Problems with Constant Compound Interest (6)

Doctored Photo Credit: Marvin Isidore Macatol || And I say this is heresy!

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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.