**By Martin T., Macronomics**

*Courtesy of our good friends at Rcube Global Macro Research, please find enclosed their recent note focusing on US Equities’ Long Term Real Returns. Enjoy!
*

Our research generally focuses on tactical investment horizons (3‐6 months). In this paper, however, we consider long‐term real returns for US equities, for which we have reliable data since 1871.

Nota bene:

By real returns, we mean total returns (i.e. dividend included) divided by the CPI. We chose to analyze the US market as it has longest and most accurate historical data. Our data originates from Shiller’s website: http://www.econ.yale.edu/~shiller/data.htm. Earlier data exists (as early as 1802), but is plagued with survivorship bias.

When we look at price alone (as many observers do), we see no evidence of a long term trend. Rather, we have two distinct 70‐year periods: pre‐WW2: +1.0% annual price appreciation; and post‐WW2: +7.4% annual price appreciation. However, as we know, price appreciation is insufficient to quantify returns, especially when we consider long investment periods. Indeed, a rational long‐term investor should look at (and hope to maximize) real total returns, which take into account dividends and inflation.

When we look at the S and P 500’s real total return, the picture looks very different:

Taking into account dividends and inflation, we can admire the remarkable stationarity of S and P 500’s real returns around a long‐term trend (6.5% per year). Even the 1929 crash and the 1970s’ stagflation represent small deviations from the overall trend.

A long‐term trend of around 6.5% essentially means that an equity investor’s purchasing power doubles every 11 years, which is in itself the strongest argument for permabulls and buy‐and‐hold proponents.

That being said, many believe that the 6.5% real return – which is also known as “Siegel’s Constant” – is a historical freak and is unlikely to continue further.

In a controversial Investment Outlook published last August, Bill Gross compared this 6.5% long‐term real return to long‐term real GDP growth (around 3.5%), and concluded that the stock market was a “Ponzi scheme”, with stockholders having been “skimming 3% off the top each and every year, at the expense of lenders, laborers and the government”. In a comment that reminisced Business Week’s famous 1979 cover, the “Bond King” then proclaimed that the “cult of equity was dying”.

It appears to us that this analysis is flawed (and indeed, it was immediately rebutted by Dr. Jeremy Siegel, as well as other academics). Although it is true that the market value of equities cannot grow above GDP forever, Bill Gross seems to have ignored the fact that around half of stock returns originate from distribution to shareholders, in the form of dividends and share buybacks.

There is therefore nothing wrong in the fact that equity real returns are higher than real GDP growth. Even in a zero‐growth economy, companies would still have earnings that can be used to distribute dividends or buy back shares, which would lead to higher than zero real returns for equities. We’ll return later to the question of the link between equity real returns and economic growth.

Regardless of the sustainability of 6.5% real returns in the future, nobody would dispute that it is hardly a“constant”, especially for short‐term horizons.

If we define 10 years as the lower range of what constitutes a long‐term investment horizon, the standard deviation of forward returns is still fairly wide (around 5.2%). This highlights the need to look for methods of predicting 10‐year forward returns.

One such method, introduced by Robert Shiller in his 2000 book Irrational Exuberance, involves using cyclically adjusted P/E ratios (CAPEs) to predict 10‐year forward returns. CAPEs are P/E ratios that use past 10‐year average earnings in order to smooth out cycles.

The S and P 500’s CAPE is currently around 21, which is substantially higher than its long‐term average (16.5). Although bearish observers use these figures as a sign of overvaluation, it is worth noting that 10‐year forward real returns would be around 4.4% according to the above regression equation.

In any case, the CAPE regression only explains around 25% of 10‐year forward returns. Moreover, this analysis is performed in‐sample, whereas an investor operating in real time during the sample period would not have access to the whole dataset.

If we remain in an in‐sample framework, we can obtain R2s that are much better than 25%.

First we can note that corporate profits as a proportion of GDP are one of the most mean‐reverting time series in economics.

Nota bene:

Although total corporate profits and S and P 500 profits are not the same thing, their growth rate is rather similar over long time periods (3.23% per year for total corporate profits vs. 3.17% for S and P 500 profits between 1947 and 2008):

Low profits as a proportion of GDP lead to business failures, reduced competition, and therefore higher margins further down the road (and vice versa).

From this point of view, buying when earnings are high and selling when earnings are low (as suggested by PE‐based methods) does not seem such a great idea.

Rather than taking the 10‐year earnings average as the denominator, we could therefore use real GDP.

Incidentally, the total market cap / GDP ratio (which is a related concept) is Buffet’s favourite macro measure of value for stocks.

This time, we find a long‐term trend of around 3% for the ratio (i.e. the same 3% that stockholders

supposedly “skim off” at the expense of others, according to Bill Gross).

Although the S and P 500 real return / real GDP ratio looks rather trend‐stationary, it has had rather wild swings around the trend, which indicate potentially interesting opportunities to trade in and out of the market.

Indeed, we obtain a rather nice R2 of 57% when we regress the detrended ratio against 10‐year forward real returns.

Currently, we’re close to fair value, as the overshoot from the 90s (Greenspan’s “irrational exuberance”) finally seems to have been digested. This does not preclude another “undershoot”, such as the one we had in 2008, as investors revise their economic growth assumptions downwards, especially in deleveraging developed economies.

Nota bene:

Although there seems to be a long‐term elasticity of one between equity real returns and realized economic growth, changes in long‐term growth expectations and/or risk premia can have a huge impact on valuations. If we simply look at the Gordon‐Shapiro model and assume a denominator (expected rate of return – expected growth) of around 5%, a 1% decrease in long‐term expected growth decreases the value of equities by 20%. We believe that this explains much of equities’ “excess volatility puzzle”.

Again, this is an in‐sample analysis (just like the CAPE model). Although we still get an R2 of around 40% if we use a running regression instead of a fixed in‐sample regression (and use the first 40 years of the sample as a “learning period”), no one can assert that 3% long‐term returns above real GDP growth are an intangible law of nature.

To conclude, assuming long‐term forward equity real returns to be around 3% plus foreseeable economic growth provides us with a ballpark figure. It avoids making blatantly wrong assumptions about long‐term equity real returns (such as believing that they can be around 10%, like many investors still do).

Additionally, it is important to note that this brief study concerns only the United States, a country that won two world wars and avoided socialist experiments during the last century. It would be interesting to calculate the trend of the real equity return / real GDP ratio for other countries. Unfortunately, reliable data on long‐term real returns is hard to obtain for most countries, as they generally originate in the early 1970s (e.g. MSCI Indices).

We will however try to gather more data on this vast subject, as well as publish additional short studies about long‐term returns of other asset classes.

“Common sense is the most fairly distributed thing in the world, for each one thinks he is so well-endowed with it that even those who are hardest to satisfy in all other matters are not in the habit of desiring more of it than they already have.” – Rene Descartes, French philosopher.

Stay tuned!

### Martin T., Macronomics

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