Who’s Afraid of 1929?

Earlier this year, the market was bombarded with a series of stupid charts comparing 2014 to 1929.  As happens with all incorrect predictions, the prediction that 2014 was going to unfold as a replay of 1929 has quietly faded, without a follow-up from its prognosticators. Here’s to hoping that we’ll eventually get an update ;-)

Most people think that 1929 was an inopportune time to invest–and, cyclically, it was. Recession represented a real risk as far back as 1928, when the Federal Reserve aggressively hiked the discount rate and sold three quarters of its stock of government securities in an effort to ward off a feared stock market “bubble.”  By early 1929, the classic sign of an inappropriately tight monetary policy–an inverted yield curve–was well in place (FRED).


In the months after the crash, as it became clear that the economy was in recession, the Fed took action to ease monetary conditions.  Unfortunately, in 1930, a misguided story began to gain traction among policymakers that the previous expansion had been driven by “malinvestment”, and that the economy would not be able to sustainably recover until the malinvestment was liquidated.  This story led the Fed to shift to a notoriously tight monetary stance, particularly with respect to banks facing funding strains, to whom the Fed refused to emergency-lend.  The ensuing effects on the economy, from the panic of 1930 until FDR’s banking holiday in the spring of 1933, are well-known history.

On the valuation front, 1929 also seemed like an inopportune time to invest.  Profit margins (FRED) were at record highs relative to subsequent data.  We don’t have reliable data for profit margins prior to 1929, but they had probably been higher in the late 1910s.  Still, they were very high in 1929, much higher than they’ve ever been since:


The Shiller CAPE, had gone parabolic, to never-before-seen values north of 30.  The simple PE ratio, at around 20, was at a less extreme value, but still significantly elevated.


In hindsight, valuation wasn’t the real problem in 1929, just as it wasn’t the real problem in 2007.  The real problem was downward economic momentum and a reflexive, self-feeding financial panic.  The panic was successfully arrested in the fall of 2008 by the Fed’s efforts to stabilize the banking system, and exacerbated in the fall of 1930 by the Fed’s decision to walk away and let the banking system implode on itself.

For all of the maligning of the market’s valuation in 1929, the subsequent long-term total return that it produced was actually surprisingly strong.  The habit is to evaluate market performance in terms of the subsequent 10 year return, which, for 1929, was a lousy -1% real.  But the choice of 10 years as a time horizon is arbitrary and unfair.  Growth in the 1930s was marred by economic mismanagement, and the terminal point for the period, 1939, coincided with Hitler’s invasion of Poland and the official outbreak of World War 2–a weak period for global equity market valuations.  A better time horizon to use is 30 years, which dilutes the depressed growth performance of 1929-1939 with two other decades of data and puts the terminal point for the period at 1959, a period characterized by a more favorable valuation environment.  The following chart shows subsequent 30 year real total returns for the S&P 500 from 1911 to 1984:


Surprisingly, a long-term investor that bought the market in November 1929, immediately after the first drop, did better than a long-term investor that bought the market in September 1980. For perspective, the market’s valuation in November 1929, as measured by the CAPE, was 21.  Its valuation in September 1980 was 9.  Measured in terms of the Q-Ratio (market value to net worth), the valuation difference was even more extreme: 1.21 versus 0.39.

Why did the November 1929 market produce better subsequent long-term returns than the market of September 1980, despite dramatically higher starting valuations?  You might want to blame higher terminal valuations–but don’t try.  The CAPE in 1959, 30 years after 1929, was actually lower than in 2010, 30 years after 1980: 18 versus 20.  The Q-Ratio was also lower: 0.64 versus 0.84.

Ultimately, the outperformance was driven by three factors: (1) stronger corporate performance (real EPS growth given the reinvestment rate was above average from 1929-1959, and below average from 1980-2010), (2) dividends reinvested at more attractive valuations (which were much cheaper, on average, from 1929-1959 than from 1980-2010), and (3) shortcomings in the CAPE and Q-Ratio as valuation metrics (1929 and 2010 were not as expensive as these metrics depicted.)

It’s also interesting to look at the total return in excess of the risk-free rate, which is the only sound way to evaluate returns when making concrete investment decisions (not just “what can stocks get me”, but “what can they get me relative to what I can easily get by simply holding the currency, risk-free.”)  The following chart shows the nominal 30 year total return of the S&P 500 minus the nominal 30 year total return of rolled 3 month treasury bills, from 1911 to 1984:


Surprisingly, the market of September 1929, which had a CAPE of 32 and a Q-Ratio of 1.59, outperformed the market of January 1982, which had a CAPE of 7 and a Q-Ratio of 0.31. 

The next time you see a heightened CAPE or Q-Ratio flaunted as a reason for abandoning a disciplined buy-and-hold strategy, it may help to remember the example of 1929–how it astonishingly outperformed 1982, otherwise considered to be the greatest buying opportunity of our generation.  The familiar lesson of 1929 is that you should avoid investing in recessionary environments where monetary policy is inappropriately tight, but there is another, forgotten lesson to be learned: that valuation is an imperfect tool for estimating long-term future returns. In the realm of long-term investment decision-making, it is not the only consideration that matters: the future path of risk-free interest rates matters just as much, if not more.

It seems that Irving Fisher may have been right after all, despite his inopportune timing. From September 12th, 1929:


In an ironic twist of fate, as we’ve moved forward from the crisis, the Irving Fishers of 2007-2008 have come to look more and more credible, despite their ill-timed bullishness, while the permabears who allegedly “called the crash” have been exposed as the beneficiaries of broken-clock luck.

The true speculative winners, of course, were those who managed to quickly process and appreciate the stabilizing efficacy of the Fed’s emergency interventions in late 2008 and early 2009, and who foresaw and embraced the subsequent drivers of the new bull market, as they became more evident: (1) unexpectedly strong earnings performance, driven by aggressive cost-cutting, made possible by significant technology-fueled productivity gains, that would go on to withstand the strains of a weak recovery and the feared possibility of profit margin deterioration, and (2) a low-inflation, low-growth goldilocks scenario in the larger economy that would allow for a highly accomodative Fed whose low interest rate policies would eventually give way to a T.I.N.A. yield chase.  The “story” of the bull market has been the battle between these bullish drivers and the bearish psychological residue of 2008–the caution and hesitation to take risk, driven by lingering fears of a repeat, that has prevented investors from going “all in”, at least until recently.

As for the future, the speculative spoils from here forward will go to whoever manages to correctly anticipate–or at least quickly react to–the forces that might reverse the trend of strong earnings and historically easy monetary policy, if or when they finally arrive.

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A Critique of John Hussman’s Chart of Estimated Future Equity Returns

Of all the arguments for a significantly bearish outlook, I find John Hussman’s chart of estimated future equity returns, shown below, to be among the most compelling.  I’ve spent a lot of time trying to figure out what is going on with this chart, trying to understand how it is able to accurately predict returns on a point-to-point basis.  I’m pretty confident that I’ve found the answer, and it’s quite interesting.  In what follows, I’m going to share it.


The Prediction Model

In a weekly comment from February of last year, John explained the return forecasting model that he uses to generate the chart.  The basic concept is to separate Total Return into two sources: Dividend Return and Price Return.

(1) Total Return = Dividend Return + Price Return

The model approximates the future Dividend Return as the present dividend yield.

(2) Dividend Return = Dividend Yield

The model uses the following complicated equation to approximate the future price return,

(3) Price Return = (1 + g) * (Mean_V/Present_V) ^ (1/t) – 1

The terms in (3) are defined as follows:

  • g is the historical nominal average annual growth rate of per-share fundamentals–revenues, book values, earnings, and so on–which is what the nominal annual Price Return would be if valuations were to stay constant over the period.
  • Present_V is the market’s present valuation as measured by some preferred valuation metric: the Shiller CAPE, Market Cap to GDP, the Q-Ratio, etc.
  • Mean_V is the average historical value of the preferred valuation metric.
  • t is the time horizon over which returns are being forecasted.

Assuming that valuations are not going to stay constant, but are instead going to revert to the mean over the period, the Price Return will equal g adjusted to reflect the boost or drag of the mean-reversion.  The term (Mean_V/Present_V) ^ (1/t) in the equation accomplishes the adjustment.

Adding the Dividend Return to the Price Return, we get the model’s basic equation:

(4) Total Return = Dividend Yield + (1 + g) * (Mean_V/Present_V) ^ (1/t) – 1

John typically uses the equation to make estimates over a time horizon t of 10 years.  He also uses 6.3% for g.  The equation becomes:

Total Return = Dividend Yield + 1.063 * (Mean_V/Present_V) ^ (1/10) – 1

To illustrate how the model works, let’s apply the Shiller CAPE to it.  With the S&P 500 around 1950, the present value of the Shiller CAPE is 26.5.  The historical (geometric) mean, dating back to 1947 is 17.  The market’s present dividend yield is 1.86%.  So the predicted nominal 10 year total return is: .0186 + 1.063 * (17/26.5)^(1/10) – 1 = 3.5% per year.

Interestingly, when the Shiller CAPE is used in John’s model, the current market gets doubly penalized.  The present dividend payout ratio of 35% is significantly below the historical average of 50%.  If the historical average payout ratio were presently in place, the dividend yield would be 2.7%, not 1.86%.  Of course, the lost dividend return is currently being traded for growth, which is higher than it would be under a higher dividend payout ratio.  But the higher growth is not reflected anywhere in the model–the constant g, 6.3%, remains unchanged.  At the same time, the higher growth causes the Shiller CAPE to get distorted upward relative to the past, for reasons discussed in an earlier piece on the problems with the Shiller CAPE.  But the model makes no adjustment to account for the upward distortion.  The combined effect of both errors is easily worth at least a percent in annual total return.

In place of the Shiller CAPE, we can also apply the Market Cap to GDP metric to the model. The present value of Market Cap to GDP is roughly 1.30.  The historical (geometric) mean, dating back to 1951, is 0.64.  So the predicted nominal 10 year total return is: .0186 + 1.063 * (0.64/1.30) ^ (1/10) – 1 = 0.9% per year.  Note that Market Cap to GDP is currently being distorted by the same increase in foreign profit share that’s distorting CPATAX/GDP.  As I explained in a previous piece, GDP is not an accurate proxy for the sales of U.S. national corporations.

Finally, we can apply the Q-Ratio–the market value of all non-financial corporations divided by their aggregate net worth–to the model.  The present value of the Q-Ratio is 1.16.  The historical mean value is .61.  So the predicted nominal return over the next 10 years is: 0.185 + 1.063 * (0.65/1.16) ^ (1/10) – 1 = 2.1% per year.  Note that the Q-Ratio, as constructed, doesn’t include the financial sector, which is by far the cheapest sector in the market right now.  If you include the financial sector in the calculation of the Q-Ratio, the estimated return rises to 2.8% per year.

Charting the Predicted and Actual Returns

In a piece from March of last year, John applied a number of different valuation metrics to the model, producing the following chart of predicted and actual returns:


In March of this year he posted an updated version of the chart that shows the model’s predictions for 7 different valuation metrics:


As you can see, over history, the correlations between the predicted returns and the actual returns have been very strong.  The different valuation metrics seem to be speaking together in unison, forecasting extremely low returns for the market over the next 10 years.  A number of analysts and commentators have cited the chart as evidence of the market’s extreme overvaluation, to include the CEO of Business Insider, Henry Blodget.

In a piece written in December, I argued that the chart was a “curve-fit”–an exploitation of coincidental patterning in the historical data set that was unlikely to repeat going forward. My skepticism was grounded in the fact that the chart purported to correlate valuation with nominal returns, unadjusted for inflation.  Most of the respected thinkers that write on valuation–for example, Andrew Smithers, Jeremy Grantham, and James Montier–assert a relationship between valuation and real returns, not nominal returns. They treat changes in the price index as noise and remove it from the analysis. But John doesn’t–he keeps inflation in the analysis–and is somehow able to produce a tight fit in spite of it.

Interestingly, the valuation metrics in question actually correlate better with nominal 10 year returns than they do with real 10 year returns.  That doesn’t make sense.  The ability of a valuation metric to predict future returns should not be improved by the addition of noise.


Using insights discussed in the prior piece, I’m now in a position to offer a more specific and compelling challenge to John’s chart.  I believe that I’ve discovered the exact phenomenon in the chart that is driving the illusion of accurate prediction.  I’m now going to flesh that phenomenon out in detail.

Three Sources of Error: Dividends, Growth, Valuation

There are three expected sources of error in John’s model.  First, over 10 year periods in history, the dividend’s contribution to total return has not always equaled the starting dividend yield.  Second, the nominal growth rate of per-share fundamentals has not always equaled 6.3%.  Third, valuations have not always reverted to the mean.

We will now explore each of these errors in detail.  Note that the mathematical convention we will use to define “error” will be “actual result minus model-predicted result.”  A positive error means reality overshot the model; a negative error means the model overshot reality.  Generally, whatever is shown in blue on a graph will be model-related, whatever is shown in red will be reality-related.

(1) Dividend Error

The following chart shows the starting dividend yield and the actual annual total return contribution from the reinvested dividend over the subsequent 10 year period.  The chart begins in 1935 and ends in 2004, the last year for which subsequent 10 year return data is available:


(Details: We approximate the total return contribution from the reinvested dividend by subtracting the annual 10 year returns of the S&P 500 price index from the annual 10 year returns of the S&P 500 total return index.  The difference between the returns of the two indices just is the reinvested dividend’s contribution.)

There are two main drivers of the dividend error.  First, the determinants of future dividends–earnings growth rates and dividend payout ratios–have been highly variable across history, even when averaged over 10 year periods.  The starting dividend yield does not capture their variability.  Second, dividends are reinvested at prevailing market valuations, which have varied dramatically across different bull and bear market cycles. As I illustrated in a previous piece, the valuation at which dividends are reinvested determines the rate at which they compound, and therefore significantly impacts the total return.

(2) Growth Error

Even when long time horizons are used, the nominal growth rate of per-share fundamentals–revenues, book values, and smoothed earnings–frequently ends up not being equal the model’s 6.3% assumption.  As an illustration, the following chart shows the actual nominal growth rate of smoothed earnings (Robert Shiller’s 10 year EPS average, which is the “fundamental” in the Shiller CAPE) from 1935 to 2004:


As you can see in the chart, there is huge variability in the average growth across different 10 year periods.  From 1972 to 1982, for example, the growth exceeded 10% per year. From 1982 to 1992, the growth was less than 3% per year. Part of the reason that the variability is so high is that the analysis is a nominal analysis, unadjusted for inflation. Inflation is a significant driver of earnings growth, and has varied substantially across different periods of market history.

(3) Valuation Error

Needless to say, valuation metrics frequently end 10 year periods far away from their means.  Anytime this happens, the model will produce an error, because it assumes that mean-reversion will have occurred by the end of the period.

The following chart shows the Shiller CAPE from 1935 to 2014:


As you can see, the metric frequently lands at values far away from 17, the presumed mean.  Every time that occurs at the end of a 10 year period, the predicted returns and the actual returns should deviate, because the predictions are being made on the basis of a mean-reversion that doesn’t actually happen.

Now, using a long time horizon–for example, 10 years–spreads out the the valuation error over time, and therefore reduces its annual magnitude.  But even with this reduction, the annual error is still quite significant. The following chart shows what the S&P 500 annual price return actually was (red) over 10 year periods, alongside what it would have been (blue) if the Shiller CAPE had mean-reverted to 17 over those periods.


The difference between the two lines is the model’s valuation error.  As you can see, it’s a very large error–worth north of 10% per year in some periods–particularly in periods after 1960.

Of the three types of errors, the largest is the valuation error, which has fluctuated between plus and minus 10%.  The second largest is the growth error, which has fluctuated between plus and minus 4%.  The smallest is the dividend error, which has fluctuated between plus and minus 2%. As we saw in the previous piece, growth and dividends are fungible and inversely related. From here forward, we’re going to sum their errors together, and compare the sum to the larger valuation error.

Plotting the Errors Alongside Each Other

The following chart is a reproduction of the model from 1935 to 2014 using the Shiller CAPE:


The correlation between predicted returns and actual returns is 0.813.  Note that John is able to push this correlation above 0.90 by applying a profit margin adjustment to the equation.  Unfortunately, I don’t have access to S&P 500 sales data prior to the mid 1960s, and so am unable to replicate the adjustment.

