基于异质性交易者非线性模型的中国证券市场价格波动研究
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摘要
2005年是中国证券发展史上具有里程碑意义的一年，在此之前股权分置1作为我国证券市场特有的制度性缺陷长期困扰着市场的发展，2001年政府尝试采取行政化的解决措施引发股市长达5年的非理性下跌，几乎导致了中国证券市场的推倒重来；2005年4月底沉寂多年的证券市场被市场化的股权分置改革激活，投资者以极大热情造就了我国证券市场上最大的一次狂欢，到2007年底股权分置改革完成之时上证指数从最低998点上涨到最高6124点。然而好景不长，我国证券市场在其后经历了更加剧烈的暴跌暴涨后再次进入熊市，虽然期间受到美国次贷危机导致的全球金融危机以及欧债危机等外部冲击，但我国经济增长仍然一直维持较高的增长水平，当2011年底我国GDP由十年前不到人民币10万亿增长到近40万亿以及上市公司从1073家增长到2300家时，上证综合指数却跌回到十年前点位。仔细观察指数和个股的剧烈波动中，二级市场投资者发现除了基本面因素以外还存在一种不可忽视的全新势力，即随着全流通时代的真正到来，大小限股东和高管们高位减持凶猛，大股东们的减持行为经常发生在股价大幅上涨后利好信息发布之时或在利空信息出来之前，而增持行为往往伴随着其后的基本面利好，甚至出现大量上市公司高管为了规避减持股份的制度约束而形成的离职潮。继之而来的是市场风格的大幅转变，股市上炒小、炒新、炒重组和炒题材重新盛行，公司治理规范业绩稳定的大型蓝筹公司却少人问津，短线趋势交易成为获取盈利规避风险的最佳方式，奉行长期价值投资的公私募基金等投资者由于业绩不佳而经常成为被嘲讽的对象。二级市场大量投资者认为股权分置改革等市场化制度的推行并未带来公平有效的股市，也未实现大小股东利益的双赢局面，重新陷入对股市丧失信心的境况，并呼吁监管当局采取新的制度性改革。
目前，我国监管当局和研究机构的学者对我国证券市场存在种种问题的认识上不存在明显分岐，有关政策建议似乎也高度一致，即我国资本市场是新兴的不成熟市场，推行市场化的制度建设是建立起完善有效资本市场的渐进过程，需要假以时日逐渐走向成熟。从原则上说，本文对这一结论并不持异议，但认为我国证券市场在没有有效限制内幕信息交易等整体制度安排的条件下，局部推进市场化的改革措施往往实现不了改革的预设目标。股权分置改革虽然历史性地解决了中国资本市场上同股不同价、法人股非流通的问题，但相对于法人股非流通时代，在大小非股权转为大小限股权后，也创造了制度化预期更为明确的内部交易者，这些内部交易者持有绝对控股比例的流通市值，与外部投资者相比具有天然的信息优势，由于限制流通的股票在确定的期限内会逐步流通，除了国有必须持有的控股权外，大量非国有控股股东存在创造高价减持机会或操控股价波动的较大可能性，这可能是造成我国证券市场在一些市场化改革推进后，混沌现象2更加突出的主要原因。为了研究清楚这个命题，需要开展两个细致深化的研究方向，一是要检验证实制约机制缺乏条件下，内部交易者的存在确实会导致资本市场混沌特征更加突出；二是如何推出进一步的配套制度改革，有效地消除制度性形成的、预期收益明确的内部交易者。显然第一个深化研究方向是探求症结、解开命题的基础，因而本文选择以此为突破口，即验证内部交易行为与证券市场暴涨暴跌混沌特征的相关性，以及内部交易行为对于证券市场运行的内在影响机制。本文尝试从一个新的视角出发开展相关研究工作，因而需要借鉴不同于传统经典有效市场理论的新金融理论框架。即通过理论化描述我国股市中不同类型的投资者行为，解析各类投资者追求利益最大化时其投资行为和群体的变化，并推论我国证券市场过度波动的内在原因。本文的论证过程分为几个部分：简要回顾从有效市场的静态线性理论向分形混沌市场的动态非线性理论范式转变，及对我国证券市场中国特色研究的启示意义；运用分形与混沌理论对我国证券市场的非线性特征以及股权分置改革前后市场特征的变化进行检验；构建我国证券市场异质性投资者的非线性模型；根据我国证券市场代表性投资者的行为特征对模型进行检验，实证我国证券市场价格波动特征的内生性作用机制。
1970年以后有效市场理论(EMH)曾长期主宰金融经济学的理论研究。有效市场的核心含义在于，资产价格变动充分反应了市场的基本面信息，资产价格是其内在价值的外在表现。在短期，资产价格的波动受外部随机因素影响不可预测；偏离的股价在长期会向基本价值的均值复归。资产的风险程度可以通过价格波动的方差来测度；资产价格的时间序列呈现正态分布的统计结论强烈支持了资本市场系统有效且风险可控。而上述一切能够存在的条件是，证券市场上的投资者是理性的。有效市场理论自产生并成为理论规则以来一直受到怀疑与挑战。这首先是因为，法玛（Fama，1965）发现了著名的尖峰厚尾现象，斯特基（Sterge，1989）、特纳（Turner）和魏格纳（Weigel，1990）证实了尖峰厚尾现象在金融市场是远非偶发、远非局部的普遍性现象。随着研究的深入，经济学家逐渐以小公司效应、规模溢价、价值溢价、持久性特征以及股价过度波动及波动的集群性，来定义并揭示尖峰厚尾现象的经济学意义。亚洲金融危机中黑天鹅现象的小概率事件引起广泛的骨牌效应，2008年次贷危机引起全球金融危机，则是进一步证明尖峰厚尾现象会在现实中产生难以发现且无法控制的破坏力。
希勒（Shiller1981,1984,1987）揭示了非理性投资行为与尖峰厚尾现象间的内在联系，即当多数投资者在投资决策中存在诸多的认知偏差时，其行为将系统性地偏离经济理性，造成金融市场长期地、显著地偏离有效性，形成金融市场动荡或危机。谢福润（Shefrin，2000）以有限理性假设，描述了投资者依赖于简单和习惯性的经验方法进行决策的投资行为；泰勒（Thaler，1994）提出了准理性概念(quasi-rationality)，分析了投资者受过分自信和过度反应等情绪影响会产生不完全理性的行为。显而易见的是如果投资者是非理性的，不同类型的投资者就构成了分散且相互冲突的投资行为，市场的特征就是分形的，市场的波动就不是线性的而是混沌的。当年这些观念大有离经叛道之感，现如今则已经具有了相对完善的分形市场理论和混沌市场理论的分析范式。由于非理性投资者是异质的投资群体，但同时存在于一个统一市场内，面对相同的信息，一部分投资者会因投资收益受影响而做过度的投资反应；而另一部分投资者则会认为与自己无关，而对信息不做反应。假设，认为此信息对投资收益有显著影响的投资者所占比例高，结果是尽管这一信息对投资收益的真实影响不大，也会引起市场暴涨暴跌；反之，当认为此信息对投资收益没有影响的投资者所占比例高时，市场对信息的反应就会是迟缓的。问题是当此信息的真实影响大于预先估计时，投资者又会转向过度反应，结果同样会引起暴涨暴跌。更进一步的分析表明，无论反应过度还是反应迟缓本身都只是投资决策不稳定的中间状态，在现实的高流动性资本市场中，投资者从反应过度到反应迟缓再转向反应过度往往也只是一念之差。
总之，当经济学家离开了价格波动是完全信息反映的思维束缚后，所能看到的真实世界是，价格变动对于信息的反应是非线性的，资产价格变动不再遵循随机游动过程，资本市场因此具有典型的混沌特征。对初始条件敏感，非周期性和有界性是资本市场普遍存在的现象。人们不可能改变这种市场性质，而只能通过认识这种特性降低市场失败的损失。
本文采用分形理论和混沌理论对我国证券市场进行实证研究，证实了我国证券市场具有典型的分形市场的特征、价格波动具有明显的混沌特点，进一步证实了在股权分置改革后我国证券市场的非线性特征更加明显。依据实证检验的结果，我们可以认为，所谓我国证券市场中国特色的同义语是，中国证券市场相对于发达国家成熟的资本市场，具有更明显的分形市场和混沌的特性。本文将在此基础上重点研究，我国形成分形市场的特性以及资产价格混沌波动的内在机制。
首先，分别以上海、深圳证券交易所建立以来20年的综合指数和证券市场整体滚动市盈率（TTM市盈率）为标的，对我国证券市场的价格波动和股票价格相对基本价值的波动进行非线性特征检验，确认了我国证券市场的综合指数和股票价格偏离内在价值的波动具有典型的混沌特征。中国证券市场具有分形市场的特征，价格波动为有偏随机游走、有非循环周期和股价长期不可预测性。
其次，笔者依据非线性动力学模型对动态市盈率波动性质的检验结果表明，我国证券市场上的异质性交易者对于资产未来收益折现的动态预期具有混沌特征，并由此构成了资产价格波动的混沌特征。证明这种内生性因果关系给予有关我国证券市场发展研究的重要提示意义在于，依据非理性的逻辑，研究异质投资的行为是理解我国证券市场过度波动的钥匙。
第三，有关分形市场的研究以异质投资者的分类为基础。尽管我们在理论研究中，可以依据不同的分类方法来划分异质投资者，但是判断类型划分是否合理的标准只能是，即是否更为准确地定义了一定时期内可以观察的且具有典型意义的投资行为，与此同时能否找得到可以有效反映这种投资行为的统计指标也是分类的重要依据。在研究工作中，我们对我国证券投资者所做分类如下，一是中国证券市场最受诟病的内幕信息交易者，其行为特征是通过掌握未公开的对于股票基本价值有重要影响的信息进行交易。典型代表为大小非股东、庄家和少数基金等；二是基本价值交易者，即理性交易者，其行为特征是依据公开信息判断股票基本价值并进行交易。典型代表为部分公私募基金和少数普通投资者；三是趋势交易者，亦可称为有限理性的图表交易者（包括正反馈交易者和负反馈交易者），其行为特征是依据股票市场价格的变动趋势进行交易，典型代表为大多数普通投资者和部分公私募基金。
