Summary

A recently published article, *The Paradox of Wealth*, puts forth the thesis that returns to capital decline as societies become wealthier. Using 132 years of data it shows that the U.S. stock market’s P/E ratio has been increasing by about 0.058/yr. Based on that trend the “correct” (mean reverting) Shiller P/E (cyclically adjusted P/E or “CAPE”) today is 20.3 rather than the simple average of 16.5.

I find that all of the “trend” in this 132-year data set is explained by the most recent 16 years, a period that included extreme market valuations followed by steep losses. Removing both the *initial and final* 16 years of data results in an increasing trend, but only about a quarter of that shown in the article. “Trimming” the data by excluding extreme low and high P/E ratios or by excluding high P/Es that are always followed by steep losses does not eliminate the apparent trend, but does reduce it somewhat.

Though the upward trend in P/E ratios completely depends on data since the late 1990s, we cannot be sure whether those recent data are anomalous. However, the time trimming and P/E trimming methods both result in lower P/E ratio projections than the article’s. Even if the thesis is correct, it seems quite plausible that the current P/E value of 20.3 is on the high side, unduly influenced by recent extreme valuations. Time will tell – a longer time than any of us has…

Details

GMO’s Q3 2013 letter mentioned an article, *The Paradox of Wealth* [free for CFA members, $15 for non-members], by William Berstein. (This is the same Bernstein who co-authored TheTwo Percent Dilution.)

I have no big comments on the article’s thesis (*) right now and expect to ride GMO’s thought coattails on it. However, I do want to address one component of Bernstein’s supporting evidence. Bernstein shows that the U.S. P/E ratio has marched higher over time. (Higher P/E ratios are indicative of lower expected returns to capital.)

Bernstein performs a temporal linear regression of the Shiller data P/E ratio from the monthly data set’s inception in 1881 through 2012. Though “the t-statistic [of] 1.65 [is] close, but no cigar” Bernstein’s regression is still interesting. It indicates that the P/E ratio has risen by about 0.058 per year – the P/E trend line was at 12.6 (*) in 1881 and 20.3 in 2012. In other words, the Shiller P/E ratio “should be” around 20.3 today vs., say, a simple average of the data set, which is 16.5.

That’s a big deal, because it would indicate justified stock prices nearly 25% higher than the simple average. [Aside: As of Nov. 30, 2013 stocks would need to fall 20% (to S&P500 1,440) to get back down to that 20.3 P/E or 35% (to S&P500 1,170) to the 16.5 P/E.]

I find three issues with this P/E regression analysis:

- All of the data that generate the upward slope are contained in the post-1996 years ( this is, coincidentally, after Greenspan’s “irrational exuberance” speech). Prior to 1996 no slope was detectable.
- The rate of change in wealth (via per-capita GDP) has changed during this 132 year period. The thesis relates changes in returns to capital to changes in per-capita wealth. Yet the regression is simply against time.
- The regression includes all data points, including the most extreme market highs and lows from which returns were excessively dismal or spectacular. I believe such extremes are usually demonstrations of irrational behavior that has been disconnected from fundamentals. Thus, they do not provide useful information. In fact, they may contaminate the data.

To comport with the article’s analysis, the information below is through 2012 (not to-date 2013). All P/Es are “Shiller P/Es”.

1 – Regression Recency

Since the late 1990s U.S. stock market returns have been very weak. If we exclude the post-1996 data (the most recent 16 years), a period that included two deep bear markets, we’re left with a 116 year data set. The slope disappears (very slightly negative at -0.001) with indicative starting and ending P/Es of 15.0 and 14.9, respectively.

I also ran the regression by removing both the most recent 16 years *and* the beginning 16 years. This is probably a fairer and more valid way to dispute a proposed trend over time. The 99 year data set from 1897 through 2012 does have a positive slope, but it is only 0.14 – only a quarter of the full data set’s 0.58. It indicates a beginning P/E of 14.0 and an ending P/E of 15.4. If we extrapolate to the end of 2012 the P/E is 15.7.

It’s worth noting that in both of the above treatments the simple average was also notably lower than the full set 16.5.

If the wealth effect on returns to capital were happening, why has it only meaningfully appeared in the data during the past 16 years? Per-capital GDP growth was much stronger during earlier periods, so if anything we’d expect to see more rapid increases in GDP during those periods.

In the author’s defense, he does stress that “it takes centuries for wealth to drive up security valuations and, by implication, drive down security returns…” and “the noisiness of this process cannot be overestimated.” So perhaps the recent shift in increase in valuations is a lagged response to increased wealth. Such signal discontinuities (step functions) in response to fairly smooth underlying behavior are not uncommon in natural and human systems – non-linear behavior due to cumulative effects do happen. However, perhaps much of it is “noise”. In any case, the record peaks in P/E ratios during the past 15 years have been followed by dramatic declines, so it’s hard to view them as indicative of rational expectations.

2 – Correlation with Changes in Wealth instead of Simply Time

This avenue of inquiry did not bear fruit.

The author stressed the amount of noise and other variables and lags, so it doesn’t seem that it would be fruitful to pursue this difficult analysis. Since markets must be forward looking, we would need to not simply regress P/Es against per-capita (potential) GDP, but estimate what the market anticipated for future per-capita GDP growth. Perhaps using risk-free real rates would work as a proxy, but even then there were periods of deflation and financial repression.