To see what is happening to produce the attractive fit, we need to plot the errors in the model alongside each other.  The following chart shows the sum of the growth and dividend errors (green) alongside the valuation error (purple) from 1935 to 2004 (the last year for which actual subsequent 10 year return data is available):


Now, look closely at the errors.  Notice that they are out of phase with each other, and that they roughly cancel each other out, at least in the period up to the mid 1980s, which–not coincidentally–is the period in which the model produces a tight fit.


The following chart shows the errors alongside the predicted and actual returns:


Again, look closely.  Notice that whenever the sum of the errors (the green and purple lines) is positive, the actual return (the red line) ends up being greater than the predicted return (the blue line). Conversely, whenever the sum of the errors (the green and purple lines) is negative, the actual return (the red line) ends up being less than the predicted return (the blue line).  For most of the chart, the sum of the errors is small, even though the individual errors themselves are not. That’s precisely why the model’s predictions are able to line up well with the actual results, even though the model’s underlying assumptions are frequently and significantly incorrect.

For proof that we are properly modeling the errors, the following chart shows the difference between the actual and predicted returns and the sum of the individual error terms.  The two lines land almost perfectly on top of each other, as they should.


I won’t pain the reader with additional charts, but suffice it to say that all of the 7 metrics in the chart shown earlier, reprinted below, exhibit this same error cancellation phenomenon. Without the error cancellation, none of the predictions would track well with the actual results.


In hindsight, we should not be surprised to find that the fit in the chart is driven by error cancellation.  The assumptions that annual growth will equal 6.3% and that valuations will revert to their historical means by the end of every sampling period are frequently wrong by huge amounts.  Logically, the only way that a model based on these inaccurate assumptions can make accurate return predictions is if the errors cancel each other out.

Testing for a Curve-Fit: Changing the Time Horizon

Now, before we conclude that the chart and the model are “curve-fits”–exploitations of superficial coincidences in the studied historical period that cannot be relied upon to recur or repeat in the data going forward–we need to entertain the possibility that the cancellations actually do reflect real fundamental relationships.  If they do, then the cancellations will likely continue to occur going forward, which will allow the model to continue to make accurate predictions, despite the inaccuracies in its underlying assumptions.

As it turns out, there is an easy way to test whether or not the chart and the model are curve-fits: just expand the time horizon.  If a valuation metric can predict returns on a 10 year horizon, it should be able to predict returns on, say, a 30 year horizon.  A 30 year horizon, after all, is just three 10 year horizons in series–back to back to back.  Indeed, each data point on a 30 year horizon provides a broader sampling of history and therefore achieves a greater dilution of the outliers that drive errors.  A 30 year horizon should therefore produce a tighter correlation than the correlation produced by a 10 year horizon.

The following chart shows the model’s predicted and actual returns using the Shiller CAPE on a 30 year prediction horizon rather than a 10 year prediction horizon.

30 yr

As you can see, the chart devolves into a mess.  The correlation falls from an attractive 0.813 to an abysmal 0.222–the exact opposite of what should happen, given that the outliers driving the errors are being diluted to a greater extent on the 30 year horizon. Granted, the peak deviation between predicted and actual is only around 4%–but that’s 4% per year over 30 years, a truly massive deviation, worth roughly 225% in additional total return.

The following chart plots the error terms on the 30 year horizon:


Crucially, the errors no longer offset each other.  That’s why the fit breaks down.


Now, as a forecasting horizon, the choice of 30 years is just as arbitrary as the choice of 10 years.  What we need to do is calculate the correlations across all reasonable horizons, and disclose them in full.  To that end, the following table shows the correlations for 30 different time horizons, starting at 7 years and going out to 36 years.  To confirm a similar breakdown, the table includes the performance of the model’s predictions using Market Cap to GDP and the Q-Ratio as valuation inputs.


At around 20 years, the correlations start to break down.  By 30 years, no correlation is left.  What we have, then, is clear evidence of curve-fitting.  There is a coincidental pattern in the data from 1935 to 2004 that the model latches onto.  At time horizons between roughly 10 years and 20 years, valuation and growth tend to overshoot their assumed means in equal and opposite directions.  The associated errors cancel, and an attractive fit is generated.  When different time horizons are used, such as 25 years or 30 years or 35 years, the proportionate overshooting stops occurring, the quirk of cancellation is lost, and the correlation unravels.

For a concrete example of the coincidence in question, consider the stock market of the 1970s.  As we saw earlier, from 1972 to 1982, nominal growth was very strong, overshooting its mean by almost 4% (10% versus the assumed value of 6.3%).  The driver of the high nominal growth was notoriously high inflation–changes in the price index driven by booming demography and weak productivity growth.  The high inflation eventually gave way to an era of very high policy interest rates, which pulled down valuations and caused the multiple at the end of the period to dramatically undershoot the mean (a Shiller CAPE of 7 versus a mean of 17).  Conveniently, then, the overshoot in growth and the undershoot in valuation ended up coinciding and offsetting each other, producing the appearance of an accurate prediction for the period, even though the model’s specific assumptions about valuation and growth were way off the mark.

If you change the time horizon to 30 years, analyzing the period from 1972 to 2002 instead of the period from 1972 to 1982, the convenient cancellation ceases to take place. Unlike in 1982, the market in 2002 was coming out of a bubble, and the multiple significantly overshot the average, as did the growth over the entire period–producing two uncancelled errors in the prediction.

Now, does it make sense to suggest that these divergent outcomes for the model would have been predictable, ex-ante, in 1972–that one could have known that forces were going to align on a 10 year horizon so that the errors would cancel, but not on a 30 year horizon? Obviously not.  You need the luxury of hindsight to be able to tell stories as to why the 10 year errors would bail each other out, but not the 30 year errors–which is why we can say that this is a curve-fit.

Pre-1930s Data: Out of Sample Testing

At the Wine Country Conference (ScribdYouTube), John explained that his model’s predictions work best on time horizons that roughly correspond to odd multiples of half market cycles.  A full market cycle (peak to peak) is allegedly 5 to 7 years, so 7 to 10 years, which is John’s preferred horizon of prediction, would be roughly 1.5 times a full market cycle, or roughly 3 times a half market cycle.

In the presentation, he showed the model’s performance on a 20 year horizon and noted the slightly “off phase” profile, attributing it to the fact that 20 years doesn’t properly correspond to an odd multiple of a half market cycle.  From the presentation:


What John seems to be missing here is the cause of the “off phase” profile.  The growth and valuation errors that were nicely offsetting each other on the 10 year horizon are being pulled into a different relative positioning on the 20 year horizon, undoing the illusion of accurate prediction.  As the time horizon is extended from 20 years to 30 years, the fit further unravels.  This loss of accuracy is not a problem with 20 years or 30 years as prediction horizons per se; rather, it’s a problem with the model.  The model is making wrong assumptions that get bailed out by superficial coincidences in the historical period being sampled.  These coincidences do not survive significant changes of the time horizon, and therefore should not be trusted to recur in future data.

Now, as a strategy, John could acknowledge the obvious, that error cancellation effects are ultimately driving the correlations, and still defend the model by arguing that those effects are somehow endemic to economies and markets on horizons such as 10 years that correspond to odd multiples of half market cycles.  But this would be an extremely peculiar claim to make. To believe it, we would obviously need a compelling supporting argument: why is it the case that economies and markets function such that growth and valuation tend to reliably overshoot their means by equal and opposite amounts on horizons equal to odd multiples of half market cycles?

In the previous piece, we saw that the “Real Reversion” method produced highly accurate predictions on a 40 year horizon because the growth and valuation errors in the model conveniently cancelled each other on that horizon, just as the errors in John’s model conveniently cancel each other on a 10 year horizon.  The errors didn’t cancel each other on a 60 year horizon, and so the fit fell apart, just as the fit for John’s model falls apart when the time horizon is extended.  To give a slippery defense of “Real Reversion”, we could argue that the error cancellation seen on a 40 year horizon is somehow endemic to the way economies and markets operate, and that it will reliably continue into the future data.  But we would need to provide an explanation for why that’s the case, why the errors should be expected to cancel on a 40 year horizon, but not on a 60 year horizon.  We can always make up stories for why coincidences happen the way they do, but to deny that the coincidences are, in fact, coincidences, the stories need to be compelling.  What is the compelling story to tell here for why the growth and valuation errors in John’s model can be confidently trusted to cancel on horizons equal to 10 years (or different odd multiples of half market cycles) going forward, but not on other horizons?

Even if the claim that growth and valuation errors are inclined to cancel on horizons equal to odd multiples of half market cycles is true, that still doesn’t explain why the model fails on a 30 year horizon.  30 years, after all, is an odd multiple of 10 years, which is an odd multiple of a half market cycle; therefore, 30 years is an odd multiple of a half market cycle (unlike 20 years).  If the claim is true, the model should work on that horizon, especially given that the longer horizon achieves a greater dilution of errors.  But it doesn’t work.

To return to the example of the early 1970s, the 10 year period from 1972 to 1982 started at a business cycle peak and landed in a business cycle trough–what you would expect over a time horizon equal to an odd multiple of a half market cycle.  But the same is true of the 30 year period from 1972 to 2002–it began at a business cycle peak and ended at a business cycle trough.  If the model can accurately predict the 10 year outcome, and not by luck, then why can’t it accurately predict the 30 year outcome?  There is no convincing answer.  The success on the 10 year horizon rather than the 30 year horizon is coincidental.  10 years gets “picked” from the set of possibilities not because there is a compelling reason for why it should work over other time horizons, but because it just so happens to be a horizon that achieves a good fit.

This brings us to another problem with the chart: sample size.  To make robust claims about how economic and market cycles work, as John seems to want to do, we need more than a sample size of 2, 3, or 4–we need a sample size closer to 100 or 1,000 or 10,000.  Generously, from 1935 to 2004, we only have four separate periods, each driven by different and unrelated dynamics, in which the growth and valuation errors offset each other (and one period in which they failed to offset each other–the period associated with the last two decades, wherein the model’s performance has evidently deteriorated).  In that sense, we don’t even have a tiny fraction of what we would need in order to confidently project the offsets out into the unknown future.


Ultimately, to assert that an observed pattern–in particular, a pattern that lacks a compelling reason or explanation–represents a fundamental feature of reality, rather than a coincidence, it is not enough to point to the data from which the pattern was gleaned, and cite that data as evidence.  If I want to claim, as a robust rule, that my favorite sports team wins championships every four years, or that every time I eat a chicken-salad sandwich for lunch the market jumps 2% (h/t @mark_dow), I can’t point to the “data”–the last three or four occurrences–and say “Look at the historical evidence, it’s happened every time!” It’s “happening” is precisely what has led me to the unusual hypothesis in the first place. At a minimum, I need to test the unusual hypothesis in data that is independent of the data that led me to it.

Ideally, I would test the hypothesis in the unknown data of the future, running the experiment over and over again in real-time to see if the asserted thesis holds up.  If the thesis does hold up–if chicken-salad sandwiches continue to be followed by 2% market jumps–then we’re probably on to something.  What we all intuitively recognize, of course, is that the thesis won’t hold up if tested in this rigorous way.  It’s only going to hold up if tested in biased ways, and so those are the ways that we naturally prefer for it to be tested (because we want it to hold up, whether or not it’s true).

Now, to be fair, in the present context, a rigorous real-time test isn’t feasible, so we have to settle for the next best thing: an out of sample test in existing data that we haven’t yet seen or played with. There is a wealth of accurate price, dividend and earnings data for the U.S. stock market, collected by the Cowles Commission and Robert Shiller, that is left out of John’s chart, and that we can use for an out of sample test of his model.  This data covers the period from 1871 to the 1930s.  In the previous piece, I showed that we can make very accurate return predictions in that data–indeed, just as accurate as any return predictions that we might make in data from more recent periods.  If the observed pattern of error cancellation is endemic to the way economies and markets work, and not a happenstance quirk of the chosen period, then it should show up on 10 year horizons in that data, just as it shows up on 10 year horizons in data from more recent periods.

Does it?  No.  The following chart shows the performance of the model, using the Shiller CAPE as input, from 1881 to 1935:


As you can see, the fit is a mess, missing by as much 15% in certain places.  The correlation is a lousy .556.  The following chart plots the errors, which evidently fail to cancel:


The following table gives the correlations between the model’s predicted returns and the actual subsequent returns using all available data from 1881 to 2014 (no convenient ex-post exclusions).  The earlier starting point of 1881 rather than 1935 allows us to credibly push the time horizon out farther, up to 60 years:


When all of the available data is utilized, the correlations end up being awful.  We can conclude, then, that we’re working with a curve-fit.  The predictions align well with the actual results in the 1935 to 2004 period for reasons that are happenstance and coincidental.  The errors just so happen to conveniently offset each other in that period, when a 10 year horizon is used.

There have been four large valuation excursions relative to the mean since 1935–1937 to 1954 (low valuation), 1955 to 1972 (high valuation), 1973 to 1990 (low valuation), 1991 to 2014 (high valuation).  When growth is measured on rolling horizons between around 10 and around 19 years, roughly three of these valuation excursions end up being offset by growth excursions of proportionate magnitudes and opposite directions relative to the mean (in contrast, the most recent valuation excursion, from the early 1990s onward, is not similarly offset, which is why the model has exhibited relatively poor performance over the last 20 years).  When growth is measured on longer horizons, or when other periods of stock market history are sampled (pre-1930s), the valuation excursions do not get similarly offset, indicating that the offset is a coincidence.  There is no basis for expecting future growth and valuation excursions to continue to nicely offset each other, on any time horizon chosen ex-ante–10 years, 20 years, 30 years, whatever–and therefore there is no basis for trusting that the model’s specific future return predictions will turn out to be accurate.

In Search of “Historical Reliability”

In a piece from February of last year, John laid out criteria for gauging investment merit on the basis of valuation:

The only way to adequately gauge investment merit here is to have a valid and historically reliable approach for estimating prospective future market returns. What is most uncomfortable about the present market environment is that even some people whom we respect are tossing out comments about market valuation here that are provably wrong, or at least require one to dispense with the entirety of historical evidence if their optimistic views are to be correct… Again, the Tinker Bell approach won’t cut it. Before you accept someone’s view about market valuation, examine the data – decades of it. Ignore clever-sounding valuation arguments that don’t have a strong, consistent, and demonstrated relationship with subsequent market returns.

Unfortunately, John’s model for estimating prospective future returns is not “historically reliable.”  It contains significant realized historical errors in its assumptions, specifically the assumptions that nominal growth will be 6.3%, and that valuations will mean-revert over 10 year time horizons.  The model is able to produce a strong historical fit on 10 year time horizons inside the 1935 to 2004 period only because it capitalizes on superficialities that exist on that horizon and in that specific period of history, superficialities that cause the model’s growth and valuation errors to offset.  The superficialities do not hold up in out of sample testing–testing in different periods and over different time horizons, including time horizons that correspond to odd multiples of half market cycles, such as 30 years.  There is no basis, then, for expecting them to persist going forward.

Now, to be clear, John’s prediction that future 10 year returns will be extremely low, or even zero, could very well end up being true.  There are a number of ways that a low or zero return scenario could play out: profit margins could enter secular decline, fall appreciably and not recover, nominal growth could end up being very weak, an aging demographic could become less tolerant of equity volatility and sell down the market’s valuation, inflation could accelerate, the Fed could have to significantly tighten monetary policy and reign in the elevated valuation paradigm of the last two decades, the economy could just so happen to land in a recession at the end of the period, and so on.  In truth, the market could have to face down more than one of these bearish factors at the same time, causing returns to be even lower than what John’s model is currently estimating.

The point I want to emphasize here is that these seemingly tightly-correlated charts that John presents are not evidence of the “historical reliability” of his bearish predictions.  The charts are demonstrable curve-fits that exploit superficial coincidences in the historical data being analyzed.  Investors are best served by setting them aside, and focusing on the arguments themselves.  What does the future hold for the U.S. economy and the U.S. corporate sector?  How are investor’s going to try to allocate their wealth in light of that future, as it unfolds?  Those are the questions that we need to focus on as investors; the curve-fits don’t help us answer them.

If the assumptions in John’s model turn out to be true–in particular, the assumption that the Shiller CAPE and other valuation metrics will revert from their “permanently high plateaus” of the last two decades to the averages of prior historical periods–then, yes, his bearish predictions will end up coming true.  But as we’ve seen from watching people repeatedly predict similar reversions going back as far as the mid 1990s, and be wrong, a reversion, though possible, is by no means guaranteed. Investors should evaluate claims of a coming reversion on their own merits, on the strength of the specific arguments for and against them, not on the false notion that the “historical record”, as evidenced by these curve-fits, has anything special to say about them.  It does not.

