Problems With Constant Compound Interest, Part 6

by: David Merkel, CFA

My last post produced the following question:

What if your time horizon was 60 years? Would a 5% real return be achievable?

I am answering this as part of an irregular "think deeper" series on the problems of modeling investment over the very long term… the last entry was roughly six years ago. It's a good series of five articles, and this is number six.

On to the question. The model forecasts over a ten-year period, and after that returns return to the long run average - about 9.5%/year nominal. The naive answer would then be something like this: the model says over a 60-year period, you should earn about 8.85%/year, considering that the first ten years, you should earn around 5.63%/year. (Nominally, your initial investment will grow to be 161x+ as large.) If you think this, you can earn a 5% real return if inflation over the 60 years averages 3.85%/year or less. (Multiplying your capital in real terms by 18x+.)

Simple, right?

Now for the problems with this. Let's start with the limits of math. No, I'm not going to teach you precalculus, though I have done that for a number of my kids. What I am saying is that math reveals, but it also conceals. In this case, the math assumes that there is only one variable that affects returns for ten years - the proportion of investor asset held in stocks. The result basically says that over a ten-year period, mean reversion will happen. The proportion of investor asset held in stocks will return to an average level, and returns similar to the historical average will come thereafter.

Implicitly, this assumes that the return series underlying the regression is the perfectly normal return series, and the future will be just like it, only more so. Let me tell you about some special things involved in the history of the last 71 years:

  • We have not lost a war on our home soil.
  • We have not had socialism to the destructive levels experienced by China under Mao, the USSR. North Korea, Cuba, etc. (Ordinary socialism isn't so damaging, though there are ethical reasons for not going that way. People deserve freedom, not guarantees. Note that stock returns in moderate socialist countries have been roughly as high as those in the US. See the book Triumph of the Optimists.)
  • We have continued to have enough children, and they have become moderately productive workers. Also, we have welcomed a lot of hard working and creative people to the US.
  • Technology has continued to improve, and along with it, labor productivity.
  • Adequate energy to multiply force and distribute knowledge is inexpensively available.
  • We have not experienced hyperinflation.

There are probably a few things that I have missed. This is what I mean when I say the math conceals. Every mathematical calculation abstracts quantity away from every other attribute, and considers it to be the only one worth analyzing. Qualitative analysis is tougher and more necessary than quantitative analysis - we need it to give meaning to mathematical analyses. (What are the limits? What is it good for? How can I use it? How can I use it ethically?)

If you've read me long enough, you know that I view economies and financial markets as ecosystems. Ecosystems are stable within limits. Ecosystems also can only develop so quickly; there may be no limits to growth, but there are limits to the speed of growth in mature economies and financial systems.

Thus the question: will these excellent conditions continue? My belief is that mankind never truly changes, and that history teaches us that all governments and most cultures eventually die. When they do, most or all economic arrangements tend to break, especially complex ones like financial markets.

But here are three more limits, and they are more local:

  • Can you really hold for 60 years, reinvesting and never taking a material amount out?
  • Will the number investing in the equity markets remain small?
  • Will stock be offered and retired at ordinary prices?

Most people can't lock money away for that long without touching it to some degree. Some of the assets may get liquidated because of panic, personal emergency needs, etc. Besides, why be a miser? Warren Buffett, one of the greatest compounders of all time, might have ended up happier if he had spent less time compounding, and more time on his family. It would have been better to take a small part of it, and use it to make others happy then, and not wait to be the one of the most famous philanthropists of the 21st century before touching it.

Second, returns may be smaller in the future because more pursue them. One reason the rewards for being a capitalist are large on average is that there are relatively few of them. Also, I have sometimes wondered if stock returns will fall when the whole world is employed, and there is no more cheap labor to be had. Should that bold scenario ever come to pass, labor would have more bargaining power in aggregate, and profits would likely fall.

Finally, you have to recognize that the equity return statistics are somewhat overstated. I'm not sure how much, but I think it is enough to reduce returns by 1%+. Equity tends to be offered for initial purchase expensively, and tends to get retired inexpensively. Businessmen are rational and tend to go public when stock valuations are high, pay employees in stock when valuations are high, and do stock deals when valuations are high. They tend to go private when stock valuations are low, pay employees cash in ordinary times, and do cash deals when valuations are low.

As a result, though someone that buys and holds the stock index does best, less money is in the index when stocks are low, and a lot more when stocks are high.

Inflation Over 60 Years?

I mentioned the risk of hyperinflation above, but who can tell what inflation will do over 60 years? If the market survives, I feel confident that stocks would outperform inflation - but how much is the open question. We haven't paid the price for loose monetary policy yet. A 1% rise in inflation tends to cut stock returns by 2% for a year in real terms, but then businesses adjust and pass through higher prices. Vice-versa when inflation falls.

Right now the 30-year forecast for inflation is around 2.1%/year, but that has bounced around considerably even within a calm environment. My estimate of inflation over a 60-year period would be the weakest element of this analysis; you can't tell what the politicians and central bankers will do, and they aren't sure themselves.

Summary

Yes, you could earn 5% real returns on your money over a 60-year period… potentially. It would take hard work, discipline, cleverness, frugality, and a cast iron stomach for risk. You would need to be one of the few doing it. It would also require the continued prosperity of the US and global economies. We don't prosper in a vacuum.

Thus, in closing I will tell you that yes, you could do it, but there is a large probability of failure. Don't count on buying that grand villa on the Adriatic Sea in your eighties, should you have the strength to enjoy it.

Disclosure: None.

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