However, the author’s analysis did indicate a “rough reciprocal relationship between real investment return (R) and societal per capita energy consumption (C), in kilocalories per person per day”: R ~ 5/C. I could use the inverse of the P/E (earnings yield) as a proxy for R. Domestic energy consumption per capita could be used for C. (The “true” per capita energy consumption would adjust for imported and exported “embedded energy” in products). U.S. per-capita energy consumption more than tripled from 1880 to 2010 (multiple data sources), which would imply R dropping to a third of its 1880 value or the P/E tripling.

It is worth noting that U.S. primary energy consumption per capita peaked in the 1970s and today is about 10% lower.

I think that the correlation with energy consumption probably breaks down in advanced economies as more growth shifts to services and less energy intensive activities and large advances in energy efficiency take place over time. Pre-industrial societies burn stuff for heat and to make metal tools in simple processes, so energy consumption is directly proportional to increases in well-being and output. Early and middle-stage industrial societies receive enormous benefits from increases in energy use in terms of new goods, radically improved transportation services, and in-home comforts.

3 – Trimming Extremes

Statistical analysis often involves the removal of extremes or “outliers” from the observations. I used a couple of simple methods to explore the impact of supposed outliers.

The most straight-forward method was to remove the highest and lowest P/E ratios from the analysis. I removed the highest 5% and lowest 5% of P/E ratios and substituted the highest and lowest of remaining P/E ratios, respectively. This still shows an upward trend – 0.044/yr (vs. 0.058 in the article) and a trend line P/E today of 19.1 (vs. 20.3).

However, this seemingly unbiased approach has over 80% of the trimmed lows prior to 1930 and over 90% of the trimmed highs after the 1980s. If P/E ratios were actually increasing over time, we would expect to see more of the lowest lows earlier and more of the the highest highs later. So this approach is a bit circular.

Another tact is to remove data points with P/E ratios that have *always and everywhere been associated with steep losses*. This approach does not directly address the author’s work. Instead, it looks for a trend in P/Es that are not associated with crushing losses. That is a practical question for investors.

First, we need to exclude data since the recent financial crisis lows. This is because not enough time has passed to determine if a steep loss happens from these data points forward. Thus, that data will go through March 2009.

Secondly, we need to establish a quantitative measure of “steep losses”. I went with a loss of at least 20% (real, including reinvested dividends) within seven years. Twenty percent is into bear market territory and I’m accounting for dividends. Those are losses worth avoiding if you can. (Seven years is the period GMO uses and it is founded on research.)

It turns out that this approach produces results similar to the article’s (raw) approach. This is because the late 1990s stock bubble contained high P/E ratios that were not followed by “steep losses” – the bubble grew for years and the following bear market bottomed at a high enough level to prevent “steep losses” for late 1990s buyers above P/Es of 30! It makes little difference whether we use real or nominal and whether we include dividends or not – we get a slope around 0.05. However, the levels are a bit different with a current “correct” P/E ratio in the low 19s rather than the article’s 20.3.

Finally…

Though the upward trend in P/E ratios completely depends on data since the late 1990s, we cannot be sure whether those recent data are anomalous. However, the time trimming and P/E trimming methods both result in lower P/E ratio projections than the article’s.

A proper measure of wealth includes accounting for depreciation and depletion. There are strong arguments that modern economies increasingly fail to measure these costs as they relate to the depletion of natural resources. A more complete measure of wealth might show slower growth.

Note that Berstein concludes that “Given today’s low cost of capital, some might

predict a higher-than-normal likelihood of a future crash in the prices of debt and equity followed by persistently low prices and higher returns. I see this scenario as unlikely.” However, “at some point in the next few decades, investors will almost certainly have opportunities, given adequate fortitude and cash, to purchase securities at near historically low prices, but it seems likely that these windows will be more fleeting than in the past.”

Notes

* GMO’s Inker describes the article’s thesis saying “generally increasing levels of wealth might drive down the return on capital…” If this thesis were correct then according to GMO “every endowment and foundation will find itself wasting away instead of maintaining itself for future generations. And the plight of public pension funds is probably not even worth calculating, as we would simply find ourselves in a world where retirement as we now know it is fundamentally unaffordable”. However, GMO concludes “Bernstein’s is definitely an intriguing idea, and we will have to look seriously at it in the years ahead, but for now we have not changed our estimate of equilibrium returns to equities or other assets”

The article takes an extremely long term global perspective. For example: European countries since the Middle Ages and a composite from 3000 BC Mesopotamia through the Roman Empire to the “Developed West” today. It mostly uses borrowing costs as a proxy for returns and also uses per-capital energy consumption as a proxy for wealth. It is an interesting thesis packed into a very readable, brief article.

** The article states of starting P/E value of 13.6. This appears to be a typo. My regression yields the same slope and ending value, but a starting value of 12.6.

Note that the Shiller stock market data are monthly. The monthly stock price data are calculated as the simple average of each month’s daily closing prices. This makes the analysis of total losses to be “conservative” – actual losses to the lowest daily close or intra-day value are worse than calculated.

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