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Forecasting Stock Market Returns on the Basis of Valuation: Theory, Evidence, and Illusion

In this piece, I’m going to present and explain a simple, easy-to-understand method of forecasting stock market returns on the basis of valuation.  I’m then going to insert the popular Shiller CAPE into the method to assess how well the historical predictions fit with the actual historical results.  As you can see in the chart below, they fit almost perfectly, across 133 years of available data (no arbitrary exclusions). The correlation coefficient is a fantastic 0.92.


After presenting the chart, I’m going to demonstrate that its tight correlation is an illusion. I’m going to carefully flesh out its subtle trick, a trick that is ultimately hidden in every chart that purports to use valuation to accurately predict returns in historical data. Such a feat cannot be accomplished–the historical data will not allow it.

Now, let’s be honest. When we build charts in finance and put them on display, our primary motivation isn’t to “spread truth.”  It’s to “talk our books”, broadcast to the world that the views and positions that we’re already emotionally and financially tied down to are right, and that those of our opponents and counterparties are wrong.

To that end, I might come up with a chart that really nails it. But so what? For all you know, the chart could have been the product of hours upon hours of searching, sifting, tweaking, and ultimately selectively discarding whatever didn’t fit with the thesis that I was trying to convey.  Not knowing the process through which I arrived at the chart, how can you be confident that it represents an unbiased sampling of the possibilities?  Why should you believe that its projections will hold true in the data that actually matter–the unsearched, unsifted, untweaked, undiscarded data of the future?

Ask yourself: is it possible that one carefully put-together chart out of a hundred might happen to fit well with a desired thesis, for reasons that are coincidental?  If the answer is yes, then you can rest assured: that’s the chart that defenders of the thesis are going to end up showing you, every time.  They’re going to search for it, find it, and put it on display–not because they know that it represents truth (they don’t), but because it persuasively communicates what they want to be true, and what they want you to believe is true.

The Drivers of Returns: Dividends and Per-Share Growth in Fundamentals

From January 1871 to today, U.S. equities have produced an average real total return of around 6% per year.  We can conceptualize this return as coming from two different sources: (1) real growth in stable per-share fundamentals–book values, revenues, smoothed earnings (e.g., Robert Shiller’s 10 year average of EPS), etc.–and (2) real dividend payments that are reinvested into the equity markets and that compound at the equity rate of return.

The relative contribution of growth and dividends to real total return has changed over time, but the change hasn’t mattered much to the 6% number, because the two sources of return are fungible and inversely-related.  For a given level of profit, a higher dividend payout means less reinvestment and less per-share growth.  A lower dividend payout means more reinvestment and more per-share growth.

It is not a coincidence that U.S. equities have produced an average real total return of around 6% throughout history.  That number matches the U.S. Corporate Sector’s average historical return on equity (ROE) of around 6%.  The following chart shows the ROE for U.S. national corporations (non-financial) from 1951 to 2014 (FRED):


In theory, the average real total return that accrues to shareholders should match the average corporate ROE.  For a simple proof, assume that the following premises hold true over the very long term:

(1) The corporate sector operates at a 6% average ROE (generates a 6% average profit on its true book value, defined to mean assets at replacement cost minus liabilities).

(2) Shares trade, on average, at “fair value”, which we will assume is equal to true book value.

It follows that either:

(1) the 6% average profit will be internally reinvested, and therefore added to the book value each year, with the result being 6% average growth in the book value, and therefore 6% average growth in the smoothed earnings, given that the corporate sector operates at a constant average ROE over the long-term, or

(2) the 6% average profit will be paid out as a dividend, in which case it will directly produce an average 6% return for shareholders (if shares trade, on average, at their book values, then a distributed dividend equal to 6% of the book value will also equal 6% of the market cap, therefore a 6% yield), or

(3) corporations will opt for some combination of (1) and (2), some combination of growth and dividends, in which case the sum will equal 6%.

The 6% will be a real 6% because inflation–i.e., changes in the price index–will change the nominal value of the assets that make up the book, properly accounted at replacement cost.  By our assumption (1), changes in the price index will not drive changes in the average ROE (and why should they?), therefore they will pass through to the average smoothed earnings, preserving the 6% inflation-adjusted number underneath.

Now, we can loosely test this logic against the actual historical data.  The following chart shows the trailing 70 year real return contribution from per-share growth (gold) and dividends reinvested at fair value (green) back to 1881, the beginning of the data set:

70yr Trailing 6%

(Details: After presenting a non-trivial chart, I’m going to add a “details” section that rigorously describes how the chart was created, so that interested readers can reproduce its content for themselves.  Uninterested readers should feel free to ignore these sections. In the above chart, we approximate the real return contribution from per-share growth using the real growth rate of Robert Shiller’s 10 year average of inflation-adjusted EPS, a cyclically-stable metric.  We approximate the real return contribution from dividends reinvested at fair value by making two fake indices for the S&P 500: (1) a fake real total return index and (2) a fake real price return index.  In these fake indices, we replace each historical market price with whatever price would have made the Shiller CAPE equal to exactly 15.3, its 133 year geometric average.  To calculate the annual real return contribution from the reinvested dividend over a trailing period of X years, we take the difference between the annual returns of the two indices over the X year period. That difference is the reinvested dividend’s contribution to the real return on the assumption that shares always trade at “fair value.”)

As you can see in the chart, the logic checks very closely with the actual historical data, provided that we use a long time horizon.  The average of the black line is 5.78%, roughly equal to the average corporate ROE of 5.80%.  Notice that as the return contribution from growth (yellow) rises, the return contribution from dividends (green) falls, keeping the sum near 6%.  This is not a coincidence.  It doesn’t matter what relative share of profit the corporate sector chooses to devote to growth or dividends; over the long-term, the sum is conserved.

Formally, we can express the long-term average relationship between ROE, real total return to shareholders, real per-share growth in fundamentals, and the real return contribution from reinvested dividends, in the following equation:

ROE = Sustainable Real Total Return to Shareholders = Real Per-Share Growth in Fundamentals + Real Return Contribution From Reinvested Dividends = 6%

Now, to increase the return contribution from one source–say, growth–without reducing the return contribution from the other–dividends–the corporate sector can lever up.  But this won’t refute the equation, because if the corporate sector levers up, it will increase its ROE, either by increasing its earnings at a constant book value (borrowing funds and investing in new assets that will provide new sources of profit), or by reducing its book value at a constant earnings (borrowing funds and paying them out as dividends–i.e., adding liabilities without adding assets).  The assumption is that if the corporate sector tries to use leverage to boost its ROE above the norm, the leverage will have a stability cost that will show up in the future, during times of economic distress, pushing profitability down and ensuring that the average long-term ROE stays close to the norm.

In a similar manner, to increase the return contribution of one source while maintaining the return contribution of the other source constant, the corporate sector can try to raise funds by selling equity.  But if, as we’ve assumed, shares trade on average at fair value, and the funds are deployed at an average ROE of 6%, then, whatever gets added–higher absolute growth, higher absolute dividends–will be added with a commensurate dilution that leaves the aggregate return contribution unchanged on a per-share basis.

Note that we haven’t mentioned share buybacks and acquisitions here because they have the same effect on a total return index as reinvested dividends.  The corporate sector can take money and buy back its shares in the market, indirectly increasing the number of shares that remaining shareholders own, or it can pay the money out to shareholders as dividends, which they will reinvest, directly increasing the number of shares they own.

Now, in addition to growth and dividends, there’s one other crucial factor that impacts returns–changes in valuation.  The assumption, of course, is that valuation reverts to the mean, and that any contributions that changes in it make to returns, whether positive or negative, will cancel out of the long-term average.

Suppose, for example, that a bubble emerges in the stock market, and that the valuation at time t rises dramatically above the mean.  Whoever sells at t will enjoy a return that is significantly higher than the normal real value of 6%.  But that return will be fully offset by the proportionately lower return that the buyer at t will have to endure, as the elevated valuation falls back down.  Thus, if you average real returns across all time periods, the bubble won’t affect the 6% number.  Nothing will affect that number except the sustainable drivers of real equity returns: fundamental per-share growth and reinvested dividends.

The tendency of valuation to mean-revert is precisely what allows us to use it to estimate long-term future returns.  We know what long-term future returns are going to be, on average, if shares are purchased at fair value, and if no subsequent changes in valuation occur: roughly 6%, the normal combined return contribution of growth and dividends. Therefore, we know what long-term future returns are going to be, on average, if shares are not purchased at fair value, but eventually revert to that value–6% plus or minus the boost or drag that the mean-reversion will introduce.

The Real-Reversion Method: A Technique for Estimating Future Returns

Here’s a simple but useful method, which I’m going to call “Real-Reversion”, that allows us to make specific return predictions for specific future time horizons.  For a specified time horizon, take the 6% real total return that U.S. equities have historically produced and adjust that return to reflect the increase or decrease that a mean-reversion in valuation, if it were to have occurred at the end of the time horizon, would produce.  To get to a nominal return, add a separate inflation estimate to the result.

The equations:

Real Total Return = 1.06 * (Mean_Valuation/Present_Valuation) ^ (1/t) – 1

Nominal Total Return = Real Total Return + Inflation Estimate

Here, t is the time horizon in years.  Mean_Valuation is the mean to which the valuation will have reverted at the end of the time horizon.  Present_Valuation  is the present valuation.

On this equation, if the valuation is precisely at the mean, the predicted future return will be 6% per year.  If the valuation is above the mean, the predicted future return will be 6% discounted by the annual drag that that the mean-reversion will produce over the time period.  If the valuation is below the mean, the predicted future return will be 6% accreted by the boost that the mean-reversion will produce over the time period.

Of note, if we look at the historical real returns of other developed capitalist economies, we see that numbers close to 6% frequently come up.  The following table shows the average annual real total returns for the US, UK, Japan, Germany and France back to 1955, a time when valuations were very close to the historical average (Shiller CAPE ~ 16 for the USA):


Notice that the “Real-Reversion” method uses valuation to estimate real returns, not nominal returns.  Nominal returns have to be estimated separately, using a separate estimate of inflation over the time period in question.  The reason the method has to be constructed in this way is that inflation hasn’t followed a reliable trend over the long-term, and doesn’t need to follow any trend.  Unlike real equity returns, it isn’t driven by a factor, ROE, that mean-reverts.  It’s driven by policy, demographics, culture, and supply dynamics–factors that can conceivably go in whatever direction they want to.  If we try to incorporate it directly in the forecasting method, we will introduce significant historical error into the analysis.

Now, let’s plug the familiar Shiller CAPE into the method to generate a 10 year total return prediction for the present S&P 500.  With the S&P 500 at 1940, the GAAP Shiller CAPE is approximately 26.5.  If, over the next 10 years, we assume that it’s likely to revert to its post-war (geometric) mean of 17, we would estimate the future annual real total return to be:

1.06 * (17/26.5)^(1/10) – 1 = 1.4%

If we wanted a nominal number, we would add in an inflation estimate: say, 2%, the Fed’s present target.  The result would be a 3.4% nominal annual total return.  Note that we haven’t made any adjustments for the effects that emergent changes in dividend payout ratios and accounting practices (related to FAS 142 and also to the provable fact that corporations lied more about their earnings in the past than they do today) have had on the Shiller CAPE.  To be fair, we also haven’t made any of the punitive profit-margin adjustments that valuation bears would have us make.

To give credit where credit is due, “Real-Reversion” is (basically) the same method that James Montier used in a recent piece on the Shiller CAPE.  It’s a simplification of GMO’s general asset class forecast method–take the normal expected real return, and adjust it for the effects of mean-reversion.  There really isn’t any other way to reliably use valuation to estimate long-term future equity returns–GMO’s method is essentially it.

In James’ piece, he showed the performance of the method across GMO’s preferred 7 year mean-reversion time horizon.


He explained:

“We simply revert the P/E towards average over the course of the next seven years and then add a constant to reflect growth and income (let’s call it 6% for simplicity’s sake). It does a pretty reasonable job of capturing realised returns.  If anything, it tends to overpredict returns, rather than underpredict them (which is another of the charges levelled by the critics).”

The following is my recreation of the 7 year chart using Robert Shiller’s data:


I would disagree that the method does a pretty reasonable job of capturing realized returns.  In my view, it does a terrible job.  The fit is a mess, with a linear correlation coefficient of only 0.51.  That’s an awful number, particularly given that the expressions being correlated–“present valuation” and “future returns”–share a common oscillating term, present price.  Analytically, those terms already start out with a trivial correlation between them (which is the reason the squiggles in the two lines tend to move in unison).

I would also disagree that the method tends to overpredict returns.  It only tends to overpredict returns in the pre-war period.  In the post-war period, it tends to underpredict them.  The following table shows the frequency of 7 year underprediction, using a generous 17 as the mean (if we used the actual 133 year geometric average of 15.3, the underprediction would be even more frequent):


Since 1945, the method has underpredicted returns roughly 58% of the time.  Since 1991, it’s underpredicted them roughly 95% of the time–half of the time by more than 5% annually.  Compounded over a 7 year time horizon, that’s a big miss.

The fact that the method has failed to make accurate predictions in recent decades shouldn’t come as a surprise to anyone.  Since early 1991, roughly the end of the first Gulf War, the Shiller CAPE has only spent 10 months below its assumed mean–out of a total of 278 months. There is no way that a forecasting method that bets on the mean-reversion of a valuation metric can produce accurate forecasts when the metric only spends 3.6% of the time at or below its assumed mean.

I prefer to look at return estimates over a 10 year period, because 10 years sets up a convenient comparison between the expected return for equities and the yield on the 10 year treasury bond. The following chart shows the performance of the method over a 10 year horizon, from 1881 to 2014:


The correlation coefficient rises to 0.59–better, but still grossly inadequate.

Point-to-Point Comparison: “Shillerizing” the Returns

What we’re doing in the above chart is we’re comparing the predictions of the method at each point in time to the total returns that subsequently occurred from that point to a point 10 years out into the future.  So, for example, we’re looking at the Shiller CAPE in February of 1991 at 17.3, we’re estimating a 10 year real total return of 5.8% per year (6% reduced by the drag of a 10 year mean reversion from 17.3 to 17), and then we’re comparing this estimate to the actual annual return that occurred from February of 1991 to February of 2001.

The problem, of course, is that from February of 1991 to February of 2001, the Shiller CAPE didn’t revert from 17.3 back down to the mean of 17, as the model assumed it would.  Rather, it skyrocketed from 17.3 to 35.8.  The actual real total return ended up being 13.5%, more than twice the model’s errant 5.8% prediction.

Ultimately, if the 6% normal return assumption holds true, then any time the Shiller CAPE ends a period with a value that is not 17, this same error is going to occur.  We will have estimated the future return on the basis of a mean-reversion that didn’t actually happen; the estimate will therefore be wrong.  So unless we expect the Shiller CAPE to always equal something close to 17, for all of history, we shouldn’t expect the model’s predictions to fit well with the actual historical results on a point-to-point basis.  Point-to-point success in historical data is a highly unreasonable standard to impose on the method.


As you can see in the chart above, the Shiller CAPE has historically exhibited a very large standard deviation–equal to more than 40% of its historical mean–with extremes as low as 5 (early 1920s) and as high as 40 (late 1990s).  30% of the overall data set consists of periods in which it was below 10 or above 22.  In those periods, the model should be expected to produce very incorrect results.

Indeed, if the model doesn’t produce incorrect results in those periods, then either the 6% normal real return assumption is wrong, or the two errors–the error in the 6% normal real return assumption and the error in the 10 year mean-reversion assumption–are by luck cancelling each other out.  In other words, we’ve data-mined a curve-fit, a superficial exploitation of coincidental patterning in the data set.  Obviously, if our goal is to build a robust model that will allow us to successfully predict returns out of sample, in the unknown data of the future, we shouldn’t want it to pass a backtest in such a spurious manner.

To get around the problem, we need to rethink what we’re trying to say when we issue future return estimates.  We’re not trying to say that the future return will necessarily be what we predict–that would be hubris.  Rather, we’re trying to make a conditional statement, that the return will be what we predict if our assumptions about 6% “normal” returns and mean-reversion in valuation hold true for the period.  We’re additionally asserting that those assumptions probably will hold true–not always, but on average.