第四，三种不同类型的投资者投资行为显著不同，仅仅是权重组合发生变化就会使我国证券市场产生不同的波动机制。特别需要引起关注的是，在统一的市场体系中，三种类型投资者的行为会相互影响，造成初始条件的微小变化引起巨大的市场波动的混沌现象。现代股市中虽然我们不可能认识到每天出清的股票市场价格是否偏离了股票的真实价格，但肯定知道投资者有输赢之分；我们所划分的三种类型的投资者每天、每月与每年的投资收益都有差别，由此就会产生出学习过程，更准确地说是投资行为的转换过程。例如，理性投资者听说有更多的人是依靠内部消息盈利，可能会放弃理性投资的选择。但是，转换投资行为需要付出成本，成本的高低与证券市场的制度建设和投资者成熟度等具有高度相关性，高的转换成本尤如高门槛使得转换成为不可能。例如：内幕信息的获得要花费成本，基本价值交易者无疑要受过良好的教育，在付学费之余要付信息收集加工处理的费用，趋势交易者付出的成本也不低，能够分析股价走势图表除了统计学知识外就是要在市场上付出大量学费。在内幕交易成本低且盛行的市场上，许多有条件的投资者必然会进行风险低收益大的内幕交易；而其他普通投资者会根据价格变动、成交量变化等技术指标推测可能隐含的内幕信息，进而跟风操作，当趋势操作具有赚钱效应会有更多的投资者跟进。这种集体的转换行为不仅会改变全社会投资者类型的动态比例，而且直接引起社会性的追涨杀跌的跟风性操作。对于信息的过度反应和过度迟缓的转换会越来越快，对于股价变动的反馈交易也会越来越厉害，由此形成了我国资本市场上特有的暴涨暴跌现象。作为理论概括，我们可以将之定义为投资者行为引起资产价格非线性波动，资产价格波动影响投资者行为的双向交互共激的混沌动态过程。在此过程中，投资者结构变迁对资本市场估值水平（动态市盈率）和资产价格波动的内生性影响居核心地位，或者说是我国资本市场特征产生和发展的内生性因素。
最后，有关我国资本市场微观结构中异质投资者行为以及相互行为间随机挠动引发的混沌现象的研究，说明我国证券市场制度的市场化改革中，尽管出发点是良好的，当相关配套制度不健全时，反而会制度性形成扭曲的市场微观结构，导致更加混沌的非理性有效的市场。这个研究结论对于我国资本市场的未来制度建设有着重要意义。
The year2005was the milepost sense year of China security market in the history,before the share-trading as the special and institutional defects of our country’s sharemarket have long-term plagued the development of the market, in the year2001thegovernment tried to take administrative measures caused the stock market up to5years of irrational fall, which almost resulted in the Chinese security marketretrograding to the start again; April2005after the quiet years of the securities market,the market was activated by the equity division reform. Investors with greatenthusiasm created one of the largest carnival in the securities market of China. Bythe end of2007when the equity divison reform completed, the Shanghai CompositeIndex was soaring from the lowest points of998up to a maximum of6124points.However, good times did not last long. The share market in China experienced moreintense fall and jump again entering a bear market. Although experienced externalshocks of United States sub-loan crisis which led to the global financial crisis and thedebt crisis, China economy still maintained high growth level. At the end of2011,when the GDP of our country grew from less than RMB10trillion ten years ago tonearly40trillion and the listed companies increased from the1073growth to2300,the Shanghai Composite Index fell back to the points ten years ago. After Carefullyobserved the index and stock volatility, the secondary market investors found thatbesides the fundamental factors of corporate, there was a noticeable new forces,namely with the full circulation times came true, the non-tradable stockholders andcompany’s high executives fiercely sold their shares, and the point was that the timemajor shareholders reduced the stocks occured frequently when good informationrelease or before the bad information out, and the holdings of shares was oftenaccompanied by subsequent good information. Even in order to avoid reduction ofshare system constraints, large number of executives quit their jobs. Then with thedramatic transformation of market style, the stock market speculation was popularagain. The large blue chip companies with good corporate governance and stableprofits was abandoned by investors, on the other hand, short-term trend tradingbecame the best ways to make profits and evade risk, and the public and privateequity funds aimed at long-term investment value were often recognized as theobjects of satire as a result of the poor performance. A large number of secondaryshare market’s investors reckoned the reform of equity division neither brought a fairand effective market nor realized the win-win situation between the minorityshareholders and majority shareholders, therefore they lost the confidence of stockmarket and required the authorities to adopt a new system reform.
At present, China's regulatory authorities and institution scholars do not haveobvious differences on all sorts of problems of China's securities market and therelated policy suggestions also appears to be highly consistent. The capital market ofour country is emerging in the immature market, implementing market-orientedsystem construction is to establish a perfect and effective capital market gradualprocess, which take some time to move toward maturity gradually. In principle, thisarticle is not dissent this conclusion, however under the condition of no overallsystem arrangement such as lack of effective restriction of insider informationexchange in our share market, partially improving the reform measures often fail torealize the goals. Although the equity division historically solve the chinese capital onthe market with different stock price, and legal person shares non-circulationproblems, compared to the legal person share non-circulation time, the non-tradableshares converted into