The Secret Life of Numbers: 50 Easy Pieces on How Mathematicians Work and Think (2006)
Chapter: 46 Turbulent Liquids and Stock Markets (Finance, Economics)
46
Turbulent Liquids and Stock Markets (Finance, Economics)
There is nothing surprising about the stock market going up or down on any given day, indeed at any given minute. Any economics student will have learned in the first weeks of his or her freshman year that the supply and demand of investors wishing to maximize their profits will affect share prices. The implicit assumption made is that traders react to all incoming information in a rational and reasonable way.
But then there are times when wholly unexpected fluctuations occur on the financial market that just cannot be explained by turning to “classical theory.” A particularly dramatic market event took place on the London exchange on September 20, 2002. On this day, at 10:10 a.m., the FTSE 100 index rose from 3,860 to 4,060 within a span of five minutes. Within another few minutes the index fell to 3,755. After some further oscillations, which lasted for 20 minutes, the index returned to the initial value. This completely inexplicable spook saw some traders cashing in on hundreds of millions of pounds while others faced losses running into the same figures—and it all happened in less than half an hour.
Wild deviations, as observed in London, and the more generally observed regular oscillations remind observers, respectively, of turbulences in liquids and of muted vibrations produced by guitar strings. It is thus not surprising that physicists feel called on to search for explanations that could shed light on stock market behavior. Sorin Solomon from the Hebrew University in Jerusalem together with his student Lev Muchnik developed a model that offers some explanations for the puzzling events taking place on stock markets.
The difference between their model and the more conventional models is that the Israeli physicists did not assume that there exist classes of traders who differ from each other merely in terms of their reactions when faced with risk. What they did do was postulate different investor types. The interaction between these diverse participants in the stock market was too complicated, however, to be described by mathematical formulas. To get to the bottom of what actually happens on the stock market, they simply observed a simulated model over a period of time. This, they thought, was the way to get a firm grasp of what happens on the trading floor.
In Solomon and Muchnik’s model there are investors who buy and sell based on whether the current price of shares is above or below market value. Then there are a few large investors who practically dominate the market and whose activities have a direct impact on share prices. Finally, the model also includes naive traders who base their buy and sell decisions simply on their past investments. In this model, which also considers other factors like the arrival of news items and various market mechanisms, virtual traders act autonomously. But their collective actions determine the behavior of the market.
After feeding all the variables into a computer, Salomon and Muchnik set up a simulation model for a virtual stock market. Can the existence of the three types of investors help explain the puzzling oscillations on the stock market? Lo and behold, their program produced behavior as it is observed in real-life stock markets. Damped oscillations occurred, suddenly interspersed with violent turbulences. Does that mean that real markets consist of these three types of traders? This is by no means certain, but what the model does at least show is how the interactions between different types of investors may lead to the surprising and sometimes colossal events that happen on the stock market and how the value of an investor’s portfolio can change drastically in the time span of a coffee break.