A better way to test the reliability of the method, then, is to test it on averages of points, rather than on individual points.  To illustrate, suppose that we do the following: for each point in time, we use the method to generate an estimate of the future 10 year return, the future 11 year return, the future 12 year return, and so on, covering a 10 year span, all the way to the future 19 year return.  We then calculate the average of each of these 10 estimates.  We compare that average to the average of the actual subsequent returns over the same 10 year span: the actual subsequent 10 year return, the actual subsequent 11 year return, the actual subsequent 12 year return, and so on, all the way up to the actual subsequent 19 year return.

If, at a given point in time, the Shiller CAPE looking 10 years out just so happens to be abnormally high or low, our estimate of the future 10 year return will end up being incorrect.  But, to the extent that the abnormality is infrequent and bidirectional, the error will get diluted and canceled by the other terms in the average.  Assuming that deviations in the terminal Shiller CAPEs in the other years average out to the mean–which they generally should if we’re making reliable assumptions about mean-reversion–the averages of the predictions will still closely match the averages of the actual results.

This approach is similar to the approach that Robert Shiller famously uses to analyze earnings.  When calculating earnings growth, he calculates the growth in the trailing 10 year average of earnings, not the growth in point-to-point earnings, which is highly cyclical. We’re doing the same thing with returns, which, on a point to point basis, are also highly cyclical.  In a word, we’re “Shillerizing” them.

The following chart shows predicted and actual 10 year “Shillerized” returns from 1881, the beginning of the data set, to present:


(Details: For each point in the chart, the average of the return predictions 10, 11, 12, 13, 14, 15, 16, 17, 18, and 19 years out is compared to the average of the actual realized returns 10, 11, 12, 13, 14, 15, 16, 17, 18, and 19 years out.)

The correlation between the predicted returns and the actual returns rises to 0.72.  Better, and certainly more visually pleasing, but still not adequate.  To improve the forecasting, we need to take a closer look at the sources of error in the method.

Three Sources of Error: Why A Very Long Horizon is Needed

There are three sources of error in the method.  These errors are:

(1) Growth Error: errors driven by historical variabilities in fundamental per-share growth rates.

(2) Dividend Error: errors driven by historical variabilities in the valuations at which dividends are reinvested, which lead to variabilities in the net contribution of dividends to total return.

(3) Valuation Error: errors driven by historical variabilities in the Shiller CAPE–in particular, the secular upshift seen over the last two decades, which remains even after “Shillerizing” to smooth out cyclicality.

Let’s look at the first source of error, historical variabilities in fundamental per-share growth rates. Recall that we built the model on the assumption that growth and dividends are fungible and inversely-related, and that if you buy shares at fair value, their respective contributions to real return will sum to 6%.  On this assumption, if you know the real return contribution of the reinvested dividend, you should be able to predict the real return contribution of growth–6% minus the reinvested dividend’s contribution.

But there have been multiple periods in history where corporate performance, levered to the health of the economy, was very strong (1950s) or very weak (1930s).  In those periods, real per-share growth deviated meaningfully from what it should have been given the amount of profit that the corporate sector was devoting to dividends.  When used in those periods, the method breaks down.

The following chart illustrates the trailing magnitude of this error from 1891 to 2014.  The blue line is the actual realized 10 year trailing Shiller EPS growth rate.  The red line is the 10 year trailing Shiller EPS growth rate that would have been expected, given the dividend’s return contribution.


As you can see, the blue and red lines frequently deviate.  To illustrate the impact of the deviation, the following chart shows the sum (black line) of the trailing 10 year return contributions from growth (gold) and dividends (green) from 1891 to 2014.

10 yr trailing

As you can see, the growth contribution on a 10 year horizon (yellow) is highly variable, despite relatively stable dividend contributions.  The consequence of this variability is that the method’s total return estimates, based on a nice, neat 6% assumption, frequently turn out to be wrong.

For a concrete example, suppose that you try to use the method to estimate 10 year real total returns from November 1948 to November 1958. Your estimate will be way off, even though the CAPE ended the period almost exactly at the mean value of 17.  The reason your estimate will be off is that corporate performance during the period was unusually strong, reflecting, in part, the high productivity growth and pent-up demand that was unleashed into the post-war economy. From November 1948 to November 1958, the real growth rate of the Shiller EPS was an abnormally high 6%, versus the 1% that the model would have predicted based on the dividend contribution.  The actual return contribution from the sum of growth and dividends was 11%, versus the 6% that the model uses.

Given the depressed starting point of the CAPE in November 1948 (around 10), the method’s estimate of the future 10 year return was 11%.  But the actual 10 year return that ensued was a whopping 17%, even though the method’s assumption that CAPE would  mean-revert to 17 turned out to be true.  The following chart highlights the large deviation.


Note that “Shillerization” of the returns cannot eliminate the deviation, because the deviation is driven by errors associated with a variable that is already a “Shillerization” of sorts–Shiller’s 10 year average of inflation-adjusted EPS.  As a general rule, Shillerization only works for errors associated with excursions that are brief relative to the Shillerization time horizon.  This error is not brief, but persists over a multi-decade period.


It turns out that the only way to eliminate the deviation is to use a longer time horizon.  In practice, the method’s 6% assumption doesn’t hold over 10 year periods–there’s too much 10 year variability in corporate performance across history.  It only holds over very long periods–north of, say, 40 years.

The following chart shows the trailing 10 year and the trailing 40 year Shiller EPS growth rate errors from 1921 to 2014 (actual Shiller EPS growth rate minus model-expected Shiller EPS growth rate given the contribution of dividends):


As you can see, using a longer time horizon pulls the error (red line) down towards zero, rendering the 6% assumption, and the method in general, more reliable.

The following chart shows the sum (black line) of the growth (gold) and dividend (green) contributions from 1921 to 2014 using a trailing 40 year horizon instead of a trailing 10 year horizon:


As you can see, on a trailing 40 year horizon, the black line gets much closer to a consistent 6%.  It stays roughly within 1% of that value across the entire period, minimizing the error.

To return to the previous 1948-1958 example, if you use the method to predict the return over the trailing 40 years instead of the trailing 10 years–starting in November of 1918 instead of 1948–you dilute the 1948-1958 anomaly with three decades worth of additional economic data.  The 6% assumption ends up being significantly closer to the actual sum of the growth and dividend contributions, which from 1918 to 1948 turned out to be 5.3%.

Now, let’s look at the second source of error, variabilities in the valuations at which dividends are reinvested.  This error rarely gets noticed, but it matters.  In a recent piece, I gave a concrete example of how powerful it can be–over the long-term, it’s capable of rendering a permanent 66% market crash more lucrative for existing investors than a permanent 200% market melt-up (assuming, of course, that the crash and the melt-up are driven by changes in valuation, rather than changes in actual earnings).

Recall that our method rested on the assumption that dividends are reinvested in the market at “fair value”, defined as true book value, which we took to correspond to a Shiller CAPE equal to the long-term average.  This assumption is obviously wrong.  Markets frequently trade at depressed and elevated levels, which means that dividends are frequently reinvested at higher and lower implied rates of return–sometimes over long periods of time, in ways that don’t net out to zero.

Interestingly, even if periods of high and low valuation were to be perfectly matched over time, their net effect on the returns associated with reinvested dividends would still be greater than zero. To illustrate with a concrete example, suppose that the market spends 5 years at a price of 100, and 5 years at a price of 50.  The mean is 75.  Suppose that the implied return at that mean is 6%, consistent with earlier assumptions.  The bidirectional excursion will actually boost the return above 6%.  For 5 years, dividends will be reinvested at a price of 100–which, simplistically, is an implied return of 4.5%. For another 5 years, dividends will be reinvested at a price of 50–which, simplistically, is an implied of 9%.  These two deviations, when combined, do not average to the 6% mean. Rather, they average to 6.75%.  The 9% period earned a return 3% higher than the mean, whereas the 4.5% period earned a return only 1.5% below the mean.  When combined, the two deviations do not fully cancel.  We can see, then, that symmetric price volatility around the mean actually boosts total returns relative to the norm.

The following chart shows the effect that reinvesting dividends at market prices rather than “fair value” has had on 10 year real total returns, from 1891 to 2014:


(Details: We calculate the effect by creating two “fake” real total return indices.  In the first index, we set prices equal to “fair value”, a Shiller CAPE equal to the historic average of 15.3.  We reinvest dividends at those prices.  In the second index, we set prices equal to “fair value”, but we reinvest the dividends at whatever the actual market price happened to be. The chart shows the difference between the trailing 10 year annualized returns of each index.)

Notice that if we look backwards from 1925 and 1984 (circled in green), the effect added a healthy 3% and 2% to the real total return respectively.  That’s because the markets in the ten years preceding 1925 and 1984 were very cheap–they traded at average CAPEs in the single digits.  Dividends were reinvested into those cheap markets, earning abnormally high rates of return.

At the other extreme, if we look backwards from 1906 and 2005 (circled in red), the effect added -1% and -1.5% to the actual real total return respectively, reflecting the fact that the markets in the ten years that preceded 1906 and 2005 were expensive–with the former trading at an average CAPE near 20 (despite a high dividend payout ratio), and the latter trading at an average CAPE north of 30.  Dividends were reinvested into those expensive markets, earning abnormally low rates of return.

As before, the only way to reduce the effect that this error–the error of assuming that dividends are always reinvested at fair value, when they are not–will have on our method is to extend the time horizon. 10 years is too short, there’s too much variability in the average valuations seen across different 10 year historical periods.  As the chart below illustrates, when we use a longer time horizon, 40 years (red), we successfully dilute the impact of the variability.

trailing 40 yrs

The extension of the horizon to 40 years dilutes the outlier periods and flattens out the net error towards zero.  In the 40 year period from 1925 back to 1885, the extreme cheapness of the late 1910s and early 1920s is mixed in with the expensiveness seen at the turn of the 19th century, when the CAPE was well above 20 (despite a very high payout ratio).  In the 40 year period from 2005 back to 1965, the extreme expensiveness of the tech bubble and its aftermath is mixed in with the extreme cheapness of the bear markets of the late 1970s and early 1980s, where the CAPE traded in the single digits.

Notice that both lines have trended lower across the full period–that’s because, on trailing 10 year and 40 year average horizons, equity valuations, as measured by the CAPE, have trended towards becoming more expensive.  Notice also that the average value of both lines is greater than zero.  This is due, in part, to the fact that symmetric price volatility has a positive net effect on the reinvested dividend’s contribution.  It does not cancel out.

This brings us to the third source of error in the method, the most obvious one–the fact that the volatile Shiller CAPE often spends significant amounts of time far away from its assumed mean of 17.  This error has been especially acute in recent times.  Over the last 23 years, the Shiller CAPE hasn’t even come close to reverting to its assumed mean–it’s only spent 4% of the time at or below it.  Regardless of the reasons why the Shiller CAPE has failed to revert to its assumed mean, the fact remains that it hasn’t–consequently, the method hasn’t reliably worked to predict returns. It’s missed the mark, dramatically.

Unfortunately, not even Shillerization can solve this recent problem.  That’s because the 10 year averages of CAPE over the last two decades are just as elevated as the spot values. The following chart shows the trailing 10 year average CAPE from 1891 to 2014.

Shillerized avg

To manage the problem, all that we can really do is increase the time horizon.  10 years is hopeless, but 40 years might have a chance.  Superficially, it can spread the error out over a larger period of time, shrinking the error on an annualized basis.  In general, as time horizons get longer, valuations have a smaller annual impact on future returns–albeit a smaller annual impact imposed over more years.  In the infinite limit, valuation has an infinitesimally small impact–but an infinitesimally small impact imposed over an infinity of years.

Alternatively, we could extend the Shillerization time span from 10 years to something larger, like 3o or 40 years (whatever is needed to adequately dilute out the shift in the CAPE seen over the last 23 years).  But, from a testing standpoint, this approach would be highly suspicious.  Method doesn’t work?  No problem, just make the Shillerization time span as big as you need it to be in order to dilute out the periods of history that are causing problems.  The approach would also eliminate a huge chunk of data from the analysis. We would run out of actual realized returns to measure the method’s predictions against at 39 + 40 = 79 years ago, 1925.  So our effective sample period wouldn’t even reach WW2 as a starting point.

We don’t want our backtest of the method to devolve into one great big “averaging” of all of history.  On that approach, the correlation between predicted and actual returns will end up being high simply because we will be working with a small sample size of predictions and realized results (as the time horizon increases, the pool of realized returns to compare the predictions with decreases), and because both the predictions and the realized results will have been massively smoothed over decades and decades into numbers that converge on the average, 6%, regardless of the starting valuation.  Strong results in such a backtest will prove nothing, at least nothing of value to present investors.

If our point is to say that the CAPE is higher than its long-term historical average, we should say this, and then stop.  It’s higher than its long-term historical average, period, proceed as you wish.  Showing that we can use the CAPE to predict long-term returns if they are Shillerized across enormous periods of time, three or four decades, doesn’t say anything more.

Spectacular Long-Term Predictions: The Tricks of the Trade

The following chart shows the performance of the “Shillerized” metric on a 40 year time horizon, comparing the average of future annual 40, 41, 42, …, 49 year return predictions to the average of the actual subsequent annual returns over the next 40, 41, 42, …, 49 years.


Bullseye–we’ve nailed it, a near perfect hit.  The correlation rises to 0.92.  Note that this is a correlation across all 133 years of available data, all 1,584 months–not some arbitrarily chosen sample that coincidentally happens to fit well with the author’s desired conclusions. Of note, the method gets the prediction wrong in the late 1940s and early 1950s–this is because the subsequent returns in those years ended in the late 1990s and early 2000s, a period where the CAPE was dramatically elevated, and where even a “Shillerization” of the results couldn’t save the method from its incorrect mean-reversion assumptions.  But we’ll be reasonable and let that error slide.

Now, to the fun part.  We’re going to look under the hood to see what’s actually going on in this chart.  When we do that, we’re going to discover numerous other “hidden” places where the method failed, but where coincidences bailed it out, contributing to the illusion of the robust fit seen above.

We saw earlier that even on 40 year horizons, the assumption of a 6% normal real return from growth and dividends was not fully accurate.  The post-war period up to the 1980s, for example, exhibited a number above 7%; the pre-war period up to the late 1940s exhibited a number closer to 4%.


We also know that the Shiller CAPE has been substantially elevated, not just from the late 1990s to the early 2000s, but for the entirety of the last 23 years, from 1991 until today, save for a few brief months during the financial crisis.  A 10 year “Shillerization” of prices and returns should not be enough to dilute out the powerful impact of that deviation.

So what gives?  Where did those errors and deviations go?  Why don’t they appear as errors and deviations in the chart?  To answer the question, we need to plot the errors alongside each other.  Then, everything will become crystal clear.

The following chart shows the actual “Shillerized” errors in the “6% growth plus dividends” assumption and in the “Terminal CAPE = 17” assumption, on a subsequent 40 to 49 year horizon, for each month from 1881 to the most recent realized data point.


(Details: The green line is the difference between (1) the average of what the actual subsequent 40, 41, 42, …, 49 year annual real returns ended up being, and (2) the average of what those annual real returns would have been if the final CAPE had been 17, per the model’s assumptions.  The purple line is the difference between (1) the average of the actual realized sums of the real return contribution from Shiller EPS growth and dividends reinvested at market prices over the subsequent 40, 41, 42, …, 49 years, and (2) what the model assumed those sums should have been–6%.)

Now, look closely at the chart.  What’s interesting about it?  The purple line and the green line are 180 degrees out of phase.  Therefore, they cancel each other out.  That’s why the curve fits so well, despite the persistent errors.

errors offset

To prove that we’re calculating the errors correctly, the following chart shows the predicted error, given the deviations in the two assumptions (of a 6% normal real return, and a terminal CAPE of 17), alongside the actual error (the difference between the actual return that occurred in the market and the return that the model predicted would occur).  The two track each other almost perfectly.


(Details:  Here we’re calculating the “Terminal CAPE = 17” error by taking the difference between what the annualized real price return actually was over the horizon, and what it would have been if the CAPE had ended up being 17, as the method assumed.  We’re calculating the “Growth + Dividends = 6% Error” by subtracting 6% from the sum of–(a) the real Shiller EPS growth that actually occurred, (b) the dividend return that would have occured if dividends were reinvested at fair value, and (c) the effect of reinvesting dividends at market prices instead of fair value.)

The following chart shows the errors alongside the actual and predicted returns from 1881 to the most recent realized data point:


Notice that whenever the sum of the purple and green lines is positive–for example, from around 1914 to around 1929, and from around 1947 to around 1958–the red line, the actual return, exceeds the blue line, the predicted return.  Whenever the sum of the purple and green lines is negative–for example, from around 1881 to around 1911–the blue line, the predicted return, exceeds the red line, the actual return.  For most of the period, the sum is reasonably close to zero, creating the perception of a robust fit.

