Evolutionary computation for trading systems
Evolutionary computations, also called evolutionary algorithms, consist of several heuristics, which are able to solve optimization tasks by imitating some aspects of natural evolution. They may use different levels of abstraction, but they are always working on populations of possible solutions for a given task. The basic idea is that if only those individuals of a population which meet a certain selection criteria reproduce, while the remaining individuals die, the population will converge to those individuals that best meet the selection criteria. If imperfect reproduction is added the population can begin to explore the search space and will move to individuals that have an increased selection probability and that hand down this property to their descendants. These population dynamics follow the basic rule of the Darwinian evolution theory, which can be described in short as the “survival of the fittest”. Although evolutionary computations belong to a relative new research area, from a computational perspective they have already showed some promising features such as: • evolutionary methods reveal a remarkable balance between efficiency and efficacy; • evolutionary computations are well suited for parameter optimisation; • this type of algorithms allows a wide variety of extensions and constraints that cannot be provided in traditional methods; • evolutionary methods are easily combined with other optimization techniques and can also be extended to multi-objective optimization. From an economic perspective, these methods appear to be particularly well suited for a wide range of possible financial applications, in particular in this thesis I study evolutionary algorithms • for time series prediction; • to generate trading rules; • for portfolio selection. It is commonly believed that asset prices are not random, but are permeated by complex interrelations that often translate in assets mispricing and may give rise to potentially profitable opportunities. Classical financial approaches, such as dividend discount models or even capital asset pricing theories, are not able to capture these market complexities. Thus, in the last decades, researchers have employed intensive econometric and statistical modeling that examine the effects of a multitude of variables, such as price- earnings ratios, dividend yields, interest rate spreads and changes in foreign exchange rates, on a broad and variegated range of stocks at the same time. However, these models often result in complex functional forms difficult to manage or interpret and, in the worst case, are solely able to fit a given time series but are useless to predict it. Parallelly to quantitative approaches, other researchers have focused on the impact of investor psychology (in particular, herding and overreaction) and on the consequences of considering informed signals from management and analysts, such as share repurchases and analyst recommendations. These theories are guided by intuition and experience, and thus are difficult to be translated into a mathematical environment. Hence, the necessity to combine together these point of views in order to develop models that examine simultaneously hundreds of variables, including qualitative informations, and that have user friendly representations, is urged. To this end, the thesis focuses on the study of methodologies that satisfy these requirements by integrating economic insights, derived from academic and professional knowledge, and evolutionary computations. The main task of this work is to provide efficient algorithms based on the evolutionary paradigm of biological systems in order to compute optimal trading strategies for various profit objectives under economic and statistical constraints. The motivations for constructing such optimal strategies are: i) the necessity to overcome data-snooping and supervisorship bias in order to learn to predict good trading opportunities by using market and/or technical indicators as features on which to base the forecasting; ii) the feasibility of using these rules as benchmark for real trading systems; iii) the capability of ranking quantitatively various markets with respect to their profitability according to a given criterion, thus making possible portfolio allocations. More precisely, I present two algorithms that use artificial expert trading systems to predict financial time series, and a procedure to generate integrated neutral strategies for active portfolio management. The first algorithm is an automated procedure that simultaneously selects variables and detect outliers in a dynamic linear model using information criteria as objective functions and diagnostic tests as constraints for the distributional properties of errors. The novelties are the automatic implementation of econometric conditions in the model selection step, making possible a better exploration of the solution space on one hand, and the use of evolutionary computations to efficiently generate a reduction procedure from a very large number of independent variables on the other hand. In the second algorithm, the novelty is given by the definition of evolutionary learning in financial terms and its use in a multi-objective genetic algorithm in order to generate technical trading systems. The last tool is based on a trading strategy on six assets, where future movements