Explorations in LCS Models of Stock Trading

In previous papers we have described the basic elements for building an economic model consisting of a group of artificial traders functioning and adapting in an environment containing real stock market information. We have analysed the feasibility of the proposed approach by comparing the final wealth generated by such agents over a period of time, against the wealth of a number of well known investment strategies, including the bank, buy-and-hold and trend-following strategies. In this paper we review classical economic theories and introduce a new strategy inspired by the Efficient Market Hypothesis (named here random walk to compare the performance of our traders. In order to build better trader models we must increase our understanding about how artificial agents learn and develop; in this paper we address a number of design issues, including the analysis of information sets and evolved strategies. Specifically, the results presented here correspond to the stock of IBM. 1 Forecasting Financial Markets Modelling real financial markets is not an easy task, it was once said that: “anybody doing applications of artificial intelligence (AI) in financial trading and investment management must possess considerable determination and vast reserves of optimism.” [13] Why? The generalised growth in complexity of financial markets has been one of the most significant changes seen in the past decade. As a result, the difficulty of the decision making process has increased dramatically, becoming more dependent upon the analysis of information gathered and available data coming from many different sources and in various forms. The results of various quantitative forecasting techniques, as well as human subjective skills and judgment, serve as an important tool for strategic decisions to most financial institutions. The high levels of activity seen in financial markets nowadays, along with the vast amounts of information available, produce multidimensional financial time series where the general mechanism that generates them is poorly understood. Much research has been devoted to trying to find some kind of model that has good explanatory power of the variables involved but is still of relatively low complexity. With the hope of finding the key to increased wealth, a common approach to follow is to try to look for previously undetected nonlinear regularities (such as daily or intra-daily fluctuations) from economic time series. This can be done in several ways. In some models, data derived from only one time series is used, such as a specific stock’s price, a given index or the one-day rate of return to holding a stock. Readers interested in a neural net (NN) model of this type are referred to [42], where inputs are defined as the one-day return of a stock rt , and for a genetic programming model where inputs are defined as the difference between the current price of a single stock and its moving averages, highest and lowest prices, refer to [40, 41, 26, 27]. In addition to using a single price series, other approaches use more variables and in different levels of sophistication (see [8, 18, 21]). These models can include over 120 inputs coming from other stock prices, volume of transactions, macro economic data, market indicators such as indexes, profit and earnings ratios, etc. More recently, as a result of the fast growth of the Internet, other approaches started to emerge, such as the work on text in finance [43, 38, 39]. Much of this effort concentrates on finding profitable trading rules from the analysis of text information of financial interest publicly available on the Internet – chat boards or news stories. The problem of designing trader models with relevant indicators has been addressed in [32], where it is also proposed to use genetic algorithms to optimise simple trading models. Also, a number of conferences report many papers on financial time series analysis and prediction. Specially, during the early nineties, when the use of neural networks appeared to be an area of great potential in securities forecasting, dozens of papers using neural networks were published. A good review of these results can be found in [1–4], and for a good summary of techniques used, see [30]. Although later on the revolution came to an end, what that era brought to the surface was perhaps the need to address the fallacies encountered with traditional approaches and the need to search for non-linear models capable of handling the complex task of forecasting. Too much was expected from NNs, and soon people were going to realise that, as pointed out by Halbert White when reporting his results, “in either case the implication is the same: the neural network is not a money machine” [42]. It then seems reasonable to suppose that in financial markets, investment decisions must involve taking into account a significant number of elements and their relationships, which due to the complex nature of economic systems, are usually difficult to understand and highly non-linear. Even though some investment managers and traders could factor in such dependencies in the analysis, they often cannot explain their decisions and point out the significant elements and relationships contributing to their current positions; other times, due to secrecy policies, they are just not willing to do so. This makes the problem of economic forecasting very hard, as there is no actual knowledge easily available and controversies and debates as to what is the right investment approach are still in question. In the following section we will review some of these. 1 The one-day return of a stock is defined as rt = pt−pt−1+dt pt−1 , where p1 is the closing price of the stock in question on day t and dt is the dividend it paid on day t. This value should be adjusted to stock splits and dividends if appropriate. 2 Classical Economic Theories With tremendous impact in industry and academia, the Efficient Markets Hypothesis (EMH) has been perhaps one of the strongest weapons against the development of economic forecast approaches described in the previous section. The hypothesis first appeared in the famous and highly controversial PhD dissertation of Eugene F. Fama at the University of Chicago, under the title “The Behaviour of Stock Market Prices”, and was originally published in the Journal of Business [15]. In addition to this work, Fama also published ideas of this kind in a number of journal papers, such as “Random Walks in Stock Market Prices” which appeared in, amongst others, the Institutional Investor [14], where the following excerpt is taken: “An ‘efficient’ market is defined as a market where there are large numbers of rational, profit-maximisers actively competing, with each trying to predict future market values of individual securities, and where important current information is almost freely available to all participants. In an efficient market, competition among the many intelligent participants leads to a situation where, at any point in time, actual prices of individual securities already reflect the effects of information based both on events that have already occurred and on events which, as of now, the market expects to take place in the future. In other words, in an efficient market at any point in time the actual price of a security will be a good estimate of its intrinsic value.” The great impact of EMH dispersed rapidly from academia to the investment community. Fama’s 1970 paper on the topic “Efficient Capital Markets” [16] argues that on average, it is nearly impossible for an individual to consistently beat the stock market as a whole because of the broad availability of public information. Therefore markets are assumed to be efficient if all available information is reflected in current market prices [16, 17]. Some people think this is equivalent to saying that an investor who throws darts at a newspaper’s stock listings has as much chance at beating the market as any professional investor. In summary, the statement that stock price behaviour is random and not predictable by any forecasting method had become a dominant paradigm used by economists to understand and investigate the behaviour of financial markets. Looking for more evidence to sustain this theory, Fama later studied all the funds that survived during a 20-year period starting in 1976. But because these funds were naturally biased from being survivors during the period, he reduced the sample by choosing only the 20 biggest winners from the first ten years and analysed their performance over the second 10 years relative to a risk-corrected model. Not surprisingly for him, he found out that exactly half of them were above average and the other half below. This means that the best performers had a 50% chance to succeed over the next period. With this new evidence he continues to favour passive management over active management. But still, for those who do not follow the EMH, there were some winners over the whole period. (The biggest winner of all was Fidelity Magellan, credited to Peter Lynch.) The EMH also comes in many strengths, the first one being the “Weak form” of efficiency, which asserts that in a market that assimilates information efficiently it is impossible to predict the future price of a security on the basis of its past price because all past market prices and data are fully reflected in security prices, so there cannot be investment strategies which yield extraordinary profits on the basis of past prices – technical analysis is of no use. An argument in favour of this form of efficiency says that a short-term market-timing rule cannot make money because the opportunity goes away if everyone follows the same strategy. So the belief is that markets do not follow major patterns in stock prices, and the minor patterns caused by momentum are costly to explote. Evidence suggests that prices do appear to be random. The “Semi-strong” form refers to the degree of market rea