conditional shares also created a system is expected to be moreclear the insiders. These internal traders hold absolute majority of proportion ofcirculation stock’s market value, and compared with outside investors naturally theyhave internal information advantages. Due to the limitation of current stock in certainperiod will be gradually circulated, besides state-owned must hold the controllingright, a large number of non-state-owned controlling shareholders create highreduction opportunities or manipulate stock price fluctuations high possibilities,which may be the cause the chaos phenomenon after a series of reformation ofChina's securities market. To find out this proposition, there are two deepen researchdirections, the first one is to test whether under the condition of lack of restrictionmechanism, the existence of internal traders will lead to capital market chaos furthermore outstanding; the other one is how to make a further supporting system reform,which may effectively eliminate the institutional formed and clear expected profitreturn internal traders. Apparently the first research direction is to search the crux tosolve the basis of proposition, so this paper chooses it as the breakthrough, namelyverifying the correlation of internal transactions and the stock market rises and falls,and the effect of internal transactions of securities market operation for the innermechanism. This paper try to start the research work from a new perspective, and usethe new financial theory frame which is different from traditional classical andeffective market theory. That is through the theoretical description of the differenttypes of investors’ behavior in China's stock market to analize all kinds of investorspursuing the maximal profit when its investment behavior and groups changed, andfinally inference the internal reason of excessive volatility of our share market. Thispaper's reasoning process is divided into several parts: a brief review of the marketfrom effective static linear theory to the nonlinear dynamic model chaotic markettheoretical paradigm shift, and on China securities market research significance ofChinese characteristics; By using the chaos theory to verify the nonlinearcharacteristics of China securities market and the change of market characteristic before and after equity division reform; Constructing China's securities marketnonlinear model of heterogeneity investors; According model test of therepresentative behavior of investors, the endogenous mechanism of the Chinesesecurities market price fluctuation is verified.
After1970years, efficient market theory (EMH) has long time dominated thetheory research of financial economics. Effective market core meaning is that assetprice change fully reflects the market information, asset prices is the externalperformance of the intrinsic value. In the short term, the external random factorscaused volatility of the asset prices is unpredictable; Shares’ deviation in thelong-term will return to the fundamental value of the mean economics. The level ofrisk assets can be measured by fluctuations in the price variance; the normaldistribution statistical of the assets’ present price of time series strongly support thecapital market system effectiveness and risk control. And the existing conditions ofthe above all can be controlled is that the stock market investors are rational.Effective market theory since it becomes the rule has been suspected and challenged.First of all because. Jordan Fama (Fama,1965) found the famous Fat-tailphenomenon, Sterge (Sterge,1989). Turner (Turner) and Weigel (Weigel,1990)confirmed the Fat-tail phenomenon is far from occasional, and the local commonphenomenon. With the development of research, economists in small company effectgradually. Scale premium. With the development of research, economists define andreveal the economical meaning of Fat-tail phenomenon though the small companyeffect, Scale premium, Value premium, Persistence characteristics and excessivevolatility and the cluster of volatility of the stock price. Small probability events of‘Black Swan’ phenomenon in the Asian financial crisis caused extensive dominoeffect, and in2008the subprime crisis caused the global financial crisis, are furtherprove that the Fat-tail phenomenon produced the destructive power in reality isdifficult to discover and can not be controlled.
