Why can’t something go on forever?
The key ideas here are exponential growth and physical limits. Exponential growth is the bigger factor, as physical limits are often surprisingly malleable, much more so than you might expect.
When we consider growth, the first thing to think about is the rule of 72, which states that something will double in the number of years that is 72 divided by the growth rate. At an 8-percent growth rate, for example, the doubling will happen in 9 years (or 72/8); at a 12-percent growth rate, the doubling will happen in 6 years (or 72/12). It’s not exact, but it’s usually pretty close.
Another factor that comes into play is doublings in order: 2x, 4x, 8x, 16x, 32x, and so forth.
Combining these two concepts, we can look into the future and see what certain growth assumptions actually mean. If you start with $1 million and grow it at 8 percent for 90 years, you get (neglecting taxes and inflation) 10 doublings, which is 1,024 times the original amount, or about $1 billion. This is what we mean by the power of long-term compounding in investing.
Things get a bit more problematic when you think about things like people. With a current world population of around 7 billion, a growth rate of 2 percent would mean a doubling time of about 36 years, or roughly 3 doublings over the next century—to a population of 8 times the current level, or 56 billion. Clearly not sustainable.
This math led Thomas Malthus to lay out, for the first time, the limits on population growth implied by the exponential growth of populations along with the linear growth in food supplies. Unsustainable trends in population growth would have to stop.
In the past, Malthus was right. Population growth was interrupted by war or famine. In recent centuries, he has been wrong in general, as food production has grown far faster than expected due to the Green Revolution, but he’s also been right in many cases. Population growth is perhaps the best example of the quote “If something can’t go on forever, it will stop.” And, in fact, population growth has slowed dramatically. The trend is stopping, even if in a less dramatic fashion than war or famine.
For a more recent example, consider the Internet stock bubble. At the peak, investors surveyed expected stock value to increase 15 percent per year, indefinitely. Using the rule of 72, that means doubling every 5 years. In 15 years, then, which is to say around now, stock prices would be at 8x the starting point. The Nasdaq peaked at just over 5,000, implying a level of around 40,000 today. In fact, the Nasdaq is still below 5,000 as I write this. Clearly, that trend was unsustainable—and stopped.
The assumptions that underpin many trends, when subjected to this kind of analysis, become visibly unrealistic. If the foundation is weak, you know the trend will end—although not, of course, when. This analysis can also provide a guide to when trends switch from sustainable to unsustainable.
On that note, one tradition that I very much hope is indefinitely sustainable is Thanksgiving. I will be writing tomorrow and Wednesday as well, but if you don’t get a chance to read those posts, I hope you have a very happy Thanksgiving!
The formula used for the rule of 72 approximates the time it will take for a given amount of money to double at a given compound interest rate. Compound illustrations are not predictions of investment performance, and investment principal and interest are not guaranteed and are subject to market fluctuation.