Seite 2: An Artificial Stock Market

Around 1988, Brian Arthur, an economist from Stanford, and John Holland, a computer scientist from the University of Michigan, were sharing a house in Santa Fe while both were visiting the Santa Fe Institute. During endless hours of evening conversations over many bottles of wine, Arthur and Holland hit upon the idea of creating an artificial stock market inside a computer, one that could be used to answer a number of questions that people in finance had wondered and worried about for decades. Among these questions are:

Does the average price of a stock settle down to ist so-called fundamental value, the value determined by the discounted stream of dividends that one can expect to receive by holding the stock indefinitely?

Is it possible to concoct technical trading schemes that systematically turn a profit greater than a simple buy-and-hold strategy?

Does the market eventually settle into a fixed pattern of buying and selling? In other words, does it reach stationarity'?

Arthur and Holland knew that the conventional wisdom of finance argued that today's price of a stock was simply the discounted expectation of tomorrow's price plus dividend, given the information available about the stock today. This theoretical price-setting procedure is based on the assumption that there is an objective way to use today's information to form this expectation. But this information typically consists of past prices, trading volumes, economic indicators and the like. So there may be many perfectly defensible ways based on many different assumptions to statistically process this information in order to forecast tomorrow's price.

The simple observation that there is no single, best way to process information led Arthur and Holland to the not-very-surprising conclusion that deductive methods for forecasting prices are, at best, an academic fiction. As soon as you admit the possibility that not all traders in the market arrive at their forecasts in the same way, the deductive approach of classical finance theory begins to break down. So a trader must make assumptions about how other investors form expectations and how they behave. He or she must try to psyche out the market. But this leads to a world of subjective beliefs and to beliefs about those beliefs. In short, it leads to a world of induction rather than deduction.

In order to answer the questions above, Arthur and Holland recruited physicist Richard Palmer, finance theorist Blake LeBaron and market trader Paul Tayler to help them construct their electronic market, where they could, in effect, play god by manipulating trader's strategies, market parameters and all the other things that cannot be done with real exchanges. This surrogate market consists of :

a) a fixed amount of stock in a single company;

b) a number of traders (computer programs) that can trade shares of this stock at each time period;

c.) a specialist who sets the stock price endogenously by observing market supply and demand and matching orders to buy and to sell;

d.) an outside investment (bonds) in which traders can place money at a varying rate of interest;

e) a dividend stream for the stock that follows a random pattern.

As for the traders, the model assumes that they each summarize recent market activity by a collection of descriptors, which involve verbal characterization like the market has gone up every day for the past week, or the market is nervous, or the market is lethargic today. Let's label these descriptors A, B, C, and so on. In terms of the descriptors, the traders decide whether to buy or sell by rules of the form: ``If the market fulfills conditions A, B, and C, then BUY, but if conditions D, G, S, and K are fulfilled, then HOLD.'' Each trader has a collection of such rules, and acts on only one rule at any given time period. This rule is the one that the trader views as his or her currently most accurate rule.

As buying and selling goes on in the market, the traders can re-evaluate their different rules in two different ways: (1) by assigning higher probability of triggering a given rule that has proved profitable in the past, and/or (2) by recombining successful rules to form new ones that can then be tested in the market. This latter process is carried out by use of what's called a genetic algorithm, which mimics the way nature combines the genetic pattern of males and females of a species to form a new genome that is a combination of those from the two parents.

A run of such a simulation involves initially assigning sets of predictors to the traders at random, and then beginning the simulation with a particular history of stock prices, interest rates and dividends. The traders then randomly choose one of their rules and use it to start the buying-and-selling process. As a result of what happens on the first round of trading, the traders modify their estimate of the goodness of their collection of rules, generate new rules (possibly) and then choose the best rule for the next round of trading. And so the process goes, period-after-period, buying, selling, placing money in bonds, modifying and generating rules, estimating how good the rules are and, in general, acting in the same way that traders act in real financial markets. The overall flow of activity in this market is shown below.

A typical moment in this artificial market is displayed in Figure above. Moving clockwise from the upper left, the first window shows the time history of the stock price and dividend, where the current price of the stock is the black line and the top of the grey region is the current fundamental value. So the region where the black line is much greater than the height of the grey region represents a price bubble, while the market has crashed in the region where the black line sinks far below the grey. The upper right window is the current relative wealth of the various traders, while the lower right window displays their current level of stock holdings. The lower left window shows the trading volume, where grey is the selling volume and black is the buying volume. The total number of trades possible is then the minimum of these two quantities, since for every share purchased there must be one share available for sale. The various buttons on the screen are for parameters of the market that can be set by the experimenter.

After many time periods of trading and modification of the traders' decision rules, what emerges is a kind of ecology of predictors, with different traders employing different rules to make their decisions. Furthermore, it is observed that the stock price always settles down to a random fluctuation about its fundamental value. But within these fluctuations a very rich behavior is seen: price bubbles and crashes, psychological market moods, overreactions to price movements and all the other things associated with speculative markets in the real world.

Also as in real markets, the population of predictors in the artificial market continually coevolves, showing no evidence of settling down to a single best predictor for all occasions. Rather, the optimal way to proceed at any time is seen to depend critically upon what everyone else is doing at that time. In addition, we see mutually-reinforcing trend-following or technical-analysis-like rules appearing in the predictor population.

Let's now turn to the realm of biology and look at another example of complex adaptive systems in action.