Shiller (1981,1984,1987) revealed the intrinsic link between the non-rationalinvestment behavior and a peak fat-tail phenomenon, that is when the most investorshave cognitive biases in investment decision-making, their behavior willsystematically deviate from economic rationality, which could cause the financialmarket deviating from the effectiveness strikingly for a long time, resulting in theturmoil or crisis in financial market. Shefrin(2000) described that the investors relyon simple and habitual method and experience to make their investment decisionswith the limited rational hypotheses; Thaler put forward quasi-rationaliyt, thisconcept analyzed some emotions, such as over self-confidence and overreaction willlead to noncompletely rational behavior. Obviously, if investors are irrational,different types of investors would constitute decentralized and conflicting investmentactivities, at the same time, the market feature is fractal and the volatility of themarket is not linear but chaotic. Years ago these concepts are very unorthodox, nowadays there is a relatively perfect fractal market theory and a model of chaoticmarket theory. Because non-rational investors are heterogeneous groups, when theyare in the same market facing the same information, Some of them will have aexcessive investment response due to yield, while the others have nothing to do.Assumption that the proportion of investors who believe that this information hassignificant effect on investment income are higher, the result would be an unevenmarket, even if this information has little effect on investment income actually.Conversely, when most of them believe the information has no effect on investmentincome, the market's response to the information would be delayed. Real question iswhen the effect is greater than the estimate in advance, investors will turn to overreact,which also can cause slump and boom. Further analysis showed that the overreactingand the delayed response are just intermediate state. In the real liquidity capitalmarket, the distance between overreaction and delayed response is only an investor'sidea.
In a word, when economists free themselves of the thought that the price volatilityis the response of complete information, the real world they can see is, the pricefluctuation for the information is nonlinear, while the asset price change no longerfollow the process of random walk, so the typical characteristic of capital market ischaos. Furthermore, sensitive to initial conditions, non-cyclical and boundedness arewidespread phenomenons in capital markets. Since it is impossible to change thisnature of the market, what we can do to reduce the loss is only understanding thesefeatures.
The paper adopts Fractal Theory and Chaos Theory to do the empirical research onthe securities market in China, proves that our securities market has the classicalcharacteristics of fractal market and price fluctuation is characterized by chaosobviously, and further verifies that non-linear characteristics of our securities markethave been more obvious since the reform of equity division. According to the resultsof the empirical test, we can see that the characteristic of Chinese securities market isthat it has more obvious fractal market and chaos properties by comparing withmature capital market of developed countries. The paper studies on properties offractal market and internal mechanism of chaotic fluctuation of capital prices on thisbasis.
Firstly, it uses the comprehensive indexes which have been established byShanghai Stock Exchange and Shenzhen Stock Exchange for two decades and thetotal TTM price-to-earnings ratio as targets, undertakes the non-liner characteristictest on price fluctuation of our securities market and fluctuation of stock pricescorresponding to basic values, and confirms that fluctuation of comprehensiveindexes and stock prices deviating from internal values in our securities market hasthe classical chaos characteristic. China’s securities market has the characteristics including fractal market, random walk of price fluctuation, acyclic period andlong-term unpredictability of stock prices.
Secondly, inspection results of non-liner dynamic model on dynamicprice-to-earnings ratio fluctuation nature show that heterogeneous traders’ dynamicexpectation on future income discount of asset is characterized by chaos, whichconstitutes the chaos characteristic of asset price fluctuation. Proving the importantindication significance of this internal cause and effect relationship on the research ondevelopment of China’s securities market lies in the fact that study on acts ofheterogeneous investment according to irrational logic is the key to understandexcessive fluctuation of our securities market.
Thirdly, the relevant study on fractal market is based on classification ofheterogeneous investors. Although we can divide heterogeneous investors accordingto different classification methods in the theoretical study, the standard of judgingwhether classification is reasonable is whether investment act is defined moreaccurately which can be observed in certain period and has classical significance;meanwhile, whether statistical indexes which reflect this investment act effectivelycan be obtained is the important basis of classification. In the study works, we canclassify our securities investors as follows: the first type is insider information traderswho are criticized severely in China’s securities market, they trade by graspinginformation which isn’t publicized but has important influence on basic values ofstocks, and the classical representatives are large and small part of non-tradableshareholders, market makers and a few funds etc.; the second type is basic valuetraders, i.e. rational traders, who trade by judging basic values of stocks according topublic information, and the classical representatives are some privately offered funds,public offer funds and a few common investors; however, position traders, who canbe called as limitedly rational icon traders (including positive feedback traders andnegative feedback traders), who trade according to changing tendency of marketprices of stocks, and the classical representatives are most of common investors andsome company-offered funds.
Fourthly, investment acts of the three different investors differ greatly, changes ofweight combination will make our securities market have different fluctuationmechanisms. Special attention shall be paid to mutual influence of acts of the threetypes of investors, and small changes of primitive conditions lead to enormous chaosphenomena of market fluctuation. Although we cannot know whether daily marketprices of stocks deviate from real prices of stocks in modern stock market, we knowthere are losing and winning investors; the three types of investors have differentdaily, monthly and yearly investment incomes, which form study process, moreaccurately, that is switching process of investment acts. For example, rationalinvestors hear that more people make profits by relying on insider information, andthey might give up choices of rational investment. However, changing investment act needs to pay costs, which are highly related to establishment of securities marketmechanism, and maturity of investors, and high switching cost makes impossibility ofswitching like a high threshold. For example, obtaining insider information needscosts, basic value traders must receive good education, they shall pay fees ofinformation collection and processing undoubtedly, costs paid by position tradersaren’t low, analyzing stock price trend chart needs knowledge of statistics and a lot oftuition in the market. In market of low-cost and prevailing insider trading, manyconditional investors will undertake low-risk and large-profit insider trading; andother common investors will predict implied insider information according totechnical indexes such as price variations and volume rate changes. The collectiveswitching act will change dynamic proportion to be invested by the whole society,and cause social market timing operation. Excessive reaction and slow switching ofinformation will become quicker, feedback trades become stronger because of stockprice changes, and special phenomenon of large price movement is formed in ourcapital market. To sum up theoretically, we can define it as dynamic chaos processthat investor acts cause non-linear fluctuation of capital prices and fluctuation ofcapital prices affects investor acts, which is two-way interactive attack. During theprocess, structural change of investors has the core internal influence on evolutionlevel (dynamic price-to-earnings ratio) of capital market and fluctuation of capitalprices or it is the internal factor for the making and development of the capital marketin China.
