Exponential: What a word!

We hear this word all the time. “There is a exponential rise in cases of opioid overdoses,” “This stock price is going exponential,” “The climate is changing at an exponential pace.” And when we hear it, our minds recall the picture above. It’s a time series graph showing a moderate slope that suddenly turns almost vertical. You can see how sometimes it’s referred to as a “hockey stick graph.”

It certainly draws the eye, but we always focus on that last part on the right. We look at that and say, “Wow, nothing can sustain a rate of rise like that. That’s a bubble.” Or we might think, “Who couldn’t see that that couldn’t last.”

What if I told you that the left side of the graph was the same as the right? What if I told you that everything that happens on the right hand side of the graph was completely predictable way over on the left hand side that looks completely flat to you right now? No way, right?

Wrong.

The graph above represents a certain percentage rise on an annual basis. That’s all exponential means. There’s not a $50 a year rise; that’s linear. There’s a 5% rise a year; that’s exponential.

Now consider that a moment. We all expect, on average, 8–10% stock market returns a year, we all expect 2–5% cost of living raises a year, and worst of all, the Fed expects 2% inflation a year. All those things we expect to go up (or down) a certain percent a year end up like the picture above. Yes, even the Fed’s 2% will end up in a hockey stick. In fact, the graph at the top of this article is a 2% a year curve. It just takes a very long time.

So that’s the difference in exponential time series. The higher the rate of rise, the faster it goes vertical in nominal values. The one above is 200 years at 2%.

Here’s a graph comparing the curves based on different rates of growth over a 70 year period with an initial $100:

You can see that $100 at 15% a year left alone will be quite a handsome figure in 70 years. But that, of course, sets aside the problem of where you’d find 15% a year, and what human would keep a $100 investment untouched that long.

And here’s you’ll say, “Howard, so what?” What’s the point?

Here’s the point. We can see the exponential effect over a lifetime at 15%, but this curve is actually the same curve the entire way through. It’s the same curve at years 1–5 as it is from years 20–25. It just looks different to us because we live in a linear world. Using a linear frame, the kind that we’re used to in real everyday life, this is the picture we get.

But if we plotted the same data on a semi-log scale, the picture looks different:

What that means, is that while 15% impresses us quickly, 2% does the same thing over so long a period of time that we don’t notice it. 2% population growth, 2% inflation, 2% growth in an investment, it doesn’t matter. It takes so long that when the hockey stick hits, we’re all surprised. But let’s examine the effect of 2% inflation. After all, 2% is nothing, right?

When I was born, in 1959, a friend of my mother’s gave me a silver dollar. She put an H on it in fingernail polish so my mother would know it was mine. Maybe she thought my mother had a lot of silver dollars all over the house. She told my mother it was to start my savings, because savings were very important. I still have that coin.

In 1959, a cup of coffee was selling for 33 cents. That silver dollar could buy me 3 cups. Even the terrible coffee at an office canteen would cost you a dollar today, and that’s the effect of 2% inflation. Now, since 1959, we’ve had more than 2% inflation and an average cup of coffee costs a lot more than that, but 2% is what the Fed says we want. They want a world in which a cup of coffee will cost a child born today 3 times more than today when he’s my age. They want the dollar in your pocket to be worth 33 cents in 58 years. That’s what 2% inflation does.

I’m lucky that my mom’s friend gave me a silver dollar to start my savings. She could have given me a dollar bill, and I’d be able to put it in a jar in some office and get a terrible cup of coffee. Instead, I could go sell that coin for melt value and get $13.50 for it. I probably could get 3 pretty good cups of coffee for that, just like in 1959. But the power of precious metals to retain their value is another article.

So here’s the point. When you hear people talking about debasing your money by 2% a year, that isn’t safe. It will go exponential. There will come a day when the price of a cup of coffee will go up $20 a year at that rate. But it won’t be in our lifetimes. That’s what they are saying when they suggest inflation is good. They know it will be unsustainable at some point, that the currency will fail, that there will be a crisis. They just want it to happen to your kids or your grandkids, long after they themselves are gone. It’s the ultimate kick of the can down the road.

So whenever you hear of something rising X% a year, know that it will one day “go exponential.” It will one day hit levels that are no longer sustainable within the current system. That means that there will be a dislocation. The percentage gain only tells you in which generation it will be. That’s a horrible way to make economic policy, and it’s a horrible way to treat our kids.

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Dr Wetsman is the author of Questions and Answers on Addiction, Healing Stories, and A Beginner’s Second Text of Psychotherapy. He currently blogs at TOCDR.com and consults with medical and other industries on Theory of Constraint process improvement. His current project is Dragonsbane and can be found most days hanging out with people smarter, younger, and more energetic at decstack.

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