Now, before we launch allegations of curve-fitting–i.e., building a fit out of coincidental patterning that cannot be trusted to hold out of sample–we need to ask, is there a potential relationship between these two errors, a story we can tell to connect them?  If the answer is yes, then maybe the method is capturing something real.  Maybe it’s predictions should be trusted.

Here’s one interesting story we can tell: lower than normal growth (negative green lines) leads to lower than normal interest rates, which leads to higher than normal Shiller CAPEs (positive purple lines), and vice versa.  If this story is true, then the method is capturing a real relationship in the data, and the robustness of the fit shouldn’t be discounted.

Stories are easy to tell, and hard to refute.  Fortunately, in this case, we have a simple way to test them.  Just change the time horizon.  Surely, if the method can predict returns on a 40 year time horizon, it should be able to predict them on, say, a 60 year time horizon. Any convenient error-cancelling relationship that the method exploits should not be unique to just 40 years–it should apply across all sufficiently long time horizons.

So let’s look at a 60 year time horizon instead.  The following chart shows the performance of the metric on a 60 year “Shillerized” time horizon, comparing the average of future annual 60, 61, 62, …, 69 year return predictions to the average of the actual subsequent annual returns over the next 60, 61, 62, …, 69 years.


Lo and behold, the fit devolves into a mess.  The correlation falls from 0.92 to 0.40. What happened?  Ultimately, the errors that just so happened to cancel on a 40 year time horizon ceased to cancel on a 60 year horizon.  It may look like the predictions do OK–the maximum deviation between predicted and actual is only around 1%.  But that’s 1% per year over 70 years.  And we’ve Shillerized the returns.  Clearly, the fit is unacceptable.


What we have, then, is de facto proof of a curve-fit.  When you change the time horizon appreciably, the fit unravels.  The following chart shows the two errors alongside the actual and predicted returns.


Now–and this is the key takeaway–every single forecasting method in existence that purports to use valuation to accurately predict point-to-point equity market returns in U.S. historical data exploits this same trick.  The data set that we’re working with, covering the U.S. equity market from 1871 to 2014, contains significant variability in the average valuations and average rates of return that it exhibits.  That variability can be dampened by limiting the analysis to very large time horizons and by using Shillerization, but it can’t be eliminated. It’s been especially pronounced in the last two decades, with valuations having migrated to what might otherwise be described as a “permanently high plateau.”  Given this migration, any model that attempts to predict returns in the data set on the basis of a normal rate of return is bound to produce significant errors, even when the returns are Shillerized.  The only way for the predictions of the model to fit with the actual results in the presence of the errors is for the errors to cancel.  When you see a tight fit, that’s always what’s happening.

When a person sits behind a computer and sifts through different configurations of a model (different prediction time horizons, different mean valuations, different growth rate assumptions, different date ranges for testing, etc.) to find the configuration in which the predictions best “fit” with the actual subsequent results, that person is unwittingly “selecting out” the configuration that, by chance, happens to best achieve the necessary cancellation of the model’s errors.  The result ends up being inherently biased. For this reason, we should be deeply skeptical of models that claim to reliably predict returns in historical data on the basis of successful in-sample testing.  We should judge them not by the superficial accuracy of their fits (an accuracy that is almost always engineered), but by the accuracy of their underlying assumptions.

Mean-reversion methods make the assumption that non-cyclical valuation metrics will eventually fall from their “permanently high plateaus” of the last two decades down to their prior long-term averages–with respect to the the Shiller CAPE, the assumption is that the metric is going to fall from 26.5 to 17.  Is that assumption going to prove true? Forget the curve-fits, forget the backtests, forget the data-mining, and just examine the assumption itself.  If it’s going to prove true, and if the normal return would otherwise be 6% real, then the actual return will be 1.4% real. If it isn’t going to prove true, then the return will be something else.

Final Results and Conclusion

Here are the full performance results for “Real-Reversion”, with starting points in 1881 and 1935 (post-Depression, effective post-Gold-Standard):


Across the full spectrum of time horizons, the correlation just isn’t very strong.  That’s because valuations aren’t reliably mean-reverting.  There’s too much valuation variability in the historical data set, even when we use “Shillerized” averages over 10 year time spans. For the correlation to get tight, the growth and dividend errors have to superficially cancel with the valuation errors–but that doesn’t consistently happen, hence the breakdown.

Now, to be clear, I’m not saying that valuation doesn’t matter.  Valuation definitely matters–its power as a return factor has been demonstrated in stock markets all over the world.  Holding other factors constant, if you buy cheap, you’ll do better, on average, than if you buy expensive.  This is true whether we’re talking about individual stocks, or the aggregate market.

What I’m taking issue with is the notion that we can use valuation to build “historically reliable” prediction models whose specific predictions closely align with actual past results, models that give us warrant to attach special “scientific” or “empirical” privilege to our bullish or bearish opinions.  That, we cannot do.  Given the significant variability in the historical data set, the best we can do is mine curve-fits whose errors conveniently offset and whose deviations conveniently disappear.  These are not worth the effort.

In the end, valuation metrics are only capable of giving us a crude idea of what future returns will be.  In the present context, they can tell us what we already know and accept: that future real returns will be less than the 6% historical average (a perfectly appropriate outcome that we should expect at equilibrium, given the secular decline in interest rates and the below-average implied returns on the assets that most directly compete with equities: cash and bonds). But they can’t tell us much more. They can’t arbitrate the debate between those of us who expect, say, 3% real returns for U.S. equities going forward, and who therefore judge the market to be fairly valued (relative to cash at a likely negative long-term real return), and those of us who expect negative real returns for equities, and who therefore find the market to be egregiously overvalued.  The reason valuations can’t arbitrate that debate is that they don’t reliably mean-revert.  If they did, we wouldn’t be having this discussion.

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Profit Margins: Accounting for the Effects of Wealth Redistribution


In the previous piece, I addressed a popular argument for the necessity of profit margin mean-reversion grounded in the Kalecki-Levy profit equation:

Profit/GNP = Investment/GNP + Dividends/GNP – Household Saving/GNP – Government Saving/GNP – ROW Saving/GNP

I made three points.  First, proponents of the argument are ignoring the Dividends/GNP term, which can adjust upward (and has adjusted upward) to satisfy the equation at higher long-run profit margins.  Second, retained corporate profit is household saving, therefore the equation’s model of a competitive transfer between the two is specious.  Third, the high-end share of spending and consumption has increased alongside the profit margin increase, rendering the associated wealth transfer from the lower and middle classes to the wealthy more sustainable than it would otherwise be.

Ultimately, the Kalecki-Levy profit equation is an equation about the limits that wealth inequality imposes on corporate profitability.  If there were no wealth inequality–specifically, no inequality in the distribution of household equity ownership–there would be no “balance of payments” constraints on corporate profitability.  Any constraints that do arise in association with the equation are attributable to the hard reality that the distribution of household equity ownership is radically skewed towards a small, affluent segment of the population. A transfer of income from labor to profit is a transfer of income from the masses to them, a transfer that cannot go on forever.

In this piece, I’m going to explore an issue that is often forgotten in discussions about wealth inequality: wealth redistribution.  It is true that there is currently an enormous amount of wealth inequality in the U.S. economy.  But there is also an enormous amount of wealth redistribution, much more than in any prior period in U.S. history.  The Kalecki-Levy profit equation fails to properly account for the impact of this wealth redistribution.

In the early 1950s, a meaningful share of the wealth redistribution that took place in the U.S. economy took place at the corporate level, via the corporate tax.  Since then, the corporate tax burden has fallen dramatically and the household tax burden has risen dramatically, particularly for high-end households.  This shift has created the appearance of an unsustainable “transfer” of wealth from households to corporations in the form of higher after-tax profits, but the “transfer” is actually a transfer from wealthy households to corporations–an entirely fungible and sustainable transfer, given that wealthy households own the corporate sector.

To account for the impact of the shift, I’m going to derive and test an improved formulation of the Kalecki-Levy profit equation, a formulation that puts the full burden of wealth redistribution on the corporate sector at all times.  This improved formulation will allow for a more accurate apples-to-apples comparison between the present and the past. Interestingly, on the improved formulation, profit margins end up being roughly at their historical averages.

The Original Kalecki-Levy Profit Equation

Before I introduce the improved form of the equation, I’m going to briefly derive and explain the original.  The reason for the brief derivation and explanation is so that the next section, which discusses, household saving, deficit reduction, and the 2012-2013 fiscal cliff, makes more sense to the reader.

First, some definitions.  Saving means “increasing your net wealth.”  Investment means “creating new net wealth.”  Wealth can mean whatever you want it to mean–the only constraint here is that you have to apply the definition consistently.

On these definitions, the only way an economy can save in aggregate–collectively increase its net wealth by some amount–is if it invests that same amount on a net basis, that is, collectively creates new net wealth equal to that amount.  If it doesn’t invest and create new net wealth, then its people, when they try to save, will be fighting over a finite supply of existing net wealth.  The result will be zero sum–any one person’s saving (increase in wealth) will necessarily have to come at the expense of another person’s dissaving (decrease in wealth).  Aggregate saving will be nil.

We arrive, then, at the following maxim, which doesn’t necessarily hold true on an individual basis, but always holds true on an aggregate macroeconomic basis:

(1) Saving = Investment

Now, let’s divide the economy into four sectors: households, corporations, government, rest of the world (ROW).  On this division, the aggregate saving of the overall economy equals the individual saving of each of these sectors:

(2) Saving = Household Saving + Corporate Saving + Government Saving + ROW Saving

Combining (1) and (2) we get:

(3) Household Saving + Corporate Saving + Government Saving + ROW Saving = Investment

Note that the term “investment” here doesn’t just refer to corporate investment; it refers to the total combined investment of all of the sectors–not only the building of new factories by corporations, but also the building of new homes by households.  In the present context, it’s actually an investment rate–how much is invested per year.  Saving is also a rate–how much the net wealth increases per year.

Now, Corporate Saving equals Profit minus Dividends.  So (3) becomes:

(4) Household Saving + (Profit – Dividends) + Government Saving + ROW Saving = Investment

Rearranging we get an equation for profit:

(5) Profit = Investment + Dividends – Household Saving – Government Saving – ROW Saving

This is the Kalecki-Levy profit equation, an equation discovered, in a different form, by the economist Jerome Levy in 1908, and refined by the economist Michal Kalecki in the 1930s. If we divide each term by GNP, we get an equation for profit as a percentage of GNP, which crudely approximates the corporate profit margin (profit as a percentage sales).

(6) Profit/GNP = Investment/GNP + Dividends/GNP – Household Saving/GNP – Government Saving/GNP – ROW Saving/GNP

The NIPA sources for each term are given in the table below.  They are directly available online from the BEA here:


To test the equation, we can compare its predictions to actual NIPA reported profits from 1947 to year-end 2013:


What the equation is saying, in simple terms, is this.  Profit/GNP cannot rise net of dividends unless one of the following, or some adequate combination thereof, occurs: (1) corporations invest the increased profit back into the economy, (2) the other sectors increase their investment without also increasing their saving (meaning they lever up their balance sheets–that is, invest with borrowed funds rather than with their own income, so that their new assets are matched to new liabilities, creating no net increase in wealth, and therefore no additional saving), or (3) the other sectors reduce their savings rates.

There’s a limit to how much corporations can invest.  There are only so many profitable projects to invest in.  There’s also a limit on the extent to which the other sectors can lever up their balance sheets or reduce their savings rates.  For the Household and ROW sectors, the leverage constraint is preference-based and market-based (Households and ROW don’t like to borrow, and lenders will only fund a certain amount of it), whereas the saving rate constraint is need-based (people need to maintain a stock of wealth for retirement or emergencies).  For the government, both limits are political (driven by the decisions of policymakers).

The implication, then, is that there is a limit on how high the profit margin can sustainably get.  If it is elevated, it will necessarily be elevated because corporate investment is elevated, because non-corporate leveraging is elevated, or because the savings rate is depressed.  As these abnormal conditions revert to the mean, so too will the profit-margin. Or so the argument goes.

Household Saving and Deficit Reduction: The 2012-2013 Fiscal Cliff

In recent years, the Government Deficit has risen substantially relative to its long-term average.  Its rise has been driven by the plunge in Investment that took place in the Great Recession, a plunge that the U.S. economy has yet to fully recapture.  In general, Investment and the Government Deficit tend to be closely inversely correlated.


In 2012-2013, the U.S. economy embarked on a deficit reduction program.  Investment was in the process of recovering, so there was room for the deficit to fall.  The concern, however, was that if the deficit reduction was too large, or if it was instituted faster than the investment recovery could keep up with, that the result would be excessive consumer strain, a reduction in corporate revenues and profits, and an associated recession.

Those who voiced this concern, myself included, failed to appreciate the inherent flexibility of the household saving term.  With the exception of corporate tax increases and direct contract spending cuts, fiscal overtightening doesn’t directly hit corporate revenues or cause recessions.  Instead, it puts a choice on households–reduce your savings rates or reduce your expenditures (which, if chosen, will force a reduction in corporate revenues and profits and cause a recession.)

For obvious reasons, households naturally prefer to reduce their savings rates over reducing their standards of living.  And so, in response to the 2012-2013 deficit reduction program, they predictably chose the former.  Rather than decrease their consumption, they saved less than they otherwise would.  The Household Saving term fully absorbed the portion of the deficit reduction that rising investment couldn’t make up for, allowing corporate revenues to continue to grow and the economy to avoid a recession.

In truth, there is currently room for the household saving rate to fall further, should it need to.  If policymakers were to impose another misguided fiscal austerity program, the hit would most likely be absorbed in lower household saving.  For households to choose to maintain or increase their savings rates at the expense of their standards of living, they need to get scared–specifically, scared that their jobs are no longer secure.  Then, they will cut back on spending and increase their savings–which is what we saw them do in 2008, as their homes values were fell, as unemployment rose, and as the negative mood in the economy grew.  A 2% payroll tax increase, or a small spending reduction, such as what we saw with the furloughing of government employees, isn’t going to be capable of creating that level of fear in the present environment.

We tend to think that reductions in household saving are “unsustainable.”  But we have to remember that we’re talking about a savings rate.  It’s not as if households are depleting or burning down their wealth when they reduce their savings rates.  What they are actually doing is reducing the pace at which their net wealth is growing each year.  There is no rule that says that their net wealth has to grow at any specific pace; the important point is that it’s growing rather than contracting.

Now, it’s true that younger generations need to save for retirement.  But older generations are free to anti-save, spend down their wealth.  The high saving of younger generations tends to offset the anti-saving of older generations, allowing younger generations to prepare for retirement without pushing up the aggregate household saving term.  Indeed, as the demography of an economy shifts towards old age, aggregate household saving tends to fall.  The number of older anti-savers comes to offset the number of young savers.  If Japan’s experience provides any sign of what’s to come for the US, we should expect to see household saving continue to fall over the next several decades, and possibly even go outright negative at some point.  Note that this won’t necessarily generate further increases in the profit margin, because investment will also fall as the population ages.

For reference, here are the values for each of the terms in the equation from 2Q 2006 to 4Q 2013, alongside the average from 1947 to 2013:


As you can see in the table, investment plunged in the Great Recession.  The government deficit expanded to absorb the impact of the investment plunge and the increase in household saving associated with the deteriorating economic mood.  As the recovery and expansion have taken hold, investment has gradually risen back towards normal levels, and household saving has gradually fallen.  Given that most of the 2012-2013 austerity is behind us, a continued rise in investment–which still has a very long way to go before it reaches normal levels (current: 3.93%, average: 8.35%)–will be the key ingredient in achieving a normalized deficit going forward (not that it matters–deficits don’t really matter, but it’s an optical thing for policymakers).

It turns out that in the fiscal cliff, the government deficit was forcibly reduced by a larger amount (3%) than the rise in investment (less than 1%) could keep up with.  But there was no problem, household saving fell by the amount that it needed to (roughly 2%) in order to absorb the difference.  The economy avoided recession, corporate revenues continued to grow (albeit at a pathetic nominal rate), and the profit margin held like a rock–on NIPA profits, it’s currently within a couple bps of a record high, and on company reported S&P profits, it’s at a new all time high.