Lastly, the relevant study on the chaos phenomena caused by random perturbationbetween heterogeneous investor acts and interactive acts in the micro-structure of ourcapital market explains that the starting point is excellent in the market reform of oursecurities market systems, but relevant imperfect supporting systems will formtortured micro-structure of market systematically, and lead to more chaotic marketwhich is effective irrationally. The conclusion of the study has an importantsignificance on the establishment of future systems of our capital market.
目前，我国监管当局和研究机构的学者对我国证券市场存在种种问题的认识上不存在明显分岐，有关政策建议似乎也高度一致，即我国资本市场是新兴的不成熟市场，推行市场化的制度建设是建立起完善有效资本市场的渐进过程，需要假以时日逐渐走向成熟。从原则上说，本文对这一结论并不持异议，但认为我国证券市场在没有有效限制内幕信息交易等整体制度安排的条件下，局部推进市场化的改革措施往往实现不了改革的预设目标。股权分置改革虽然历史性地解决了中国资本市场上同股不同价、法人股非流通的问题，但相对于法人股非流通时代，在大小非股权转为大小限股权后，也创造了制度化预期更为明确的内部交易者，这些内部交易者持有绝对控股比例的流通市值，与外部投资者相比具有天然的信息优势，由于限制流通的股票在确定的期限内会逐步流通，除了国有必须持有的控股权外，大量非国有控股股东存在创造高价减持机会或操控股价波动的较大可能性，这可能是造成我国证券市场在一些市场化改革推进后，混沌现象2更加突出的主要原因。为了研究清楚这个命题，需要开展两个细致深化的研究方向，一是要检验证实制约机制缺乏条件下，内部交易者的存在确实会导致资本市场混沌特征更加突出；二是如何推出进一步的配套制度改革，有效地消除制度性形成的、预期收益明确的内部交易者。显然第一个深化研究方向是探求症结、解开命题的基础，因而本文选择以此为突破口，即验证内部交易行为与证券市场暴涨暴跌混沌特征的相关性，以及内部交易行为对于证券市场运行的内在影响机制。本文尝试从一个新的视角出发开展相关研究工作，因而需要借鉴不同于传统经典有效市场理论的新金融理论框架。即通过理论化描述我国股市中不同类型的投资者行为，解析各类投资者追求利益最大化时其投资行为和群体的变化，并推论我国证券市场过度波动的内在原因。本文的论证过程分为几个部分：简要回顾从有效市场的静态线性理论向分形混沌市场的动态非线性理论范式转变，及对我国证券市场中国特色研究的启示意义；运用分形与混沌理论对我国证券市场的非线性特征以及股权分置改革前后市场特征的变化进行检验；构建我国证券市场异质性投资者的非线性模型；根据我国证券市场代表性投资者的行为特征对模型进行检验，实证我国证券市场价格波动特征的内生性作用机制。
1970年以后有效市场理论(EMH)曾长期主宰金融经济学的理论研究。有效市场的核心含义在于，资产价格变动充分反应了市场的基本面信息，资产价格是其内在价值的外在表现。在短期，资产价格的波动受外部随机因素影响不可预测；偏离的股价在长期会向基本价值的均值复归。资产的风险程度可以通过价格波动的方差来测度；资产价格的时间序列呈现正态分布的统计结论强烈支持了资本市场系统有效且风险可控。而上述一切能够存在的条件是，证券市场上的投资者是理性的。有效市场理论自产生并成为理论规则以来一直受到怀疑与挑战。这首先是因为，法玛（Fama，1965）发现了著名的尖峰厚尾现象，斯特基（Sterge，1989）、特纳（Turner）和魏格纳（Weigel，1990）证实了尖峰厚尾现象在金融市场是远非偶发、远非局部的普遍性现象。随着研究的深入，经济学家逐渐以小公司效应、规模溢价、价值溢价、持久性特征以及股价过度波动及波动的集群性，来定义并揭示尖峰厚尾现象的经济学意义。亚洲金融危机中黑天鹅现象的小概率事件引起广泛的骨牌效应，2008年次贷危机引起全球金融危机，则是进一步证明尖峰厚尾现象会在现实中产生难以发现且无法控制的破坏力。
希勒（Shiller1981,1984,1987）揭示了非理性投资行为与尖峰厚尾现象间的内在联系，即当多数投资者在投资决策中存在诸多的认知偏差时，其行为将系统性地偏离经济理性，造成金融市场长期地、显著地偏离有效性，形成金融市场动荡或危机。谢福润（Shefrin，2000）以有限理性假设，描述了投资者依赖于简单和习惯性的经验方法进行决策的投资行为；泰勒（Thaler，1994）提出了准理性概念(quasi-rationality)，分析了投资者受过分自信和过度反应等情绪影响会产生不完全理性的行为。显而易见的是如果投资者是非理性的，不同类型的投资者就构成了分散且相互冲突的投资行为，市场的特征就是分形的，市场的波动就不是线性的而是混沌的。当年这些观念大有离经叛道之感，现如今则已经具有了相对完善的分形市场理论和混沌市场理论的分析范式。由于非理性投资者是异质的投资群体，但同时存在于一个统一市场内，面对相同的信息，一部分投资者会因投资收益受影响而做过度的投资反应；而另一部分投资者则会认为与自己无关，而对信息不做反应。假设，认为此信息对投资收益有显著影响的投资者所占比例高，结果是尽管这一信息对投资收益的真实影响不大，也会引起市场暴涨暴跌；反之，当认为此信息对投资收益没有影响的投资者所占比例高时，市场对信息的反应就会是迟缓的。问题是当此信息的真实影响大于预先估计时，投资者又会转向过度反应，结果同样会引起暴涨暴跌。更进一步的分析表明，无论反应过度还是反应迟缓本身都只是投资决策不稳定的中间状态，在现实的高流动性资本市场中，投资者从反应过度到反应迟缓再转向反应过度往往也只是一念之差。
总之，当经济学家离开了价格波动是完全信息反映的思维束缚后，所能看到的真实世界是，价格变动对于信息的反应是非线性的，资产价格变动不再遵循随机游动过程，资本市场因此具有典型的混沌特征。对初始条件敏感，非周期性和有界性是资本市场普遍存在的现象。人们不可能改变这种市场性质，而只能通过认识这种特性降低市场失败的损失。
本文采用分形理论和混沌理论对我国证券市场进行实证研究，证实了我国证券市场具有典型的分形市场的特征、价格波动具有明显的混沌特点，进一步证实了在股权分置改革后我国证券市场的非线性特征更加明显。依据实证检验的结果，我们可以认为，所谓我国证券市场中国特色的同义语是，中国证券市场相对于发达国家成熟的资本市场，具有更明显的分形市场和混沌的特性。本文将在此基础上重点研究，我国形成分形市场的特性以及资产价格混沌波动的内在机制。
首先，分别以上海、深圳证券交易所建立以来20年的综合指数和证券市场整体滚动市盈率（TTM市盈率）为标的，对我国证券市场的价格波动和股票价格相对基本价值的波动进行非线性特征检验，确认了我国证券市场的综合指数和股票价格偏离内在价值的波动具有典型的混沌特征。中国证券市场具有分形市场的特征，价格波动为有偏随机游走、有非循环周期和股价长期不可预测性。
其次，笔者依据非线性动力学模型对动态市盈率波动性质的检验结果表明，我国证券市场上的异质性交易者对于资产未来收益折现的动态预期具有混沌特征，并由此构成了资产价格波动的混沌特征。证明这种内生性因果关系给予有关我国证券市场发展研究的重要提示意义在于，依据非理性的逻辑，研究异质投资的行为是理解我国证券市场过度波动的钥匙。
第三，有关分形市场的研究以异质投资者的分类为基础。尽管我们在理论研究中，可以依据不同的分类方法来划分异质投资者，但是判断类型划分是否合理的标准只能是，即是否更为准确地定义了一定时期内可以观察的且具有典型意义的投资行为，与此同时能否找得到可以有效反映这种投资行为的统计指标也是分类的重要依据。在研究工作中，我们对我国证券投资者所做分类如下，一是中国证券市场最受诟病的内幕信息交易者，其行为特征是通过掌握未公开的对于股票基本价值有重要影响的信息进行交易。典型代表为大小非股东、庄家和少数基金等；二是基本价值交易者，即理性交易者，其行为特征是依据公开信息判断股票基本价值并进行交易。典型代表为部分公私募基金和少数普通投资者；三是趋势交易者，亦可称为有限理性的图表交易者（包括正反馈交易者和负反馈交易者），其行为特征是依据股票市场价格的变动趋势进行交易，典型代表为大多数普通投资者和部分公私募基金。
