The Ten Equations That Rule the World by David Sumpter

Author:David Sumpter
Language: eng
Format: epub, pdf
Publisher: Flatiron Books

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There is no way of unlocking the secret of financial markets without starting with this fundamental equation:

Equations simplify the world by condensing lots of knowledge into a few symbols, and the market equation is a brilliant example of this. To unpack it, we need to go through it step by step, very carefully.

The equation describes how X, which represents the “feeling” of investors about the current value of a stock, changes. The feeling can be either positive or negative, so X = −100 is a really bad feeling about the future and X = 25 is a pretty good feeling. Economists talk about markets being bullish or bearish. In our model, a bullish market is positive (X > 0) about the future, and the bear market is negative (X < 0). To be more concrete, we might think of our X as the number of bullish people minus the number of bearish people. But at this stage, we don’t want to get tied down to a particular unit for measuring X. Instead, think of X loosely, as capturing emotions. Instead of investors, it could be the feeling in a meeting after layoffs are announced or after your company has received a big order.

As a convention in mathematics, we tend to put the things we want to explain on the left and the things that we think will do the explaining on the right. And this is exactly what we do in this case. The left-hand side in this instance is dX. The letter d denotes change. So dX means “the change in feeling.” Notice how the atmosphere in the room dips as you find out your jobs are at risk. This threat of redundancy might be dX = −12. Or the newly placed order that is going to sustain your company for the next few years might be dX = 6. An even bigger order could be dX = 15.

The units, the magnitude of the numbers I use, are not what you should focus on. Math problems in school tend to be about adding and subtracting real things like apples and oranges or money; here, we can allow ourselves more freedom. I realize there is no such thing as a dX = −12 change in the emotions of your colleagues, but that doesn’t mean we can’t try to capture changes in how a group of people feel. That is exactly what a share price is: it is how investors feel about the future value of a company. We want to explain changes in our collective feeling about a particular stock investment or the feeling in the office at work, or our feeling about a political candidate, or our feeling about a consumer brand.

The right-hand side of the equation consists of three terms—hdt, f(X)dt, and σ · εt—which we add together. We have already seen two of these terms. The terms for the signal, h, and the noise, σ, both appeared in equation 3. Their role is similar here:

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