The Impact of Wealth Inequality

In the present context, the Kalecki-Levy profit equation is something of a red herring. Those who cite it as a reason for the necessity of profit margin mean-reversion tend to forget about a crucial term that fixes everything: the Dividends/GNP term.  In theory, an economy can sustain profit as high as 100% of GNP, as long as the uninvested balance of that profit is paid out as dividends, where it will explicitly add to the household and ROW saving terms (via the increased dividend income).  In practice, the uninvestable balance of profit is always eventually paid out as dividends (or utilized in the equivalent: acquistions and share buybacks).  Over the last 30 years, Dividends/GNP have risen alongside Profits/GNP, as expected (FRED).


More importantly, the equation treats corporations as if they were actual separate members of the economy, with their own selfish interests.  They are not.  They are inanimate property–the property of households and foreigners.  When corporations retain profit, the net wealth of the households and foreigners that own them increases, therefore the households and foreigners are effectively “saving.”  Given the way the BEA defines terms in NIPA, that saving isn’t reflected in the equation.  But it’s 100% real.  It can be monetized at any moment through sales in the market, provided that market prices sufficiently reflect corporate value (and right now, they most definitely do).  The following chart compares what household saving would be if it reflected household claims on retained profit (red) with household saving as actually tabulated using NIPA definitions (blue) (FRED):

actual hhold

The problem, of course, is that the household sector is not composed of one big happy family that “saves” together.  Rather, it is composed of millions of families.  Most of these families do not own equities.  And so “household saving” that takes place in the form of higher dividends, higher corporate net worth and a higher stock market does not accrue to them.  To the extent that such saving comes at the expense of other forms of income–in particular, wages and interest receipts–the end result may not be sustainable.

It is in this sense that the Kalecki-Levy profit equation is really an equation about household wealth inequality.  If there were no inequality in the household distribution of equity ownership, the equation would be of little relevance to the present profit margin debate.

The following charts show the distribution of household asset ownership among the top 1%, the top 10% and the bottom 90%:

pension accts

As you can see, the top 10% of households own 81% of the stock market.  When corporations save, it is that small contigency–not the larger pool of households–that receives the “household saving.”

Now, the top 10% of households also owns 70% of all cash deposits and 94% of all financial securities (the balance of which consists of credit assets).  For this reason, the portion of the recent profit margin increase that has been driven by the Fed’s low interest rate policy is entirely sustainable.  That policy does not take money from lower and middle class households to give to wealthy households.  Instead, it transfers money from one part of wealthy household portfolios (cash and credit) to another part of those same portfolios (equities).

Note that a similar shift is sustainable in the areas of pension and life insurance.  The payouts associated with pension and life insurance obligations tend to be defined.  Thus interest rates tend to affect the corporate sector for which those payouts are a liability, not the household sector to which those payouts are due.  A low interest environment makes it more difficult for the corporate sector to meet its pension and life insurance obligations, but such an environment also make the corporate sector more profitable.  As before, the result is a wash.

Risk-averse investors will obviously lose out in such a transfer, and will therefore view it negatively.  But we mustn’t confuse their plights with the plights of average households. Average households are not in the business of owning financial securities–of any type. They are in the business of taking on debt to fund the purchase of a real asset: a home that they can live in.  As you can see in the table, they owe a hugely disproportionate amount of the debt in the economy relative to their asset base, and therefore foot a hugely disproportionate amount of the bill for the interest–mostly mortgage interest, but also credit card interest and student loan interest.  Low interest rate policies are of significant benefit to them, not only because they stimulate the economy relative to the alternative, but also because they reduce the interest payments that the households have to make to wealthier savers.  That’s why the Federal Reserve has kept interest rates at zero, and will continue to do so for the foreseeable future.

Now, the situation is very different when we talk about the shift in income from wages to profit, which is the shift that has driven the majority of the present profit margin increase. That shift takes money from the low and middle classes of the economy, who earn their income almost entirely from wages, and gives it to the wealthy.

The following chart shows wages as a percentage of GNP from 1947 to 2013:


The plunge is striking.  Note that this chart doesn’t reflect the wealth shift inside the wage space.  The wages of the wealthy have increased much more over the last 60 years than the wages of the lower and middle classes, making the situation more extreme.

The large increase in wealth inequality that has ensued over the last 60 years should cause us to worry about what is actually going on inside the Household Saving term in the Kalecki-Levy profit equation.  If Households in aggregate are saving only 3% of GNP every year, and if that saving includes the high-saving of the wealthy, to include saving related to the elevated dividend income that only they receive, what is happening to the savings rates of the lower and middle classes?  Might we be in a situation where their savings rates have to actually be negative in order for them to be able to spend, consume, and participate at the level that a growing economy needs?  It’s a fair question to ask.

As I pointed out in the previous piece, the worry is alleviated by the fact that the wealthy consume a much larger share of the overall pie than the lower and middle classes, and that the share of their consumption has increased meaningfully alongside the increase in their income share.  Their increased consumption has made it possible for the lower and middle classes to consume less without harming the economy.


But is the increased consumption of the wealthy enough to allow the lower and middle class to maintain an adequate savings rate without derailing the economy?  Again, it’s a fair question to ask.

The Impact of Wealth Redistribution

It turns out that there is an important ingredient in the mix that we’re ignoring here: the redistribution of wealth.  Wealth inequality has increased dramatically, but so has the amount and the extent of wealth redistribution.

The previous chart of wages, frequently cited, is deceptive in two respects.  First, it doesn’t include benefits such as employer contributions to healthcare and retirement, which are a type of wage. Second, it doesn’t account for the enormous rise in transfer payments–income that accrues almost entirely to the non-equity-owning, wage-earning lower and middle classes via the redistribution of pre-tax income.

The following chart shows wages as a percent of GNP (green), wages plus benefits as a percent of GNP (blue), and wages plus benefits plus transfer payments as a percent of GNP (red), from 1947 to 2013 (FRED):


As you can see, total non-capital income properly measured to include supplements paid to the poor and middle class (the red line), is at a record high relative to GNP.  Now, some of these transfer payments are paid for via the government deficit.  But the vast majority is paid for by taxpayers.  And just as the wealthy earn most of the capital income, they pay most of the taxes.  They therefore fund most of these transfers.

To highlight the example of federal income taxes, the following charts show the share of total federal taxation and income paid by the top 1%, 2%-5%, 5%-10%, 10%-25%, 25%-50%, and bottom 50% from 1980 to 2013:


As you can see, the top 10% pay roughly 70% of all federal income taxes, up from roughly 49% in 1980.

share income

On the income side, the top 10% earn roughly 45% of all income, up from roughly 32% in 1980.  So their tax share has grown much more than their income share.

An Improved Formulation of the Kalecki-Levy Profit Equation

The problem with the Kalecki-Levy profit equation is that it can’t account for the impact of increased wealth redistribution inside the household sector.  To illustrate, suppose we start with the terms in the equation in the following configuration, which was the configuration at the end of 2013:


Suppose we then reduce wages by 10% of GNP.  Wages are a cost to the corporate sector, therefore profits will rise from roughly 10% of GNP to roughly 20% of GNP. Suppose that all of the profit increase goes to increased dividends.  Dividends, then , will rise from roughly 5% of GNP to roughly 15% of GNP.

Assume, for simplicity, that households own 100% of the corporate sector, and that the rest of the world owns 0%.  If household consumption stays constant, the 10% wage reduction will have no effect on household saving.  This is because dividends will rise by the same amount that wages fall (the dividend increase is being accomplished by taking from wages). Because both types of income feed into household income, household income will stay constant through the change.  But saving is just income minus consumption.  Therefore if consumption stays constant, saving will stay constant too.  We will end up with the equation in the following configuration:


Obviously, the shift would be unsustainable–with the unsustainability revealed in the ridiculously high profit margin.  It would represent a wealth transfer of 10% of GNP from the bottom 80% to the top 20%.  Crucially, household consumption would not be able to stay constant through the transfer.  The top 20% of would end up with extra income equal to 10% of GNP that they wouldn’t know what to do with–they certainly wouldn’t be able to consume an extra 10% of GNP, nor would they be able to invest it in the economy; there aren’t enough useful projects to go around.  Their only choice would be to hoard it–take it out of the economy.  The lower and middle class would therefore lose it for good, without a way to get it back.  They would have to cut their expenditures by 10% of GNP–either that, or run a massive borrowing deficit.  The balance of payments between the sectors would therefore unravel, revealing the profit margin increase as unsustainable.

Now, to illustrate the equation’s shortcoming, suppose we put in place the exact same wage reduction and profit increase, except this time we tax and redistribute 100% of the associated increase in dividends.  The top 20% will earn an extra 10% of GNP in dividends, but they will pay an extra 10% of GNP in taxes back to the government, so their after-tax income will end up unaffected.  The bottom 20% will lose 10% of GNP in wages, but will receive that 10% of GNP back in the form of transfer payments.  Their after-transfer income will be unaffected, and therefore the system will remain unperturbed.  However, the equation will register the same profit margin extreme as before, with profits at a ridiculous 20% of GNP:


As before, the temptation is to look at this configuration and conclude that it’s unsustainable.  Given the skewed distribution of equity ownership, profits and dividends cannot sustainably rise by 10% of GNP at the expense of an associated 10% reduction in wages.  The result would be a massive transfer of wealth from the bottom 80% that earns income through wages to the top 20% that effectively receives all of the economy’s profit and dividend income.  But the transfer is sustainable in this case, because redistribution will fully transfer it back.  The equation, as applied, is flawed because it doesn’t account for the effect of the redistribution, the transferring back.  It therefore creates the false impression of an impending balance of payments crisis, where there is none.

Now, consider a final twist.  Instead of taxing the increased profit at the household level, via a dividend tax, and then redistributing it via transfer payments, suppose that we tax it at the corporate level, via a corporate tax, and then redistribute it.  There’s no difference between this option and the previous option–both options identically redistribute the money from the top 20% back to the bottom 80%, undoing the previous transfer.  But the ensuing configuration of the Kalecki-Levy profit equation will turn out to be very different under this option.  The equation will rightly register no change at all.  Profit margins will remain exactly what they were before the round trip transfer:


Evidently, if redistribution occurs at the corporate level, profit margins don’t change.  But if it occurs at the wealthy household level, which is ultimately the exact same thing, profit margins do change–they increase, creating the false perception of a wealth transfer from the poor and middle class to the rich that isn’t actually happening.

In the 1950s and 1960s, a larger portion of “wealth redistribution” was accomplished through the corporate tax, and a smaller portion was accomplished through income taxes on wealthy households.  Since then, the general amount of “wealth redistribution” has significantly increased, and the target of that redistribution has shifted away from corporations and towards the wealthiest households–specifically, the top 10% to 20% of earners, who now pay the lion’s share of total taxes.

For this reason, evaluating today’s profit margin against the profit margin of the past is illusory from a balance of payments perspective.  The current profit margin ends up looking much higher than the profit margin of the past, even though the final balance of payments condition, after redistribution is taken into account, is no more extreme now than then.

To accurately reflect the impact that rising amounts of wealth redistribution have had on the sustainability of higher profit margins, and also the effect of the shift in the tax burden from corporations to wealthy households (that own the corporate sector), we need to reconfigure the equation so that 100% of the economy’s tax burden falls on the corporate sector at all times across history.  Then, comparisons with the past will be appropriately apples-to-apples.

To modify the equation, then, we take the taxes that households (and the ROW) pay, to exclude sales taxes, property taxes, and social insurance contributions, and add those back to household and ROW savings (simulating a scenario where they aren’t taxed at the household or ROW levels).  We then subtract them instead from corporate profits (simulating a scenario where they are taxed at the corporate level instead).  The equation becomes:

(7) Fully-Taxed Profits/GNP = Investment/GNP + Dividends/GNP – Pre-tax Household Saving/GNP – Government Saving/GNP – Pre-tax ROW Saving/GNP

The following chart shows the calculated and actual reported profit margin under this improved formulation of the equation, followed by table with NIPA references:



As you can see, in this formulation, the profit margin, which was 63% above its historical mean in the prior formulation, ends up being roughly on par with its historical average, and below the average of the pre-1970 period.

Now, to be clear, a comparison of the present values of the “fully-taxed” profit margin with the historical average does not give an accurate picture of the sustainability of current profit margins from the perspective of competition.  The “fully-taxed” profit margin is not a real profit margin that any business actually sees–it’s just a construct.  It’s deeply negative because corporate profits are a very thin slice of the economy, smaller than the total quantity of taxes raised.  Corporations cannot afford to pay all of the economy’s taxes; their pre-tax profits are too small.

But a comparison of the present values of the “fully-taxed” profit margin with the historical average does give an extremely useful picture of the sustainability of current profit margins from the perspective of the balance of payments of the different sectors of the economy, specifically between the wealthy and the lower and middle classes. The “fully-taxed” profit margin gets pulled down during periods where wealth redistribution is high and pushed up during periods where it is low, a necessary adjustment if we want to properly compare the balance of payments implications of various profit margin levels across history.  The comparison should not be an absolute comparison; it needs to be a comparison net of wealth redistribution.

It is true that the actual corporate profit margin is higher now than in the past, reflecting a transfer of wealth from the lower and middle class to the wealthy.  But the transfer is sustainable because the wealth is ultimately being transferred back, via higher levels of redistribution and higher levels of taxation of wealthy households relative to the past. That sustainability is reflected in the fully-taxed profit margin, which is roughly on par with its historical average (rather than 63% above, as it is in the earlier formulation).

The following chart shows what happens to household savings under the improved formulation of the equation:


Relative to the respective averages, the upper line, the pre-tax household saving, is significantly less depressed than the lower line, the after-tax saving.  The vast majority of the difference between the two lines is borne by the wealthy, through their tax contributions.  So when we ask the question, how can the lower and middle classes be saving anything when the saving of the total household sector, to include the saving of the high-saving wealthy, is only 3% of GNP, the answer, again, is wealth redistribution.  If you netted out the cost of wealth redistribution (taxes), without netting out the benefits (the incomes that accrue to the lower and middle class via government spending), the household sector would actually be saving 15% of the entire economy. The difference between the 15% and the 3% is what the wealthy directly give back.  It’s a much larger number than it used to be.

Now, the “fully-taxed” corporate profit margin above excludes sales, property, and social insurance taxes.  The rich pay a disproportionate share of those taxes (a disproportion which has also been rising), but the disproportion is not as extreme as it is in the area of the income tax proper (where the top 20% pay almost everything), therefore we leave them out.  For perspective, the following chart and reference table show the “fully-taxed” corporate profit margin with sales, property, and social insurance taxes with them added in:



As you can see, the profit margin on this accounting is even less elevated.  It’s well below the levels of the idealized 1940s, 1950s, and 1960s.

To conclude, rising profit margins do not pose a threat to the economy’s financial stability because they’ve been coupled to rising levels of wealth redistribution.  We would do best to stop worrying about profit margins, which are ultimately a distraction, and focus instead on the variable that drives outcomes in capitalist economies: the return on equity.

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Profit Margins Don’t Matter: Ignore Them, and Focus on ROEs Instead

Mean-reversion in a system doesn’t happen simply for the sake of happening.  It happens because forces in the system cause it to happen.  With respect to profit margins, the following questions emerge: What are the forces that cause profit margins to mean-revert? Why do those forces pull profit margins towards any one specific mean value–11%, 9%, 7%, 5%, 3%, 1%–rather than any other?  And why can’t secular economic changes–for example, changes in interest rates, corporate taxes, and labor costs–affect those forces in ways that sustainably shift the mean up or down?

In what follows, I’m going to explore these questions.  I’m going to argue that profit margins are simply the wrong metric to focus on.  The right metric to focus on, the metric that actually mean-reverts in theory and in practice, is return on equity (ROE).  Right now, the return on equity of the U.S. corporate sector is not as elevated as the profit margin, a fact that has significant implications for debates about the appropriateness of the U.S. stock market’s current valuation.

The piece has three parts.  In the first part, I critique profit margin mean-reversion arguments grounded in the Kalecki-Levy profit equation, put forth most notably by James Montier and John Hussman.  In the second part, I challenge the claim that competition drives profit margin mean-reversion, and argue instead that competition drives mean-reversion in ROE.  In the third part, I use NIPA and flow-of-funds data to quantify the current ROE of the U.S. corporate sector, and discuss how a potential mean-reversion would impact future equity returns.