第四，三种不同类型的投资者投资行为显著不同，仅仅是权重组合发生变化就会使我国证券市场产生不同的波动机制。特别需要引起关注的是，在统一的市场体系中，三种类型投资者的行为会相互影响，造成初始条件的微小变化引起巨大的市场波动的混沌现象。现代股市中虽然我们不可能认识到每天出清的股票市场价格是否偏离了股票的真实价格，但肯定知道投资者有输赢之分；我们所划分的三种类型的投资者每天、每月与每年的投资收益都有差别，由此就会产生出学习过程，更准确地说是投资行为的转换过程。例如，理性投资者听说有更多的人是依靠内部消息盈利，可能会放弃理性投资的选择。但是，转换投资行为需要付出成本，成本的高低与证券市场的制度建设和投资者成熟度等具有高度相关性，高的转换成本尤如高门槛使得转换成为不可能。例如：内幕信息的获得要花费成本，基本价值交易者无疑要受过良好的教育，在付学费之余要付信息收集加工处理的费用，趋势交易者付出的成本也不低，能够分析股价走势图表除了统计学知识外就是要在市场上付出大量学费。在内幕交易成本低且盛行的市场上，许多有条件的投资者必然会进行风险低收益大的内幕交易；而其他普通投资者会根据价格变动、成交量变化等技术指标推测可能隐含的内幕信息，进而跟风操作，当趋势操作具有赚钱效应会有更多的投资者跟进。这种集体的转换行为不仅会改变全社会投资者类型的动态比例，而且直接引起社会性的追涨杀跌的跟风性操作。对于信息的过度反应和过度迟缓的转换会越来越快，对于股价变动的反馈交易也会越来越厉害，由此形成了我国资本市场上特有的暴涨暴跌现象。作为理论概括，我们可以将之定义为投资者行为引起资产价格非线性波动，资产价格波动影响投资者行为的双向交互共激的混沌动态过程。在此过程中，投资者结构变迁对资本市场估值水平（动态市盈率）和资产价格波动的内生性影响居核心地位，或者说是我国资本市场特征产生和发展的内生性因素。
最后，有关我国资本市场微观结构中异质投资者行为以及相互行为间随机挠动引发的混沌现象的研究，说明我国证券市场制度的市场化改革中，尽管出发点是良好的，当相关配套制度不健全时，反而会制度性形成扭曲的市场微观结构，导致更加混沌的非理性有效的市场。这个研究结论对于我国资本市场的未来制度建设有着重要意义。
The year2005was the milepost sense year of China security market in the history,before the share-trading as the special and institutional defects of our country’s sharemarket have long-term plagued the development of the market, in the year2001thegovernment tried to take administrative measures caused the stock market up to5years of irrational fall, which almost resulted in the Chinese security marketretrograding to the start again; April2005after the quiet years of the securities market,the market was activated by the equity division reform. Investors with greatenthusiasm created one of the largest carnival in the securities market of China. Bythe end of2007when the equity divison reform completed, the Shanghai CompositeIndex was soaring from the lowest points of998up to a maximum of6124points.However, good times did not last long. The share market in China experienced moreintense fall and jump again entering a bear market. Although experienced externalshocks of United States sub-loan crisis which led to the global financial crisis and thedebt crisis, China economy still maintained high growth level. At the end of2011,when the GDP of our country grew from less than RMB10trillion ten years ago tonearly40trillion and the listed companies increased from the1073growth to2300,the Shanghai Composite Index fell back to the points ten years ago. After Carefullyobserved the index and stock volatility, the secondary market investors found thatbesides the fundamental factors of corporate, there was a noticeable new forces,namely with the full circulation times came true, the non-tradable stockholders andcompany’s high executives fiercely sold their shares, and the point was that the timemajor shareholders reduced the stocks occured frequently when good informationrelease or before the bad information out, and the holdings of shares was oftenaccompanied by subsequent good information. Even in order to avoid reduction ofshare system constraints, large number of executives quit their jobs. Then with thedramatic transformation of market style, the stock market speculation was popularagain. The large blue chip companies with good corporate governance and stableprofits was abandoned by investors, on the other hand, short-term trend tradingbecame the best ways to make profits and evade risk, and the public and privateequity funds aimed at long-term investment value were often recognized as theobjects of satire as a result of the poor performance. A large number of secondaryshare market’s investors reckoned the reform of equity division neither brought a fairand effective market nor realized the win-win situation between the minorityshareholders and majority shareholders, therefore they lost the confidence of stockmarket and required the authorities to adopt a new system reform.
