#### January 24, 2018

### Going Exponential

We live in a mostly linear existence. Generally, things in our lives stay the same or change slowly over time at fairly fixed rates. Sure, there are times when drastic changes happen, such as when we leave our families for the first time, when we move, when we start a new job, etc. But for the most part, we experience change at a steady pace. As we age, we progress through the years at the rate of one year per year. We don’t ever skip years, and we don’t ever slow down, though we wish we could do both at times. At 16, we wish we were 21, and at 40, we wish we were 25. No matter what we wish, our lives progress steadily ever forward.

So time is linear, in our experience, and market indices that the TSP Funds are based on tend to be as well. For sure there are spikes and drops and volatility, but on longer time lines, such as the span of a human life, markets move in long straight lines. It’s a lot like driving. Yes we accelerate and slow down fairly often, but usually we don’t accelerate that quickly, and we usually don’t stop very quickly. Over long timelines, your *average* rate of speed is pretty consistent. You accelerate up to the speed limit (or maybe a little over), and you maintain that speed over time.

In this context, a straight line represents linear growth (or loss), which is a constant rate of change. If you recall back to your early math days, the rate of change is the slope of the line, and a straight line’s slope doesn’t change. So if you graph y = x, or y = 1.2x, or y = 2.6x, you get a straight line because the slope is constant.

Now compare that to an exponential curve. Remember that an exponential curve is graphed as a curved line, which is just a line with a *changing* rate of change. For instance, if you graph y = x^{2} (which has an exponent of 2), or y = x^{1.2}, or y = x^{3}, you get a line that gets steeper and steeper over time. The actual slope is changing, so it goes higher at a faster pace over time. This would be like constantly accelerating in a car, which we all know cannot happen forever. And that is because, for most of our experiences, life is linear.

Take a look at this graph. This is the S&P 500 on a long time line.

Notice the examples of long periods of time I have highlighted when the slope of the graph remains approximately the same, meaning that the market is changing at approximately the same rate over time. There are ups and downs, accelerations and corrections, and periods of transitioning between, but for the most, the S&P operates in long straight lines.

Now look to the far right of the graph, which corresponds to the last few years. The line of the S&P 500 may be starting to do something is has never done. Historically, when the market goes up, it starts to slow, levels off, and goes down, and then constantly repeats this cycle. However, just very recently, the market has been going up, but it has stopped slowing down. It has stopped leveling off. And it has stopped going down. The rate of change of the line is changing, *but the rate is increasing over time*. The market appears to be starting to go exponential. It seems to be actually *curving upward*. If the market truly is curving upward, it would be the first time I’ve ever seen it, and the first time it has happened in the time frame represented by this graph.

Exponential growth is not a new concept, but it is a new phenomenon. Historically, breakthroughs in various industries have tended to happen individually, not necessarily in conjunction with one another. A new cure for a disease hasn’t coincided with a new type of alloy to build with. A new manufacturing process hasn’t necessarily happened at the same time as new safety features in vehicles were developed. But recently, with the ubiquitous spread of powerful computing throughout our world and throughout all major industries, new breakthroughs are not only happening more often in each industry, they are happening across all industries at the same time. This has never happened before. And I think it is causing a change in the way that markets act. Companies are more profitable at a faster rate and across a broad span of industries than ever before. And they keep getting faster. We have hit the beginnings of exponential growth and a very exciting time to be investors.

I read a great book that explains the phenomenon of exponential growth much more thoroughly than I have here. It is called *Abundance*, by Peter Diamandis. If this concept at all intrigues you, please give this book a try. It is well worth the read.

Welcome to our Exponential World.