Balance of Payments: The Kalecki-Levy Profit Equation

A common argument for the mean-reversion of profit margins involves an appeal to the balance of payments between different sectors of the economy.  We can crudely summarize the appeal as follows.  Assuming constant total income for the overall economy, the profit margin reflects the quantity of income that goes to the corporate sector.  If that quantity rises, the quantity that goes to other sectors–households, the government, and the rest of the world–must fall.  Trivially, if the quantity that goes to the other sectors falls, those sectors will have to reduce their expenditures.  But their expenditures are the revenues of the corporate sector.  All else equal, the revenues of the corporate sector will have to fall, in direct opposition to the profit margin increase.

James Montier and John Hussman state the argument in more precise terms by appealing to the Kalecki-Levy profit equation, which we derived and explained in a previous post:

(1) Corporate Profit = Investments + Dividends – Household Saving – Government Saving – Rest of the World (ROW) Saving

If you divide each of the terms in the equation by GNP, you get an equation for Profit/GNP, which is an approximation of the aggregate profit margin of the U.S. corporate sector.  Thus,

(2) Profit/GNP = Investment/GNP + Dividends/GNP – Household Saving/GNP – Government Saving/GNP – ROW Saving/GNP

The equation expresses the intuitive point that if corporations hoard profit–that is, if they earn profit, and then hold it idle, rather than invest it back into the economy–they will suck the economy dry.  The other sectors of the economy will lose income.  To maintain constant expenditures and avert recession, those sectors will have to either: (1) lever up their balance sheets–that is, borrow funds and invest them–which will create new income for the economy to make up for the income that the corporate hoarding has pulled out of the economy, or (2) reduce their savings rates.

With the possible exception of the government, there’s an obvious limit to how much any given sector of the economy can lever up its balance sheet or reduce its savings rate. Likewise, there’s a limit to how much the corporate sector can realistically invest.  There are only so many profitable ventures to invest in–to invest beyond what those ventures warrant would be to incur an effective loss.  Citing the equation, Montier and Hussman therefore conclude that an upper limit exists on Profit/GNP.

But this conclusion misses what is arguably the most important term in the equation: the Dividend/GNP term.  Profit/GNP can be as high as you want it to be, without any sector needing to increase its investment or reduce its savings rate, as long as the “leftover” profits are distributed back to shareholders in the form of dividends.  And why wouldn’t they be?  The purpose of a corporation is not to earn profit for the sake of earning profit, but for the sake of paying it out to its owners.  Those owners are not going to tolerate a situation where cash sits idly on the corporate balance sheet, particularly if the stock is languishing.  They will demand that the cash be invested in something productive, or paid out to them.  Ultimately, they will get their way.

The Profit/GNP term is hovering near a record high right now.  But so is the Dividend/GNP term.  The following chart shows U.S. corporate profit (red) and U.S. corporate dividends (blue), both as a percentage of GNP, from 1947 to 2014 (FRED):


As you can see, the two terms have risen to record highs together.  Relative to the historical average, the Profit/GNP term is elevated by around 383 bps.  But of that amount, 252 bps is already accounted for in a higher Dividend/GNP term.  To achieve an equilibrium at current Profit/GNP levels, then, all that is needed is an additional net 131 bps of reduced Saving/GNP from the other sectors of the economy.  That’s a relatively modest amount–a small increase in the government deficit relative to the average could easily provide for it, and almost certainly will provide for it as baby boomers age over the next few decades.

So there really isn’t any problem here.  Corporations will earn whatever amount of profit they earn.  If they can’t find useful targets for reinvestment, they will distribute the profit as dividends (or buybacks–which get ignored here because of the way NIPA calculates “saving”), in which case the balance of payments condition set forth in the Kalecki-Levy equation will be satisfied.

Retained Corporate Profit Is Household Saving

It turns out that the application of the Kalecki-Levy profit equation to the profit margin debate is flawed in a much more fundamental way.  The equation makes an arbitrary distinction between retained corporate profit and household saving.  But households own the corporate sector, therefore retained corporate profit is household saving, in the fullest sense of the word “saving.”

In the current context, “saving” means “increasing your net wealth.”  When corporations that you own increase their net wealth by retaining profit, your net wealth also increases, therefore you are “saving.”  This saving is not some imaginary construct; it’s fully tangible and liquid, manifest in a rising stock market.  You can monetize it at any moment by selling your equity holdings.

To be clear, in describing retained corporate profit as a type of household saving, I’m not referring to gimmicky, transient household wealth increases that might be accomplished by pumping up the stock market’s valuation.  I’m talking about real, durable, lasting wealth increases that are backed by increases in corporate net worth and a larger implied streams of future dividend payments.  Those are the kinds of wealth increases that indirectly accrue to households when corporations retain profits.  The stock market doesn’t create them by rising in price; rather, it reflects them, makes them liquid for shareholders.

The wealth that corporations create for households can be retained and stored on the corporate balance sheet, in which case equities will sell for higher prices, leaving households with a larger reservoir of savings in the stock market that they can monetize, or the wealth can be paid out as dividends, in which case it will be stored in the bank accounts of the households directly.  In the first case, households will “save”–accrue wealth–through increases in the market value of their equity holdings; in the second case, households will “save”–accrue wealth–through increases in the quoted values of their bank accounts. There’s no difference.

Now, for obvious practical reasons, the BEA chooses not to classify retained corporate profit and associated increases in the market value of equity holdings as a type of household saving.  But it’s a real type of saving nonetheless, a type of saving that the Kalecki-Levy profit equation, in its present form, completely ignores.

The blue line in the following chart shows the household savings rate as a percentage of GNP from 1980 to 2014.  The red line shows the housing savings rate as a percentage of GNP adjusted to reflect the household share of retained corporate profits (FRED):

actual hhold

As you can see, the blue line is significantly below its average for the period.  Since the mid 1980s, it’s fallen by more than 50%.  The more accurate red line, in contrast, is only slightly below its average for the period.  It’s actually on par with the level of the mid 1980s–a period generally considered to be economically “normal.”  If, to maintain expenditures and avert recession in the presence of persistently high profit margins, households should need to reduce their savings rates, there’s plenty of room for them to do so–the current level is twice that of the cycle troughs of 2000 and 2007.

When you hear claims that record high corporate profits are coming at the cost of record low household savings, remember that the wealth in question is ultimately fungible.  When it shifts from household “saving”, as defined in NIPA, to corporate profit, it’s not disappearing from the household balance sheet–rather, it’s going from one part of the household balance sheet (the bank account) to another part (the brokerage account).  The Kalecki-Levy equation’s dichotomy between the two accounts, while helpful in some contexts, creates a distortion in this context.

A number of bullish Wall Street analysts have argued that high profit margins will likely persist because they’ve been driven, to a significant extent, by low interest rates, which are presumably here to stay.  In an interview from a few months ago, James Montier responded to their argument:

“Low interest rates are another pretty good example of the framework, because ultimately those interest rates would have to be paid to somebody. It’s generally the household sector that benefits from higher interest rates. What that really means is that household savings have to be altered, because household income is less than it would be if you had high interest rates. The household-savings element of the Kalecki equation is where low interest-rate effect shows up.”

This point misses the fact that what households are losing in the form of lower interest income, they’re gaining in the form of higher dividends and higher stock prices.  Income is not being removed from the household sector; rather, it’s being transferred from the cash and bond portions of household portfolios to the equity portions of those portfolios.  The Kalecki-Levy equation, as constructed, ignores stock market appreciation as a form of household saving, therefore it doesn’t register the transfer.  But the transfer is real, and 100% sustainable from a balance of payments perspective.

The Obvious Problem: Wealth Inequality

Low interest rates have helped drive a shift from household interest income to corporate profit.  That shift is sustainable because the same upper-class households that own the majority of the cash and credit assets in the U.S. economy, and that would receive the interest payments that corporations would otherwise pay on accumulated debt, also own the majority of the U.S. economy’s equity assets.  All that low interest rates do, then, is take income out of one part of their portfolios, and insert it in another part.

Now, a more powerful driver of increased corporate profitability has been the shift in income from wages–primarily those of the middle and lower classes–to profit.  If the ownership of the corporate sector were distributed across all classes equally, the shift would not have much effect.  What the middle and lower classes would lose in wages, they would gain in dividends and stock price appreciation.  Unfortunately, the ownership of the corporate sector is not distributed equally–far from it.  Right now, the top 20% of earners in the United States owns roughly 90% of all corporate equities. So when we talk about a shift from wages to profits, we’re talking about a shift in income and wealth from the 80% that needs more to the 20% that already has plenty.

This shift is obviously an ugly development for the larger society.  But the question for investors isn’t whether it’s ugly–it is what it is.  The question is whether it’s economically sustainable. Though it unquestionably reduces the natural growth rate, long-term financial stability, and aggregate prosperity of the U.S. economy relative to more progressive alternatives, it is economically sustainable.

One of the reasons that it’s economically sustainable is that it’s been coupled to a corresponding shift in expenditures.  The bottom 80% earns a smaller share of overall income than it did in the past, but it also conducts a smaller share of overall spending.  The simultaneous relative downshift in its income and spending has cushioned the implied blow to its savings rate.  Similarly, the asset-heavy top 20% earns a larger share of overall income than it did in the past, but it also conducts a larger share of overall spending.  The increase in its overall spending has helped to offset the otherwise recessionary implications of reduced relative spending from the bottom 80%.

The following table shows the consumption expenditure share of each income quintile for 1972 and 2011, with data taken from the census bureau’s consumer expenditure survey:


Since the early 1970s, we’ve seen a 3.90% shift in consumption expenditures from the bottom 80% to the top 20%.  Not only have the rich come to represent a larger share of total income, they’ve also become bigger consumers of the overall pie. Likewise, just as the middle and lower classes have come to represent a smaller share of total income, they’ve become smaller consumers of the overall pie.  Again, an ugly development, but a theoretically sustainable one nonetheless.

Roughly 40% of the U.S. consumption economy is driven by the consumption activities of the top quintile.  That quintile consumes twice its population share–a huge amount.  Its elevated consumption is critical in offsetting the depressed consumption of the other quintiles, especially the bottom two quintiles, which together consume half their population share.

Now, a spending reduction on the part of the bottom 80% equal to 3.90% of the total may sound like a small amount, and it is. But so is the corporate profit increase relative to the average–it’s also a small amount, 3.71% of total national income.  Corporate profit is a very thin slice of the economy.  Small changes in it as a percentage of GNP can have a big effect on the stock market and on the behaviors of corporations and investors. But the effect on the economy as a whole, in terms of the balance of payments of the various sectors (what the Kalecki-Levy equation is ultimately trying to get at), is exaggerated.

If, as income shifts from the bottom 80% to the top 20%, the spending of the top 20% fails to increase, then the bottom 80% will simply have to reduce its savings rate.  Either that, or aggregate expenditures will drop, and the economy will fall into recession (assuming no government help).  In practice, the bottom 80% has proven that it’s very willing to reduce its savings rate in order to avoid forced reductions in its consumption.  It wants to keep consuming.

It may not be desirable for the bottom 80% to save less, but that doesn’t mean that it’s “unsustainable.”  There’s no rule that says that households have to save, i.e., increase their wealth, by any specific amount each year.  In theory, the fact that households aren’t reducing their wealth–that their savings rate is positive in the first place–is enough to make the situation sustainable (if they were reducing their wealth each year, they would be on a path to bankruptcy; that obviously can’t be sustained).

The U.S. economy recently conducted a “household saving” experiment in real time.  In 2012 and 2013, it embarked on a grossly misguided fiscal austerity program that took income out of the pockets of the bottom 80% and put it into the black hole of increased government saving.  If households had insisted on maintaining their savings rates amid the lost income, they would have had to have reduced their expenditures.  Revenues, profit margins, and profits would have been pulled down, and the economy would have slipped into recession.  That was the outcome that many people, myself included, were expecting. But it didn’t happen.  Households simply reduced their savings rates to make up for the portion of lost income that other income sources–specifically, rising corporate and residential investment–failed to provide.  Here we are, a year and a half later, with the government deficit roughly half what it was at the peak, and yet profit margins continue to snub their noses at the Kalecki-Levy equation, making new record highs as recently as this last quarter.


Competition as a Driver of Mean-Reversion

Another common argument for the mean-reversion of profit margins involves an appeal to competition.  On this logic, profit margins cannot sustainably rise to elevated levels because corporations will undercut each other on price to compete for them.  The undercutting will drive profit margins back down to normal.

But if corporations are inclined to undercut each other on price when profit margins are “elevated”, so that profit margins fall to “normal”, why wouldn’t they be inclined to undercut each other on price when profit margins are “normal”, so that profit margins fall to “depressed”?  And why wouldn’t they be inclined to undercut each other on price when profit margins are “depressed”, so that profit margins fall to zero?  Why would the process of price undercutting stop anywhere other than zero, the terminal point of competition, below which there’s no worthwhile margin left to take?

If a competitor’s 11% profit margin is worth pursuing, why wouldn’t that competitors 9% profit margin also be worth pursuing?  And the competitor’s 7% profit margin?  And the competitor’s 5% profit margin?  And the competitor’s 3% profit margin?  It’s all profit, right?  Why would a corporation leave any of it on the table for someone else to have, when the corporation could go in and try to take it?

On this flawed way of thinking, there’s no reason for the margin-depressing effects of competition to stop at any specific profit margin number; corporations should cannibalize each other down to the bone.  They should try to take every meaningful amount of competitor sales volume that is there to be taken.  Profit margins in unprotected industries should therefore be something very close to zero.  But, in practice, profit margins in unprotected industries are not close to zero. Why not?

Corporations seek to maximize their total profits–not their profit margins, not their sales volumes.  They sell their output at whatever price produces the [profit margin, sales volume] combination that achieves the highest total profit.  In environments where there is significant excess capacity and weak demand, that combination usually entails a low price relative to cost, i.e., a low profit margin.  Corporations aggressively undercut each other to sell their output.  In environments where there is tight capacity and strong demand, the combination usually entails a high price relative to cost, i.e., a high profit margin. Corporations don’t have to undercut each to sell their output–so they don’t.  They do the opposite–they’ll overcut each other, raise prices.

The mistake we’re making here is to assume that corporations “compete” for profit margins.  They don’t.  Profit margins have no value at all.  What has value is a return.  The decision to expand into the market of a competitor and seek additional return is not a decision driven by the expected profit margin, the expected return relative to the anticipated quantity of sales.  Rather, it’s a decision driven instead by the expected ROE, the expected return relative to the amount of capital that will have to be invested, put at risk, in order to earn it.

Suppose that you run a business.  There is another business across town similar to your own whose market you could penetrate into.  If operations in that market would come at a high profit margin, but a low return on equity–i.e., a low return relative to the amount of capital you would have to invest in order to expand into it–would the venture be worth it? Obviously not, regardless of how high the profit margin happened to be. Conversely, suppose that the return on equity–the return on the amount of capital that you would have to invest in order to expand into the new market–would be high, but the profit margin would be low.  Would the venture be worth it?  Absolutely.  The profit margin would be irrelevant–you wouldn’t care whether it was high or low.  What would attract you is the high ROE, the fact that your return would be large relative to the amount of capital you would have to deploy, put at risk, in order to earn it.

In a capitalist economy, what mean-reverts is not the profit margin, but the ROE, adjusted for risk.  The ROE in an adequately-supplied sector cannot remain excessively high because investors and corporations–who seek returns on their capital–will flock to make new investments in it.  The new investments will create excess capacity relative to demand that will provoke competition, weaken pricing power, and drive the elevated ROE back down.  Likewise, the ROE in an adequately-demanded sector cannot remain excessively low because investors and corporations will refrain from making new investments in it.  In time, the sector’s capital stock will depreciate.  The existing productive capacity will fall, and a supply shortage will ensue that will give the remaining players–who still have capacity–increased pricing power and the ability to earn higher profits.  The ROE will thus get pushed back up, provided, of course, that what is being produced is still wanted by the economy.

Not only does the increased investment that abnormally high ROEs provoke lead to increased capacity and increased competition, it also leads to increased wage pressure and increased interest rates, both of which hit the corporate bottom line and pull down the corporate ROE, all else equal.  The same is true in the other direction–the depressed investment that inappropriately low ROEs provoke leads to downward wage pressure and falling interest rates, both of which boost the corporate bottom line and increase the corporate ROE, all else equal.  The “all else equal” here obviously requires an appropriate monetary policy and the existence of automatic fiscal stabilizers–those have to respond to maintain aggregate demand on target, otherwise the situation will spiral into an inflationary boom or a deflationary recession.

