A portfolio optimization model using Genetic Network Programming with control nodes
Introduction
Nowadays, evolutionary computation has become a subject of general interest with regard to the power to solve complex optimization problems. It has been successfully applied to many fields of science and technology. This paper presents an application of evolutionary computation method named Genetic Network Programming to the problem of multi-brands optimization in the field of financial economics, which is one kind of portfolio optimization. Portfolio optimization in the stock market consists of deciding what brands to include in a portfolio given the investor’s objectives and economic conditions. The always difficult selection process includes identifying which brands to purchase, how much, and when. The basic idea is that we want to choose a group of brands from a large number of available issues, in order to maximize the expected return given an acceptable risk rate. A rational investor needs to consider not only maximizing the profit of the investment, but also minimizing the uncertainty or risk resulting from the fluctuations that are expected in the value of the portfolio. The main problem is how to allocate the available capital in order to maximize profit and minimize risk simultaneously.
There have been increased the number of applications of Artificial Intelligence (AI) techniques, mainly artificial neural networks, genetic algorithm and genetic programming, which have been applied to technical financial forecasting (Dempster and Jones, 2001, Goldberg, 1989) as they have the ability to deal with complex non-linear problems and have the self-adaptation for dynamically changing problems. Several applications of Genetic Algorithms (GA) to the financial problems have been done, such as portfolio optimization, bankruptcy prediction, financial forecasting, fraud detection and scheduling (Loraschi et al., 1995, Skolpadungket et al., 2007). Genetic Programming (GP) (Koza, 1992) has also been applied to many problems in the time-series prediction. Although these AI approaches possess the properties required for the technical financial forecasting, they have some inherent bottlenecks. For example, Genetic Programming sometimes causes the bloating problem due to its tree structure. Neural networks cannot be used to explain the causal relationships between input and output variables because of their black-box nature.
In the past studies, we have proposed Genetic Network Programming (GNP) and Genetic Network Programming with Reinforcement Learning (GNP-RL) (Eguchi et al., 2006, Mabu et al., 2007, Mabu et al., 2007) as an extended method of GA (Goldberg, 1989) and GP (Koza, 1992). Since GNP represents its solutions using graph structures, which contributes to creating quite compact programs and implicitly memorizing past action sequences in the network flows, it has been clarified that GNP is an effective method mainly for complicated problems such as portfolio optimization systems. Moreover, in our former research, GNP-RL method was successfully applied to stock trading model (Mabu et al., 2007), and its applicability and efficiency has been confirmed.
Recently, in order to extend the functions of conventional GNP, Genetic Network Programming with control nodes (GNPcn) (Eto, Mabu, Hirasawa, & Hu, 2006) has been proposed. Since GNP has a directed graph structure, the aim of GNPcn is to improve the performance of GNP by extending the evolutionary method of it. In traditional GNP, the current node isn’t compulsorily transferred to the start node. However, in the GNPcn method, the number of control nodes are set up and a certain number of processing nodes are executed before returning to one of the control nodes, i.e., we extend the breadth and depth of searching space for GNP. It is clarified from the simulations that the performance of GNP could be improved by the combination with control nodes.
In this paper, we extend our previous research on GNP-RL and propose an algorithm that integrates the GNP-RL and control nodes in order to create an efficient portfolio optimization model for given multi-brands. The features of the proposed method compared with other traditional methods are as follows: The GNPcn method makes a stock trading strategy considering the recommendable information of technical indices and candlestick charts (Izumi, Yamaguchi, Mabu, Hirasawa, & Hu, 2006) for efficient trading decision making. Reinforcement Learning is also used in this paper for taking appropriate actions.
Section 2 presents the literature review. Section 3 describes the proposed GNPcn approach to be studied in this paper. In Section 4, we explain the optimization algorithm in brief. Section 5 presents experimental environments, conditions and results using GNPcn method. The trading profits are presented and compared with both the traditional GNP method and Buy&Hold method. Finally, Section 6 concludes this paper.
Section snippets
Literature review
In recent decades, the portfolio problem in financial engineering has received a lot of attention. The classical portfolio problem can be described like the following: Given a finite amount of resources, and the process to which these resources can be allocated, we need to get the allocation which maximizes a given goal function and minimizes the risk simultaneously. The foundation of portfolio optimization was laid by Markowitz (1959), where he proposed a mean–variance optimization model for
Genetic Network Programming with control nodes
In this section, Genetic Network Programming (GNP) with control node is explained briefly. Basically, GNP is an extension of GP in terms of gene structures. The original idea is based on the more general representation ability of directed graphs than that of trees. The graph structure of GNP has some inherent characteristics such as compact structures and an implicit memory function that contribute to creating effective action rules.
Technical indices and candlestick chart
In our proposed portfolio optimization model, technical indices and candlestick chart are used as judgment functions. Concretely speaking, each judgment node uses one of the following technical indices for its judgment: Rate of Deviation from moving average (ROD), Relative Strength Index (RSI), Rate of Change (ROC), Volume Ratio, Rank Correlation Index (RCI), Stochastics, Golden/Dead cross and Moving Average Convergence and Divergence (MACD).
As a judgment function, a candlestick chart was also
Simulations
To confirm the effectiveness of GNPcn for the portfolio optimization system, we carried out the trading simulations using 10 brands selected from the companies listed in the first section of Tokyo stock market in Japan (see Table 2). The simulation period is divided into two periods: one is used for training and the other is used for testing.
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Training: January 4, 2001–December 30, 2003 (737 days).
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Testing: January 5, 2004—December 30, 2004 (246 days).
We suppose that the initial funds, i.e.,
Conclusions
In this paper, we proposed a multi-brands optimization algorithm by using GNPcn to check the information of technical indices and candlestick chart patterns. Compared to conventional GNP, GNPcn has many control nodes, and each group of control nodes is assigned to each stock brand for creating effective portfolio strategy. Since GNPcn can adjust the distribution of the initial budget to each brand at each generation and more budget is assigned to the brands with larger profitability, we can
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