of each variable are obtained by an evolutionary procedure that integrates various types of financial variables. The contribution is given by the introduction of a genetic algorithm to optimize trading signals parameters and the way in which different informations are represented and collected. In order to compare the contribution of this work to “classical” techniques and theories, the thesis is divided into three parts. The first part, titled Background, collects Chapters 2 and 3. Its purpose is to provide an introduction to search/optimization evolutionary techniques on one hand, and to the theories that relate the predictability in financial markets with the concept of efficiency proposed over time by scholars on the other hand. More precisely, Chapter 2 introduces the basic concepts and major areas of evolutionary computation. It presents a brief history of three major types of evolutionary algorithms, i.e. evolution strategies, evolutionary programming and genetic algorithms, and points out similarities and differences among them. Moreover it gives an overview of genetic algorithms and describes classical and genetic multi-objective optimization techniques. Chapter 3 first presents an overview of the literature on the predictability of financial time series. In particular, the extent to which the efficiency paradigm is affected by the introduction of new theories, such as behavioral finance, is described in order to justify the market forecasting methodologies developed by practitioners and academics in the last decades. Then, a description of the econometric and financial techniques that will be used in conjunction with evolutionary algorithms in the successive chapters is provided. Special attention is paid to economic implications, in order to highlight merits and shortcomings from a practitioner perspective. The second part of the thesis, titled Trading Systems, is devoted to the description of two procedures I have developed in order to generate artificial trading strategies on the basis of evolutionary algorithms, and it groups Chapters 4 and 5. In particular, chapter 4 presents a genetic algorithm for variable selection by minimizing the error in a multiple regression model. Measures of errors such as ME, RMSE, MAE, Theil’s inequality coefficient and CDC are analyzed choosing models based on AIC, BIC, ICOMP and similar criteria. Two components of penalty functions are taken in analysis- level of significance and Durbin Watson statistics. Asymptotic properties of functions are tested on several financial variables including stocks, bonds, returns, composite prices indices from the US and the EU economies. Variables with outliers that distort the efficiency and consistency of estimators are removed to solve masking and smearing problems that they may cause in estimations. Two examples complete the chapter. In both cases, models are designed to produce short-term forecasts for the excess returns of the MSCI Europe Energy sector on the MSCI Europe index and a recursive estimation- window is used to shed light on their predictability performances. In the first application the data-set is obtained by a reduction procedure from a very large number of leading macro indicators and financial variables stacked at various lags, while in the second the complete set of 1-month lagged variables is considered. Results show a promising capability to predict excess sector returns through the selection, using the proposed methodology, of most valuable predictors. In Chapter 5 the paradigm of evolutionary learning is defined and applied in the context of technical trading rules for stock timing. A new genetic algorithm is developed by integrating statistical learning methods and bootstrap to a multi-objective non dominated sorting algorithm with variable string length, making possible to evaluate statistical and economic criteria at the same time. Subsequently, the chapter discusses a practical case, represented by a simple trading strategy where total funds are invested in either the S&P 500 Composite Index or in 3-month Treasury Bills. In this application, the most informative technical indicators are selected from a set of almost 5000 signals by the algorithm. Successively, these signals are combined into a unique trading signal by a learning method. I test the expert weighting solution obtained by the plurality voting committee, the Bayesian model averaging and Boosting procedures with data from the the S&P 500 Composite Index, in three market phases, up-trend, down- trend and sideways-movements, covering the period 2000–2006. In the third part, titled Portfolio Selection, I explain how portfolio optimization models may be constructed on the basis of evolutionary algorithms and on the signals produced by artificial trading systems. First, market neutral strategies from an economic point of view are introduced, highlighting their risks and benefits and focusing on their quantitative formulation. Then, a description of the GA-Integrated Neutral tool, a MATLAB set of functions based on genetic algorithms for active portfolio management, is given. The algorithm specializes in the parameter optimization of trading signals for an integrated market neutral strategy. The chapter concludes showing an application of the tool as a support to decisions in the Absolute Return Interest Rate Strategies sub-fund of Generali Investments.