At the open, we posed the question: why can’t the natural mean for profit margins change in response to secular changes in the economy–changes, for example, in corporate tax rates, interest rates, labor costs, etc.?  There is no answer, because the thesis of profit margin mean-reversion is not a coherent thesis.  But for ROEs, there is an answer.  The answer is that investors and corporations do not distinguish between the causes of high returns.  As long as high returns are expected to be sustained, investors and corporations will seek them out in the form of new investment, whether the underlying causes happen to be low taxes, low interest rates, low labor costs, or any other factor.  The elevated ROEs will therefore get pulled back down, regardless of their explanatory origins.

The only force that can sustainably cause ROEs to increase for the long-term is an increase in the risk-premium placed on investment.  By “investment”, we mean the building of new assets, new physical and intellectual property–new stores, new factories, new technologies–not the trading of existing assets.  Psychological, cultural and fundamental conditions have to shift in ways that cause capital allocators to get pickier, stingier, more cautious when it comes to investment, so that higher prospective returns become necessary to lure them in.  If such a shift occurs, the competitive process will have no choice but to equilibriate at a higher ROE.

Right now, there is a sense that the aging, mature, highly-advanced U.S. economy, whose low hanging productivity fruits have already been plucked, and whose households are weighed down by the heavy burdens of private debt, is locked in a permanent slow-growth funk.  When coupled to the traumatic experience of the financial crisis, that sense has dampened the appetite of capital allocators to make new investments.  The perception is that the returns to new investment will not be attractive, even though the existing corporate players in the U.S. economy–the targets of potential competition–are doing quite well.

Additionally, an increasingly active and powerful shareholder base is putting increased pressure on corporate managers not to invest, and to recycle capital into dividends and buybacks instead, given that capital recycling tends to produce better near-term returns than investment.  The data suggests that from a long-term perspective, shareholders are not entirely wrong to have this preference.  Historically, a large chunk of corporate investment has been unprofitable, an unnecessary form of “leakage” from capital to labor. For that reason, corporations that have focused on recycling their capital have generally produced better long-term returns for shareholders than corporations that have opted to frequently and heavily reinvest it.

For these reasons, it’s been harder than normal for presently elevated ROEs to get pulled back down.  If these conditions–investor hesitation and a preference for capital recycling over investment–last forever, then ROEs might stay historically elevated forever.  Let’s hope the condition doesn’t last forever.

To return to the issue of profit margins, in practice, profit margins and ROE are reasonably well-correlated.  That’s what creates the perception that profit margins mean-revert.  But, in actuality, profit margins do not mean-revert, not out of their own accord.  The variable that mean-reverts out of its own accord, in both theory and practice, is ROE.  If the profit margin and the ROE are saying different things about corporate profitability, as they are right now, the ROE is what should be trusted.

Measuring the ROE of the Corporate Sector

To measure the aggregate corporate ROE, we take the profit of all national U.S. corporations (CPATAX: NIPA Table 1.12 Line 15, which includes foreign and domestic profit), adjust that profit to reflect its non-financial share, and then divide the result by the net worth of those same corporations measured at replacement cost (Z.1 Flow of Funds B.102 Line 33, which appropriately includes foreign assets in the calculation).  The following chart shows the metric from 1951 to 2014 (FRED):


Right now, the corporate ROE is 31.2% above its historical mean–elevated, but nowhere near the 60% to 70% elevation that the bogus profit margin metric “CPATAX/GDP” was previously conveying.

The following table presents a running tally of all of the profitability metrics that we’ve examined so far.


As you can see, the reduction in elevation has been significant.  We started out with a deeply flawed metric that was telling us that corporate profitability was 63% above its mean.  By making a series of careful, intuitively-sound, uncontroversial distinctions, we’ve managed to cut that number in half.  Some have expressed concern with our singular focus on “domestic profitability”, given that abnormally high foreign profit margins may be a significant factor driving the overall increase profit margins.  But the ROE metric presented here includes the ROE associated with foreign profits, so those concerns no longer apply.

If we want to look at purely domestic returns on capital, we can use domestic fixed asset data from the BEA.  NIPA Fixed Asset Table 6.1 Line 4 gives the total value of all fixed assets of domestic non-financial corporations, measured at replacement cost.  This is actually the series off of which “consumption of fixed capital” in the NIPA profit series is calculated. Dividing domestic non-financial profit (NIPA Table 1.14 Line 29) by domestic non-financial fixed assets, we get a reasonable approximation of the domestic non-financial ROA–return on assets:

return on fixed assets

This measure is even less historically elevated than the U.S. corporate ROE–it’s only 24% above its historically average.  Domestic corporations clearly aren’t generating as much profit on their asset base as a superficial glance at the profit margin would suggest, which sheds doubt on the claim that “competitive arbitrage” is going to drive corporate profitability dramatically lower over the coming years.  Will we see a retreat from current record levels of corporate profitability as the cycle matures?  Probably.  But not the 40% plunge that advocates of profit margin mean-reversion are calling for.

Implications for Future S&P 500 Returns

In an earlier piece, I conservatively estimated that the S&P 500, starting from a level of 1775, would produce a 10 year nominal annual total return of between 5% and 6% per year.  The market is now at 1900.  I’m certainly not going to recommend that anyone rush out and buy it up here; using my 5% to 6% estimate, it’s roughly where it should be at year end 2016.  However, I will claim credit for warning valuation bears that they’ve been focusing on the wrong factors, that they should be focusing on monetary policy and the business cycle, not on the market’s perceived expensiveness, which participants will eventually anchor and acclimatize to.

Markets fall not because of “overvaluation”, but in response to unexpected, unsettling changes to the narrative, changes that negatively impact expectations about where prices are headed over the near and medium terms.  Rather than worry about the nebulous, unanswerable question of what “fair value” is, investors should focus on getting those changes right, particularly as they relate to monetary policy and the business cycle; the rest will take care of itself.

It turns out that we can arrive at the same 5% to 6% 10 year annual return estimate by assuming that the corporate ROE will fully revert to its mean.  At 1775, the S&P 500 P/E multiple would be around 16.5, a normal value.  So there’s no need to model for any P/E multiple contraction.  If a mean-reversion in ROE from 7.6% to 5.8% were spread across 10 years, the implied annual drag on profit growth would be 2.7%.  If the normal nominal return is 8%–say, 3% for real book value per share growth after dilution, 3% for the shareholder yield, including buybacks, and 2% for inflation–then the return implied by a full reversion in the corporate ROE would be 8% minus 2.7% = 5.3%, roughly what we estimated via different methods.

A nominal equity return between 5% and 6% isn’t “attractive” per se, but it’s acceptable, particularly in an environment where nothing else is offering any return.  The return will surely beat out the emaciated alternatives on display in fixed income markets, especially when properly adjusted to reflect tax preferences that only equities enjoy. Crucially, the current valuation isn’t so dangerously high that investors should be boycotting U.S. markets outright–and definitely not so high that they should be boycotting more attractively priced foreign markets, as some have done, on the false expectation of an impending downturn that restores “normalcy” to U.S. markets.  Corrections and pullbacks? Absolutely.  A dramatic market fall that finally clears 20 years of perceived valuation excess, causing pain around the world?  No.

Now, I readily admit, all of the arguments that I’ve given for why we should focus on ROE instead of profit margins are just that–theoretical arguments.  Valuation bears don’t have to accept them.  But I’ve also provided a metric that clearly mean-reverts.  If we want to measure mean-reversion mathematically, with ADF statistics, the ROE metric that I’ve offered is actually more mean-reverting than every iteration of the profit margin thus presented, as expected given its more intuitive connection to the competitive forces that drive mean-reversion.

When valuation bears say that CPATAX/GDP, or some other profit margin metric, is going to fall to its historical average, and stay there, they are effectively saying that my metric, the ROE of the U.S. non-financial corporate sector, is going to fall substantially below its historical average, and stay there.  Why should that happen?  Why should competitive forces drive the ROE of the U.S. corporate sector permanently below its historical average, particularly in the present environment of corporate hesitation, where shareholders continue to forcefully demand dividends and buybacks in lieu of competition-stimulating new investment?

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Profit Margins: Accounting for the Impact of a Changing Financial Share

In a prior piece, I argued that that the frequently-cited macroeconomic expression “CPATAX/GDP”, shown below in maroon (FRED), is a flawed way of measuring the aggregate profit margin of U.S. corporations.


When a U.S. corporation earns profit from foreign operations, “CPATAX/GDP” counts the profit in the numerator, but doesn’t count the costs of the profit–the wages and salaries of the employees of the foreign operations–in the denominator.  All else equal, the omission causes the profit margin to appear larger than it actually is.

If the share of U.S. corporate profit earned abroad were constant across history, then the profit margin overstatement inherent in “CPATAX/GDP” would occur equally in all years of the data set, and therefore a comparison of the present values of the metric to the averages of past values would still potentially be valid.  However, the share of profit earned abroad has not been constant across history.  In the last 60 years, it has increased dramatically–from less than 10% in 1948 to more than 40% in 2014.  Any comparison between the present values of “CPATAX/GDP” and the averages of past values is therefore invalid.

In place of the flawed “CPATAX/GDP”, I offered a more accurate profit margin metric–domestic profit divided by domestic final sales (GVA: gross value added), shown below in blue (FRED):


This metric divides the domestic profit of corporations by the revenue from which that profit was generated.  All costs associated with a given unit of profit are included in the denominator, therefore the previous overstatement is eliminated.

Unfortunately, not even this metric allows for a valid comparison with the past.  The reason the metric doesn’t allow for a valid comparison is that it fails to distinguish between financial and non-financial profit.  Historically, financial profit has been earned at a much higher profit margin than non-financial profit.  If the share of financial profit in total profit were constant across time, the distinction wouldn’t matter.  But, as before, that share has not been constant across time–it has increased substantially.  A comparison between the present values of the metric and the averages of past values is therefore invalid.

NIPA Table 1.14 conveniently divides total corporate revenue (GVA) into non-financial sector revenue (Line 17) and financial sector revenue (Line 16).  The following chart shows financial sector revenue as a share of total corporate revenue from 1947 to 2013 (FRED):


As you can see, the share has tripled, from 4% in 1947 to 12% in 2014.  Now, if financial profit were earned at roughly the same profit margin as non-financial profit, the increase would not matter.  But, as it turns out, financial profit is earned at a much higher profit margin–more than twice as high.  This isn’t a recent phenomenon–it’s been the case since at least the 1920s, as far back as the NIPA data goes.

The following chart shows the profit margin of the financial sector (red) alongside the profit margin of the non-financial sector (green) from 1947 to 2013 (FRED):


As you can see, the average profit margin for the financial sector is more than twice as large as the average profit margin for the non-financial sector, with the pattern consistent all the way back to the 1940s.  Given that the share of profit that goes to the higher-margin financial sector has increased, we should expect the total corporate profit margin to have similarly increased.  Any comparison of the total corporate profit margin with the averages of past periods needs to account for the increase.

The optimal way to account for the increase is to drop financial profit altogether and focus only on non-financial profit–profit generated from productive operations in the real economy.  The following chart shows the non-financial sector profit margin from 1947 to 2013 (FRED):


When it comes to making comparisons with the past, this chart is the most accurate chart of profit margins available.  To be clear, non-financial profit margins are elevated, but they are less elevated than aggregate profit margins, and nowhere near as elevated as the bogus “CPATAX/GDP” was suggesting.

The following table lists each type of profit margin alongside its historical mean, current elevation, and the annual drag that profit growth would suffer if the profit margin were to revert to the mean over the next 10 years:


Interestingly, the aggregate domestic profit margin is currently more elevated relative to the past than both the financial and non-financial profit margins that make it up.  The reason this is possible is that the share of profit going to the financial sector has increased.

Returning to the chart, rather than being 25% above the highs of prior cycles, as we were with the bogus “CPATAX/GDP”, we’re actually still below those highs–both the high registered in 1966, and the high registered in 1949.  In terms of past precedence, it’s therefore entirely conceivable that profit margins could continue to trek higher in the current cycle.  That is, in fact, what seems to be happening.  With approximately 94% of S&P 500 companies reporting earnings for the first quarter, the trailing twelve month net profit margin for the index is on pace to register yet another new high: 9.67% on operating earnings (as tallied by Howard Silverblatt of S&P), and 8.95% on GAAP earnings (company-reported).


On Twitter, economist Andy Harless made a clever point that replacing “CPATAX/GDP” with these more accurate metrics may actually help the valuation bear case, because the more accurate metrics don’t exhibit a “breakout” to new highs in the same way that “CPATAX/GDP” did.  If valuation bulls embrace the more accurate metrics instead of “CPATAX/GDP”, they will no longer be able to cite such a “breakout” as evidence of a structural shift in corporate profitability.

But, as the chart below illustrates, if we remove the distorting presence of higher-margin financial profits, which have increased over time, the evidence of a structural shift remains intact. In the Great Recession–the worst downturn for the corporate sector since the Great Depression–profit margins didn’t even come close to touching the lows of prior eras.  In fact, they barely touched the historical average.  In charts that include the financial sector, profit margins appear to briefly fall to record lows, but this appearance is an artifact of the huge credit losses that the financial sector incurred in the period.  The profit margins of non-financial corporations remained historically elevated, contrary to what mean-reversion analysis would have predicted.



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Why A 66% Crash Would Be Better than a 200% Melt-up

Suppose that you’re a middle-aged professional with a 30 year retirement time horizon. Your portfolio is 100% invested in U.S. equities–it consists of 100 shares of the S&P 500, worth $187K at current market prices.  Assuming that the fundamentals remain unchanged, which outcome would leave you wealthier at retirement: (1) for the S&P 500 to soar 200% in a glorious bubble-like melt-up, or (2) for the S&P 500 to plunge 66% in a brutal Depression-like crash?

Surprisingly, you would end up wealthier at retirement if the plunge occurred.  This is true even if we assume that the plunge lasts forever, and that you add no new money to the market as prices fall.

Let’s work through the details.  We can separate the drivers of equity total return into three components: dividends, earnings per-share growth, and changes in valuation.

We’ll start with dividends.  At 1870, the current S&P 500 dividend yield is somewhere between 1.8% and 2%.  The reason it’s historically low is that a significant portion of the cash flow that has traditionally gone to dividends is currently going to share buybacks.  But share buybacks are equivalent to dividends, reinvested internally.  To make things simple, then, let’s assume that from here forward, all buyback cash flows are going to be diverted to dividends.  From a total return perspective, the additional dividends will get reinvested by the shareholders, so everything will end up in the same place.  If the current buyback yield, net of dilution, were diverted to dividends, the dividend yield would be something close to 3%, which, not coincidentally, is also what the dividend yield would be right now if the corporate sector adhered to a more historically normal dividend payout ratio.

Earnings per share (EPS) growth is more difficult to estimate because we don’t know what’s going to happen to corporate profitability–it’s currently at an elevated level and could revert to the mean.  To be conservative, let’s assume that it does revert to the mean, and that EPS growth, excluding the float-shrink effects of buybacks, ends up being very low–say, 2% per year.

As for the market’s valuation, we’re comparing two different possibilities: first, that it rises by 200%, second, that it falls by 66% percent.  In both cases, we’re assuming that the move sticks–that the valuation stays elevated or depressed forever.

The following table outlines the trajectory of the total return in the two cases.


As you can see, the plunge is demonstrably better for your retirement than the melt-up, with the obvious caveat that you have to maintain discipline and stick with the investment. If you panic and sell in response to the plunge, all bets are off.  

Now, to be clear, we haven’t priced in the intangibles associated with melt-ups and crashes–specifically, the highly satisfying experience of watching investments appreciate, and the highly distressing experience of watching them crater, particularly when other people’s money is involved.  If we’re taking those intangibles into account, then we should obviously prefer the melt-up. But on a raw return basis, the plunge wins.

The reason the plunge produces a better final outcome is that the valuation at which investors reinvest dividends–or, alternatively, the valuation at which corporations buy back shares, if they choose that route instead of the dividend route–has a powerful impact on long-term total returns, an impact that increases non-linearly as valuations fall to depressed extremes.   In the case of the plunge, the dividends are reinvested at roughly 1/9 the valuation of the bubble.  Over 30 years, the accumulated effect of the cheap reinvestment is enough to fully make up for the one-time impact of a 9 bagger increase in valuation.

Investors might want to reconsider whether or not a world without corrections and crashes would actually be a good thing for the long-term, particularly given the extent to which corporations are currently recycling their cash flows into dividends and buybacks. As far as future returns are concerned, such a world would come at a cost, even for those that are already comfortably in.

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