摘要
证券市场效率问题始终是学术界和投资者的研究领域。本文重点从系统论的角度围绕中国股票市场线形和中国股票非线性两个方面探讨了中国股票市场。股票市场投资的目的是获取最大投资收益,然而收益与风险相伴,在收益与风险之间决策常常是不容易的。传统的股票投资理论认为股票市场是有效的,均衡的,收益是风险的线性函数,收益的波动符合布朗运动,收益的分布是独立同分布的,方差和均值是稳定的,即是线性的。实际情况却是股票市场影响因素以及各因素之间相互作用关系复杂,受投资者个人及群体心理因素影响明显,股票的波动以及收益与风险的关系常常是非线性的,非均衡的,收益的方差和均值是自相关的、不稳定的,收益的波动符合分形布朗运动,表现出非线性(分形和混沌)的特征。
论文首先从系统的分类与特性出发,基于有效市场理论和分形市场理论,通过复杂性深入讨论股票市场的动力学机制,将分形分析和遗传算法应用于股市预测中,最终提供证券组合的优化方案,力求在最小风险的情况下,获得最大限度的收益。在市场分形分析中,我们分别针对上海证券市场、深圳证券市场,通过不同时间标度,通过布朗运动、分形维以及Hurst指数的估算等系统、详尽的刻画各个市场特征,及其内在作用机制,并且对市场效率进行比较研究,以揭示市场运行规律。在市场投资组合研究中,通过遗传算法,借鉴物种进化原理,从证券市场基本理论出发,借助财务指标、价格指标、宏观经济指标等等,提出建立具有演化功能和适应性的动态投资组合方法和框架。
Securities market efficiency is the longstanding objective in the research domain of the academe and investors. It is mainly from two aspects to analyze Chinese stock market on the view of System Theory. One aspect is called the linear feature of Chinese stock market and the other is non-linear feature. The purpose of investing in the stock market is to maximize the benefits. However, it’s always not easy to keep the balance of risk and return because there is a positive correlation between them. In the opinions of traditional stock investment theories, the stock market is of efficiency and equilibration. The return is the linear function of the risk. The volatility in stock return moves in the Brownian motion. Distribution of stock returns is independent and identical distribution. And the variance and average of stock return are steady with the linear correlation. In fact, the impact factors on stock market and their reciprocity are completely complicated. The mentality factor of individual and group investors plays the obviously part on stock market. There exists non-linear and nonequilibrium feature of stock price fluctuation and between risk and return. The variance and average of stock return are based on self-reference and unstable. The volatility in stock return moves in Fractional Brownian Motion (FBM) with non-linear, fractal and chaos characters.
Classification and characters of system are discussed at the beginning of the paper. Then on the basis of effective market theory and fractal market theory, the optimization model of the securities combination is established due to the deep research on dynamics mechanism of stock market, and the application of fractal analysis and Genetic Algorithm to stock prediction, in order to maximize the benefits in minimum risk. The characters and internal operation mechanisms of Shanghai and Shenzhen securities market are expounded systematically and detailedly by means of estimating Brownian motion, fractal dimension and Hurst index in time series. Meanwhile, by comparison of market efficiency, market operation rules and regulations are showed up. The purpose of investment combinations research is to find out a dynamic investment combinations method and model with the functions of evolvement and adaptability, according to the Genetic Algorithm, species evolvement theory and basic securities market theories, and supported by financial index, price index, macroeconomic index and so on.
Chapter One Introduction
Firstly, the research results and trends home and overseas in related domain are reviewed. Then, the necessity of further research and its intending trend are demonstrated because there still exist some limitations on received results according to conclusions of received results and references of latest research. Thirdly, the research ideas and methods are introduced. Last but not least, the structure and innovations of this paper are given.
Chapter Two Classification and Characters of System
Learning form the research experiences and results, I give the definition of system according to the theories of dialectical materialism and modern system. System has multi-characters and it is the unification of variety and otherness. System is composed of many elements and groups with rules. These elements and groups are related and concerned with each other and system, so no independent exits in system. They interdepend, inter-effect, inter-inspirit, inter-repair and inter-restrict each other with some particular rules which differ from another system. Integration is an attribute of system.
I expatiate on the definition of system in detail from the aspects of structure, hierarchy and emergence. The system is divided to Little System, Large System, Simple Giant System and Complex Giant System by its scale and structure. And features in different system are concluded in its features, functions, behaviors and so on. Among different kinds of systems, Open Giant System is paid much more attention.
Chapter Three Efficient Market Hypothesis (EMH)
Efficient Market Hypothesis (EMH) is the foundation of Modern Finance, and also the good application of Rational Expectations Theory (Economics).In the opinion of EMH, all the assets information are reflected on securities price. Effective price change is random and unpredicted. In fact, the agreement has lasted over ten years whether EMH is true or not in academe. Behavioral Finance becomes the center of the agreement as pioneer. Scholars have found some unusual phenomena which are opposite to EMH, such as over-volatility of the market, changeable clustering, Scale Effect, over-reaction and under-reaction. Actually, these unusual phenomena are the general representation of bubbles and its burst.
