Friday, August 19, 2011

Scientific American: "Can Math Beat Financial Markets?"

We have dozens if not hundreds of posts on models and modeling; climate, financial, high fashion, you name it.
Here's the Google search: climateer models
Remember, a huge portion of the financial dislocations of the last few years were caused by over-reliance on models. AIG spent hundreds of millions on the hardware, software and wetware that blew the company up.
From SciAm:

Mathematical models help assess risk, but woe betide those who think math can predict stock market gains and losses

Wall Street's wild swings last week helped skew both retirement portfolios and mathematical models of the financial markets. After all, a standard  Gaussian function—a bell curve—would predict that such extreme dips and rises would be exceedingly rare and not prone to following one after the other on succeeding days.
Gaussian functions might be able to describe the distribution of grades in a big college class, with most students getting, say, B–/C+, and enable you to predict how many students will get A's or fail. But evidently, they do a poor job at explaining steep fluctuations in stock prices, although some economists and modelers think they are the best tool available to describe financial markets.

So can any math accurately describe market behavior and enable you to beat it? To find out, Scientific American spoke with statistical physicist H. Eugene Stanley of Boston University, a proponent of applying the approaches and concepts of physics to economics.
[An edited transcript of the interview follows.]

Can mathematical models beat markets?
They haven't yet. Science is about empirical fact. There is no question that optimistic people think they can beat the market, but they don't do it consistently with mathematical models. No model can consistently predict the future. It can't possibly be.

So what can math predict?
What you can do is predict the risk of a given event. The risk just means the chance that something bad will happen, for example. That you can do with increasing accuracy because we have more and more data. It's like insurance companies: they cannot tell you when you are going to die, but they can predict the risk that you will die given the right information. You can do the same thing with stocks. If you lose less, you get ahead of those who lose more.

Why do economists and "quants"—those who use quantitative analysis to make financial trades—have such faith in their mathematical models then?
If they're just to reduce risk, then they're very valuable. If you're worried, for example, about the segment of the Chinese economy that deals with steel, you make a model of what that whole market is all about and then you see if we did this what would likely happen. They're right some of the time. It's better than nothing.
But when they have excessive faith in these models, it's not justified. Math starts with assumptions; the real world does not work that way. Economics, which calls itself a science, too often doesn't start with looking at empirical facts in any great detail. Fifteen years ago even the idea of looking at huge amounts of data did not exist. With a limited amount of data, the chance of a rare event is very low, which gave some economists a false sense of security that long-tail events did not exist.

Why do you argue that financial markets are ruled not by Gaussian functions but by  power laws—relations in which the frequency of one event varies as a power of some attribute of that event and are generally more L-shape than bell shape?
For anything that is random and fluctuating, like a financial market, a Gaussian function is a wonderful way to make a histogram of the outcome. If the things that fluctuate are not correlated at all with one another, then it's demonstrable that a Gaussian function is the correct histogram....MORE