Most people fail to think in terms of the first derivative, let alone the second. Today’s *Exponential Investor *is about the third derivative. What’s known as “jerk” in maths. But it’ll take a while to get to the jerk that could deliver you exponential gains in 2020…

The failure to think in terms of derivatives explains why many investors don’t make money in the stockmarket. And why they struggle to understand what makes stocks go up and down.

Of course, it’s the second derivative that delivers exponential gains. But I better explain what the derivative is first. And then we’ll get to why I’m abusing physics terminology to make a point about investing.

If you’re in a car, the first derivative is its speed. The rate at which its position is changing.

The second derivative is acceleration, the rate at which the speed itself is changing.

Seems simple. But let’s apply it to something more abstract, outside of physics.

If capitalism is good for economic growth, and communism is bad, why is China outgrowing the US economy?

The answer is to think in the first derivative instead. Is China becoming more capitalist or less? Is the US becoming more capitalist or less?

Economic growth is about the direction of change between capitalism and communism, not an economy’s position at any point in time. Because economic growth is of course a measure of change itself, you need to think in terms of the first derivative.

But take care, some measures should be considered without derivative thinking. Economic growth measures a rate of change in GDP. But GDP itself is not a rate of change. So you don’t need to think in terms of the first derivative if you’re looking at GDP only. The US is the wealthier nation in terms of GDP per-capita because it is the more capitalist.

Whether you agree on capitalism and communism is beside the point here. The key is that you need to think in the right derivative given what you want to measure.

So, let me ask you, what is the right way to think about investing gains? Well, it depends on the gains you’re looking for.

But first, you need to understand that stocks can be expensive. We measure how expensive stocks are using something called a price/earnings (P/E) ratio. Here’s how it works.

For the rights to a given pound of returns (measured in earnings or dividends), you pay a price. A company with £1 of profits per share, with a share price of £15, has a P/E ratio of 15. That’s about middle of the range in terms of cheap or expensive. If the company paid out 100% of profits to its owners, they’d get their money back in 15 years.

A company with a lot of earnings per share, but a low price, is cheap. £2 of profits per share, with a share price of £15, means a P/E ratio of 7.5, which is cheap. If the company paid out 100% of profits to its owners, they’d get their money back in 7.5 years.

A company with low earnings per share, but a high price, is expensive. £0.50 of profits per share, with a share price of £15, means a P/E ratio 30, which is expensive.

With that background in mind, back to the topic.

When you invest, you’re focusing on share price gains and falls. That’s a change. Which means the rising or falling value of a company is something you should think about in the first derivative.

To figure out what drives it, you need to think in terms of the first derivative too. What’s changing? Is the company getting better somehow? Is demand for its goods going up? What is changing to make the share price move?

The simplistic view here is to measure earnings growth, because earnings drive the P/E ratio. But, especially in the tech world, things can be more abstract. The likes of Uber, Netflix and Facebook boomed based on user growth, not earnings, for example. Their P/E ratios are expensive, but they’re still top stockmarket performers. Or were…

Regardless of which measure matters, most people don’t think about this level of change. They see companies as static and forget measures over time. That’s why they struggle to predict the direction of change in the share price. Just as economics students struggle to understand why the Chinese economy is growing fast.

But even fewer investors consider the second derivative – how fast the change itself is changing.

Is the company’s product being adopted at an ever-increasing pace, or has that pace of adoption levelled off? Is earnings growth still exponential, or is the growth steady? For every pound increase in the price of what the company is selling, how much more does the company make in profits?

That’s the key to exponential gains – the point of this newsletter and most tech investing. Finding opportunities which look attractive through the lens of the second derivative, not just the first.

But what sort of change is there on the horizon which offers second derivative gains? What trends are still accelerating, let alone growing?

Today, I’d like to point out two opportunities.

The first is the last thing you’re expecting – gold.

You see, gold stocks can behave in an exponential fashion. For a simple reason which sets miners apart from other businesses.

Gold miners have what’s called an AISC – all-in sustaining cost. It’s the total cost for that miner of producing an ounce of gold.

When the gold price rises by $1, that’s a $1 increase in the profit margin for the gold miner. This is different to most other businesses, which don’t trade on markets where prices move in this way. Can you imagine the price of Coca-Cola rising by $1 worldwide? Or the price of toothpaste? It doesn’t happen. But in the gold market, it does.

Because of this difference, gold miners are far more exposed to the gold price. A $1 change has a far larger effect than you’d expect for gold miners. Often an exponential one, because it’s like pure profit to them. And that sort of rise and fall happens all the time in the gold market.

This also allows those gold miners to pay exponentially more dividends as the gold price rises. That recently happened for our *Gold Stock Fortunes* subscribers. A stock which produces a lot of gold turned the surging gold prices into whopping dividend increases over time. A 40% increase in the gold price translated into a 660% increase in dividends over the last five years.

Now that’s acceleration!

The same second derivative-style thinking is also especially true for high-cost gold miners. Those with high AISC. They can go from heading for bust to being profitable in a day’s gold trading. And their share price responds accordingly. A second derivative of the gold price.

If you’re bullish gold, and want to turn this into an exponentially profitable play, gold miners are the way to go.

But there’s a far bigger opportunity on the horizon. One simple change to our telecoms network is about to radically alter what’s possible in the rest of our economy. It will unlock so many other possibilities that the rates of technological progress in our lives will suddenly embark on another exponential growth curve.

Because of what’ll be unlocked, well beyond the telecom tech change itself, I’m calling this is a third derivative opportunity – what’s know as “jerk” in physics. That’s presumably because, when acceleration first happens, you feel a jerk.

Well, how would you like to jerk your portfolio in 2020?

Here’s how.

Nick Hubble

Editor, Southbank Investment Research