms concluded with often very high P/E ratios (1894, 1921, 1939, 1946, and 2009). The only one that did not was the 1974 bottom. Prior to the 1960s, almost every instance of P/E peaking above 20 was during a market bottom. The 1920s were uncharacteristically modern insofar as P/E was raised to the 20-level primarily by surging stock market prices rather than falling earnings. It was only in the 1960s and 1990s that this 1920s pattern was to be repeated. In 2009, the market reverted to the form it took back when long-term earnings lacked the implicit growth guarantees.

Conclusion

Fluctuations in the volatility of earnings seem to be intimately linked to stock market performance. Within the context of the cyclical and contra-cyclical behavior of the market relative to inflation, interest rates, and commodity prices, as well as earnings, greater precision in predicting markets may be possible by focusing on the relationship between cyclicality and secular trends. Until a greater understanding of these relationships can be pieced together, I would summarize the current situation in the following way:

We had not experienced an earnings shock such as the one we had five years ago for eighty years. History seems to suggest that they are followed by stock market booms that last not much longer than a decade. As the boom unfolds, the statistical rebound in earnings growth tends to peak with the market, even as the annualized fluctuations in earnings and stock prices become increasingly inversely correlated. By that point, the absolute level of P/E, by any measure, will probably be even higher than it is now. An end to the stock boom sometime around the end of the decade does not seem improbable.

Source: CAPE, Earnings Volatility And Stock Returns: 1871-2019