At present, China's regulatory authorities and institution scholars do not haveobvious differences on all sorts of problems of China's securities market and therelated policy suggestions also appears to be highly consistent. The capital market ofour country is emerging in the immature market, implementing market-orientedsystem construction is to establish a perfect and effective capital market gradualprocess, which take some time to move toward maturity gradually. In principle, thisarticle is not dissent this conclusion, however under the condition of no overallsystem arrangement such as lack of effective restriction of insider informationexchange in our share market, partially improving the reform measures often fail torealize the goals. Although the equity division historically solve the chinese capital onthe market with different stock price, and legal person shares non-circulationproblems, compared to the legal person share non-circulation time, the non-tradableshares converted into conditional shares also created a system is expected to be moreclear the insiders. These internal traders hold absolute majority of proportion ofcirculation stock’s market value, and compared with outside investors naturally theyhave internal information advantages. Due to the limitation of current stock in certainperiod will be gradually circulated, besides state-owned must hold the controllingright, a large number of non-state-owned controlling shareholders create highreduction opportunities or manipulate stock price fluctuations high possibilities,which may be the cause the chaos phenomenon after a series of reformation ofChina's securities market. To find out this proposition, there are two deepen researchdirections, the first one is to test whether under the condition of lack of restrictionmechanism, the existence of internal traders will lead to capital market chaos furthermore outstanding; the other one is how to make a further supporting system reform,which may effectively eliminate the institutional formed and clear expected profitreturn internal traders. Apparently the first research direction is to search the crux tosolve the basis of proposition, so this paper chooses it as the breakthrough, namelyverifying the correlation of internal transactions and the stock market rises and falls,and the effect of internal transactions of securities market operation for the innermechanism. This paper try to start the research work from a new perspective, and usethe new financial theory frame which is different from traditional classical andeffective market theory. That is through the theoretical description of the differenttypes of investors’ behavior in China's stock market to analize all kinds of investorspursuing the maximal profit when its investment behavior and groups changed, andfinally inference the internal reason of excessive volatility of our share market. Thispaper's reasoning process is divided into several parts: a brief review of the marketfrom effective static linear theory to the nonlinear dynamic model chaotic markettheoretical paradigm shift, and on China securities market research significance ofChinese characteristics; By using the chaos theory to verify the nonlinearcharacteristics of China securities market and the change of market characteristic before and after equity division reform; Constructing China's securities marketnonlinear model of heterogeneity investors; According model test of therepresentative behavior of investors, the endogenous mechanism of the Chinesesecurities market price fluctuation is verified.
After1970years, efficient market theory (EMH) has long time dominated thetheory research of financial economics. Effective market core meaning is that assetprice change fully reflects the market information, asset prices is the externalperformance of the intrinsic value. In the short term, the external random factorscaused volatility of the asset prices is unpredictable; Shares’ deviation in thelong-term will return to the fundamental value of the mean economics. The level ofrisk assets can be measured by fluctuations in the price variance; the normaldistribution statistical of the assets’ present price of time series strongly support thecapital market system effectiveness and risk control. And the existing conditions ofthe above all can be controlled is that the stock market investors are rational.Effective market theory since it becomes the rule has been suspected and challenged.First of all because. Jordan Fama (Fama,1965) found the famous Fat-tailphenomenon, Sterge (Sterge,1989). Turner (Turner) and Weigel (Weigel,1990)confirmed the Fat-tail phenomenon is far from occasional, and the local commonphenomenon. With the development of research, economists in small company effectgradually. Scale premium. With the development of research, economists define andreveal the economical meaning of Fat-tail phenomenon though the small companyeffect, Scale premium, Value premium, Persistence characteristics and excessivevolatility and the cluster of volatility of the stock price. Small probability events of‘Black Swan’ phenomenon in the Asian financial crisis caused extensive dominoeffect, and in2008the subprime crisis caused the global financial crisis, are furtherprove that the Fat-tail phenomenon produced the destructive power in reality isdifficult to discover and can not be controlled.
