Capital Accumulation and Rates of Return

I was thinking about the stock market and how decade after decade it’s able to deliver high rates of return and ended up formulating a primitive hypothesis based on the data I gathered. Corporate stock capitalization is cumulative sum of net stock flow, so stock market growth should be determined by the source of net stock flow, savings and reinvested profits.

What I’ve figured (and I don’t believe this is some ‘great’ insight) is since capital accumulates, over time rates of returns should decline. The denominator (capital) accumulates, and the numerator (inputs such as savings and reinvested profits) does not. The inputs do not grow proportionally to capital. Let’s model this out, and make the following assumptions:

  • Beginning GDP is $100
  • Beginning capital is $100
  • GDP grows by 2% anually
  • All saving and profits are invested
  • Savings and profits are each 10% of GDP

Under these assumptions, there’s a clear trend of falling rates of return. We do not exactly see this in real life, or at least it doesn’t look like we do. There are other factors that play into capitalization, and among them the following:

  • Savings and profits can rise or fall as a share of GDP
  • Corporate equity as a share of national wealth has risen over time
  • Taxes on capital profits, and excess income (basically savings) have fallen considerably
  • The Federal deficit varies and is sometimes monetized by Federal Reserve banks

So what happens when factor these things in? What if we cumulatively stack the net public deficit (federal borrowing from only private investors), after-tax profits, and private savings (with both starting at the same place)? Well my friends, we get these lovely graphs:

Now how about that? That’s pretty interesting. I’d give my hypothesis an B-minus just based on that graph. Clearly it’s missing a few things, since somehow wealth exceeded the sum of these inputs at several points in time, in fact, more often than not. I’d crack that up to net foreign capital flows, some profits being realized and consumed by shareholders, and perhaps loss of wealth due to periods where depreciation outstripped investment.

Overall, this is a fairly logical and consistent model. If national wealth has been more or less the sum of inputs, like profits reinvested and savings, then how come the stock market continues to grow at double-digit rates more years than not? Well, the stock market, as we know, isn’t the entirety of national wealth. Here’s a chart showing corporate equity as a share of national wealth:

What we can see here is the stock market has about tripled as a share of national wealth since 1980, roughly tripling the rate of growth of wealth as a whole, which as it happens, boomed in the 1990s, as shown by this chart which depicts the trailing 10-year compound annual growth rate in national inflation-adjusted national wealth per household:

The falling (relative) rate of accumulation I modeled has not been seen in either the stock market or national wealth, despite the model being fairly reliable. As we can see, inflation-adjusted wealth per household grew faster the last decade and in the decade of around 1996 to 2006 than it did at any other point in time. How can that be?

To add to the confusion, when put together, savings and profits were actually relatively low during both both the pre-1970s and 1997-2007 boom periods. What could possibly account for this? How can capital accumulate without resulting in lower rates of return?

The simple answer is I tricked you! There is a special thing I mentioned a couple times which I didn’t go into detail with. This magical factor has the unique ability to both increase nominal profits, savings, and GDP, or if we look at it another way, decrease the value of accumulated wealth. This is at least part of the reason why the harshest period of wealth destruction occurred (as we see back in the wealth growth chart) in the period from about 1972 to 1982, during the period known as “Stagflation.”

The drop off in corporate equity from the 1972 high of 27% of national wealth to the 1981 low of 11%, and the subsequent recovery from 1981 to 2000 is responsible for about half of the 1990’s bull market. High inflation, which took root in the mid-1960s, finally ending in about 1990, suppressed wealth creation and corporate capitalization for two decades, paving the way for an extraordinary but mostly logical stock market boom.

Fascinatingly, if we take into account all of this inflation by graphing the ratio of real national wealth to real gross domestic product, we see a different picture which is much flatter and for the most part much more consistent:

I’d hypothesize that the notable increase in wealth as a share of GDP from about ~1994 to 2006 is attributable mostly to the combination of factors I’ve mentioned, such as the absence of high inflation, as well as the profits boom in the mid 2000s.

To wind to a close what I hope you (the reader) have found to be a fascinating dialogue, I will present a retrospective model of national wealth had there been no inflation since 1947:

There’s that falling rate of return! I don’t know about y’all, but I think it’s just about the coolest thing to hypothesize, develop a model, and test it like that, with such clear results! This kind of work yields great insights. With respect to the stock market, had capitalization not fallen as a share of national wealth during the 1970s, the stock market would have looked much more similar to the wealth growth line, albeit with somewhat higher returns due to capitalization regardless growing as a share of national wealth.

As a bonus, here are the same charts but using my model which sums inputs:

Further, how the predicted CAGR (compound annual growth rate) lines look over the real ones:

The similarities between these results show my model is fairly reliable, though of course I have some more work to do perfecting it.

When we consider optimal rates of inflation, we should consider the affect that inflation has on wealth accumulation. Perhaps we want to accumulate incredible wealth as a nation, or maybe we are intent on preserving capitalism by perpetuating via inflation, both the struggle and potential of obtaining exponentially greater capital.

This information will be referenced in future blog posts that I write, especially since as it’s relevant to the future of capitalism, the stock market, and the government’s relation to both. I hope that this has all been a worthwhile thought experiment for those reading, and I hope to provoke ever greater thought in my upcoming articles and posts.

3 thoughts on “Capital Accumulation and Rates of Return

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