Financial Market Models

The other day, I heard about people who made some computer models of the financial system a few years back that more-or-less, somewhat, kind of sort of, predicted the current state of affairs — but not exactly. Throughout history, people have been keen on trying to do the same thing. If you successfully predict with enough detail which stocks are going to go up and which are going to go down, you effectively have a time machine that can peek into the future and tell you tomorrow’s winning lottery numbers.

The general problem with such systems is that there is too much chaos–in the classic mathematical sense — for them to work reliably. There are way too many input variables and way too many possible outcomes. Weather cannot currently be predicted for much the same reason. The flap of a butterfly’s wings in once place can affect something a little larger that can affect something a little larger, that can cause a monsoon half-way around the world (as the popular saying goes.) The number of people driving in two neighboring cities on any given day can cause differences in smog, which cause differences in temperature, which can cause air movement and wind, which can help pull or push passing storm clouds into or away from a third neighboring city. In the financial markets, you have so many people making so many individual decisions. Families decide to buy or sell a house. CEOs decide to expand their company, downsize it, encroach a neighboring industry. Traders see trends and buy or sell accordingly. Someone in power embezzles a sizable chunk of change. Someone with a vast fortune gives a sizable chunk to charity. A game-changing or disruptive technology gets sudden popularity. And so on. While these types of influences can perhaps be predicted with enough computing power, I don’t expect we’ll see anything like that for several centuries; certainly not in our lifetime.

My specific problem with these sorts of prediction engines is entirely different and sort of passes through the technical and into the philosophical. Let’s say that a few hundred years pass and that computers get exponentially more and more capable. Let’s say that some garage hacker invents a SimFinance application that does a reasonably good job at predicting the markets. Working isolated, outside of the system, from his garage he’s able to lotto-jackpot a lot of money. But this isn’t the likely scenario. The more likely scenario is that such a system will be made by a team of Ph.D.s. Maybe they come from academia, maybe from the commercial sector. At any rate, this will be a fairly public project with published results. It’s going to work really well for a time — maybe a few weeks, maybe a few months, but then it will stop working. Why? Ask Heisenberg. The models are designed to take a look at the system from the outside and predict its behavior. The predictions come from all of the available data up to that point. But suddenly, there is one more piece of data available: the results of the machine’s predictions itself. There will be many people who will be making decisions not based on what they know and feel, but by what the models predict. The models are not just observing from outside of the system anymore, but have become an active participant in the system. The financial models have to take themselves into account — in a way, they have to be self-aware. Not only are market factors and world events affecting the prices of stocks, but the predictions themselves are. People are going to do things that are outside of what they would ordinarily do because the model’s predictions.

All of this reminds me that I need to go back and re-read some of Asimov’s Foundation series, which features the predictive science of “psychohistory.” I’ve forgotten more of those stores than I remember of them.

Posted in: Dear Diary

2 thoughts on “Financial Market Models”

  1. Sadly, Asimov doesn’t expound much on the details or ramifications of psychohistory; it’s just used as a sort of “sufficiently advanced technology indistinguishable from magic” which gets the plot going.

    Re: what if everyone has one: If any company managed to develop a program which could get better than 50% accuracy on stock predictions, I bet it would be one of the most deeply buried secrets in the world. It won’t happen publicly unless it’s done by academia.

  2. Just as a point of clarification, no model ever made will predict the stock market to any reasonable precision. The current data set is finite, since stocks and insurance have only been going from around the 1600s, plus models suffer from precision drift, better known as “the butterfly effect”. This effect, discovered to Lorentz in the 1930s, found that two models with the same initial conditions would produce divergent results due simply to the precision (number of decimal places) of the data, as well as rounding.

    Let us not forget the effects of discontinuities in derivatives and chaotic effects. The stock market has no well defined global phase space, and as such, it fails to be periodic, thus undergoing chaotic motion. This motion is exacerbated when taking the derivative of a stock (or its double derivative), due to discontinuities at the end of trading.

    Thus, models fail for simple reasons, and no finite model will ever be able to describe the stock market.

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