Chapter Four the Fractal Analysis and Dynamic Mechanism of Chinese Stock Market
If EMH was true, there must be some kind of dynamic mechanism to support this hypothesis. The inter-mechanism has become the focus of theory horizon again since unusual phenomena occur. The facts have been realized that there is long-term memory of market yield, and the distribution is not accorded with Normality Distribution but fat tail and distinct pinnacle distribution. These facts make me to reset my thinking and try to find out a new model to explain some questions which can’t be solved by EMH. The development of the Fractal Geometry is one of the most useful and charming discovery in mathematics this century. Fractal Theory is very important to the modern study on the complexity of science theories and impresses deeply on human’s Natural Philosophy, Philosophy of Science, Scientific Method, scientific thinking and so on.
Fractal Market Hypothesis (FMH) comes into being after Fractal Theory is applied to capital market. In the opinions of FMH, the capital market is like a feedback system with critical level. The time series of securities price and yield is accorded with fractal distribution. Assets prices deviate from its balance state and are sensitive to initial conditions
In Fractal Theory, Rescaled Range Analysis (R/S) is non-parameter statistic analysis. It doesn’t matter if latency distribution is accorded with Gaussian distribution or one, while one assumption is a must that latency distribution is dependent. So objective of R/S is not only Normality Distribution, but also non-Gaussian independent processes. Hurst exponent is an important method of R/S and can be calculated by constant regression and non-constant regression.
Dynamic Mechanism of stock market is made with the thinking of Complex System. Investors predict by inductive logic and keep learning to make various decisions which are not perfect. It is dynamic and made by the structure. And its equilibrium is evolving rather than perfect.
Chapter Five the Study on Genetic Algorithm of Portfolio in Chinese Stock Market
Genetic Algorithm (GA) is a kind of Global Optimization Search Algorithm by simulating evolution process with the features of random, iteration, evolution and parallel search. The general idea of GA is to search from a group of basic feasible solutions at random, called“population”. Every unit is called“chromosome”and regarded as a solution to the problem. The quality of chromosome is up to its fitness value. The larger the chromosome fitness value is, and the higher its probability to be chosen is. On the opposite side, probability for smaller value is lower. These chosen chromosomes go into next generation and produce new chromosomes called“offspring”by crossover, mutation and other genetic manipulations. From generation to generation, GA makes it to converge at best chromosome which stands for the optimal solution or sub-optimal solution.
Thinking of the complexity of Chinese stock market, I apply GA to the research on single index and multi-index algorithm, according to modern financial knowledge, securities investment technique analysis theory, macroeconomics initial index. Then Optimal Portfolio can be selected out on the basis of the research. And the efficiency of portfolio is discussed on the conditions of different index.
Conclusions
The study on complexity of Chinese stock market is the focus of securities market study. It reveals the internal operation rules of Chinese stock market system on Systems Methodology research, and gives a new view on the study about complexity of Chinese stock market. What’s more important meaning, it proves the fractal feature of Chinese stock market after learning form the former research, and selected out the Optimal Portfolio referring to the features of random, iteration, evolution and parallel search on GA.
1、Learning from former results, I describe the classification and features of system, scientific identification of complexity, essential features of Complexity Science, pedigree of Complexity, and basic theory of Complexity. I demonstrate that Chinese stock market is a Complex Giant System by conditions, behavior, state, and evolvement of Chinese stock market’s operation.
2、The shortages of statistical structure assumption are proved in EMH. EMH use statistical structure to describe the market so it is accorded with Normality Distribution. Asymptotic normality of price change can not reflect the true market features. So that’s one of the reasons to prove that EMH can not be applied to stock market.
3、The linear model used in EMH can simply the complexity of problems. But it will reach the wrong conclusions if the linear methods are applied in non-linear fields such as stock market. So it’s another reason to believe that EMH is not suitable to stock market
4、The practical R/S research on Shanghai and Shenzhen composite indexes shows, there is long-term persistence for 5DMA (Day Moving Average), 10DMA and 20DMA have long-term. It gives the evidence that Chinese stock market yield has non-linear feature and it isn’t accorded with random process. So it is the proof that there are rescaled range and chaos dynamics features in Chinese stock market.
5、The conclusion can be reached by the practical research on Fractal that the duration of stock price in Shenzhen securities market is longer than in Shanghai’s.
6、On the qualitative research of Chinese stock market, single index and multi-index investment models are established according to GA, investment strategy, Chaos Theory, and securities investment analysis theory. Demonstrations show that these models are helpful to deal with whole emergence in Chinese stock market to increase investors’yield.
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