both theory and long-run empirical data support the notion that economic growthI would boil his argument down to the idea that when increased growth comes from capital growth, the extra returns don't accrue to the legacy capital owners, because the growth is accomplished through what is, or can be thought of as, share dilution. Further, there are diminished returns to additional capital inputs as a proportion of the economy, so the new growth produces a lower rate of return on invested capital. So, more wealth and economic growth can lower expected returns. Put in a simpler way, more supply of capital will bid down the return.lowerssecurity returns by reducing impatience for consumption and altering the supply–demand dynamics of capital—the price of living in an increasingly prosperous, safe, healthy, and intellectually gratifying world.

These changes take place over decades or centuries, with a lot of noise. Even over a lifetime, noise and business cycles can overwhelm these longer term effects. Bonds saw a spike in yields in the 1970's, followed by a long fall, but I don't see a longer downward trend in real short term bond yields in the post-WW II era. But that is probably not long a enough period of time to see it in that data series, since bonds have long term noise reactions to demographics, inflation regimes, etc.

But, I think it is interesting to look at equity returns here. Bernstein refers to the long term trend in the Shiller 10 year Cyclically Adjusted P/E ratio (CAPE). The t-statistic for a rising trend is only 1.65, so this could be statistically stronger, but since P/E is the corollary to yield, we would expect to see this trend in the face of long-term yield declines.

Separately, I have looked at past S&P 500 returns, in nominal, real, total return, and index returns (w/o dividends), and I haven't found a decline in returns over time. A sine curve can be fit over any version of the S&P 500 or Dow Jones Industrial Average with a pretty good fit. Here is the nominal index value of the DJIA back to 1928 with a sine curve fitted to it. As can be seen in the next graph, the annual return of that sine curve has a slight incline. After adjusting for inflation and for total returns, the returns over time tend to be flat, but none of the long term trends have a long term decline.

This outcome, together with rising P/E ratios, suggests that the declining market yield has been roughly offset by the resulting gain in valuations. This is analogous to the bond market of the past 30 years. In the case of bonds, yields have fallen so quickly that the resulting price increases have resulted in a 30 year bull market. Going forward, bonds will inevitably see lower returns from the flipside of this phenomenon. Yields may rise, but since they are starting from such low levels, and since the rise itself will create price losses, there is no mechanism that will allow bonds to match the returns of the previous 30 years.

Normally, references to the concern over the long term rise in the PE ratio would relate to a comparison of fundamentals versus price inflation. But, I think Bernstein's notion invites a more subtle reading. Bernstein refers to the Gordon growth model as a simple way to think through this.

If this long-term relationship between capital supply and rates of return holds, then as available capital grows, the required rate of return (k) will decline and growth (g) will decline. The effect on stock values is indeterminate, but for the broad market, the P/E ratio would increase, since it would move inversely to k.

If capital accumulation continues to grow, and this effect on rates of return exists, then

**the continued increase in P/E ratios is sustainable**. In fact, it should be expected. Looking at the first chart, with the long term trend in the CAPE, the trend P/E ratio would equate to a real yield of 7.35% in 1881, 6% in 1950, and 4.9% in 2012.

The trend in PE expansion would add about .3% to the annual return, for a total current expected return of 5.2%. If trends in required returns over the next 60 years match the previous 60 years, with a required return decreasing to 4% by 2070, the P/E ratio in 2070 would be 25, and the real return on invested capital over that time would be 5%.

These are broad numbers, but my point is that if what we are seeing is a long term downward trend in required returns, then the actual returns over generations will still be very stable, and can be partially sustained by slow inflation in P/E ratios, which itself is a reasonable product of the slowly decreasing return to capital.

There are a lot of confounding factors here. International capital flows might be increasing US corporate equity returns. Demographic and cyclical factors will affect interest rates and equity risk premiums over the next few decades to a degree that overpowers this very long-term trend. But, the point remains that of all the concerns we might have about US equity markets heading into the coming decades, an unsustainable increase in P/E ratios may not be one of them, despite the apparent evidence to the contrary.

There is a concern to consider, though. This phenomenon involves a kind of wealth illusion, similar to the effect of low rates on bond and home prices in the past 15 years. The high prices of homes and bonds were justified in the 2000's because of very low long term interest rates. But, since we conceive of wealth through nominal spot prices, our perception of our level of wealth became very volatile as those prices were whipsawed through the financial crisis.

The relationship between required returns and stock values has the same characteristic. So, if there is a regime shift in capital behavior in the US that reduces the capital stock, future returns to the remaining capital might increase. But, those increased future returns will manifest themselves through lower P/E ratios (and lower prices) in the spot market for US equities. Savers who had experienced a slight boost in their returns as they lived through a period of slightly declining return expectations will suddenly see those gains retracted in this case.

In summary, returns and asset values can experience sustainable boosts from increasing P/E ratios, as long as very long term (centuries long) normal trends remain in place. P/E ratios will rise and fall through short term and medium term market fluctuations. The fact that those peaks and valleys are trending higher is not necessarily an immediate concern. But, this boost comes at the expense of greater pain if we experience an extreme outlier event of a regime shift that includes a capital retrenchment.

Other than typical diversification of regional and asset class exposures, there may not be much that one can do to prepare for an extreme regime shift in capital behavior. Within the regime that capital planning can manage, the long trend in increasing P/E ratios does not require a significant reduction in our expectations for equity returns over the next generation. To the extent that far-future returns become significantly lower than the returns we now consider normal, it will because our descendants will be living in a world where capital is not scarce. That will be a good thing, and it will likely happen long after we have passed.

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