Shiller (1981,1984,1987) revealed the intrinsic link between the non-rationalinvestment behavior and a peak fat-tail phenomenon, that is when the most investorshave cognitive biases in investment decision-making, their behavior willsystematically deviate from economic rationality, which could cause the financialmarket deviating from the effectiveness strikingly for a long time, resulting in theturmoil or crisis in financial market. Shefrin(2000) described that the investors relyon simple and habitual method and experience to make their investment decisionswith the limited rational hypotheses; Thaler put forward quasi-rationaliyt, thisconcept analyzed some emotions, such as over self-confidence and overreaction willlead to noncompletely rational behavior. Obviously, if investors are irrational,different types of investors would constitute decentralized and conflicting investmentactivities, at the same time, the market feature is fractal and the volatility of themarket is not linear but chaotic. Years ago these concepts are very unorthodox, nowadays there is a relatively perfect fractal market theory and a model of chaoticmarket theory. Because non-rational investors are heterogeneous groups, when theyare in the same market facing the same information, Some of them will have aexcessive investment response due to yield, while the others have nothing to do.Assumption that the proportion of investors who believe that this information hassignificant effect on investment income are higher, the result would be an unevenmarket, even if this information has little effect on investment income actually.Conversely, when most of them believe the information has no effect on investmentincome, the market's response to the information would be delayed. Real question iswhen the effect is greater than the estimate in advance, investors will turn to overreact,which also can cause slump and boom. Further analysis showed that the overreactingand the delayed response are just intermediate state. In the real liquidity capitalmarket, the distance between overreaction and delayed response is only an investor'sidea.
In a word, when economists free themselves of the thought that the price volatilityis the response of complete information, the real world they can see is, the pricefluctuation for the information is nonlinear, while the asset price change no longerfollow the process of random walk, so the typical characteristic of capital market ischaos. Furthermore, sensitive to initial conditions, non-cyclical and boundedness arewidespread phenomenons in capital markets. Since it is impossible to change thisnature of the market, what we can do to reduce the loss is only understanding thesefeatures.
The paper adopts Fractal Theory and Chaos Theory to do the empirical research onthe securities market in China, proves that our securities market has the classicalcharacteristics of fractal market and price fluctuation is characterized by chaosobviously, and further verifies that non-linear characteristics of our securities markethave been more obvious since the reform of equity division. According to the resultsof the empirical test, we can see that the characteristic of Chinese securities market isthat it has more obvious fractal market and chaos properties by comparing withmature capital market of developed countries. The paper studies on properties offractal market and internal mechanism of chaotic fluctuation of capital prices on thisbasis.
Firstly, it uses the comprehensive indexes which have been established byShanghai Stock Exchange and Shenzhen Stock Exchange for two decades and thetotal TTM price-to-earnings ratio as targets, undertakes the non-liner characteristictest on price fluctuation of our securities market and fluctuation of stock pricescorresponding to basic values, and confirms that fluctuation of comprehensiveindexes and stock prices deviating from internal values in our securities market hasthe classical chaos characteristic. China’s securities market has the characteristics including fractal market, random walk of price fluctuation, acyclic period andlong-term unpredictability of stock prices.
Secondly, inspection results of non-liner dynamic model on dynamicprice-to-earnings ratio fluctuation nature show that heterogeneous traders’ dynamicexpectation on future income discount of asset is characterized by chaos, whichconstitutes the chaos characteristic of asset price fluctuation. Proving the importantindication significance of this internal cause and effect relationship on the research ondevelopment of China’s securities market lies in the fact that study on acts ofheterogeneous investment according to irrational logic is the key to understandexcessive fluctuation of our securities market.
Thirdly, the relevant study on fractal market is based on classification ofheterogeneous investors. Although we can divide heterogeneous investors accordingto different classification methods in the theoretical study, the standard of judgingwhether classification is reasonable is whether investment act is defined moreaccurately which can be observed in certain period and has classical significance;meanwhile, whether statistical indexes which reflect this investment act effectivelycan be obtained is the important basis of classification. In the study works, we canclassify our securities investors as follows: the first type is insider information traderswho are criticized severely in China’s securities market, they trade by graspinginformation which isn’t publicized but has important influence on basic values ofstocks, and the classical representatives are large and small part of non-tradableshareholders, market makers and a few funds etc.; the second type is basic valuetraders, i.e. rational traders, who trade by judging basic values of stocks according topublic information, and the classical representatives are some privately offered funds,public offer funds and a few common investors; however, position traders, who canbe called as limitedly rational icon traders (including positive feedback traders andnegative feedback traders), who trade according to changing tendency of marketprices of stocks, and the classical representatives are most of common investors andsome company-offered funds.
Fourthly, investment acts of the three different investors differ greatly, changes ofweight combination will make our securities market have different fluctuationmechanisms. Special attention shall be paid to mutual influence of acts of the threetypes of investors, and small changes of primitive conditions lead to enormous chaosphenomena of market fluctuation. Although we cannot know whether daily marketprices of stocks deviate from real prices of stocks in modern stock market, we knowthere are losing and winning investors; the three types of investors have differentdaily, monthly and yearly investment incomes, which form study process, moreaccurately, that is switching process of investment acts. For example, rationalinvestors hear that more people make profits by relying on insider information, andthey might give up choices of rational investment. However, changing investment act needs to pay costs, which are highly related to establishment of securities marketmechanism, and maturity of investors, and high switching cost makes impossibility ofswitching like a high threshold. For example, obtaining insider information needscosts, basic value traders must receive good education, they shall pay fees ofinformation collection and processing undoubtedly, costs paid by position tradersaren’t low, analyzing stock price trend chart needs knowledge of statistics and a lot oftuition in the market. In market of low-cost and prevailing insider trading, manyconditional investors will undertake low-risk and large-profit insider trading; andother common investors will predict implied insider information according totechnical indexes such as price variations and volume rate changes. The collectiveswitching act will change dynamic proportion to be invested by the whole society,and cause social market timing operation. Excessive reaction and slow switching ofinformation will become quicker, feedback trades become stronger because of stockprice changes, and special phenomenon of large price movement is formed in ourcapital market. To sum up theoretically, we can define it as dynamic chaos processthat investor acts cause non-linear fluctuation of capital prices and fluctuation ofcapital prices affects investor acts, which is two-way interactive attack. During theprocess, structural change of investors has the core internal influence on evolutionlevel (dynamic price-to-earnings ratio) of capital market and fluctuation of capitalprices or it is the internal factor for the making and development of the capital marketin China.
Lastly, the relevant study on the chaos phenomena caused by random perturbationbetween heterogeneous investor acts and interactive acts in the micro-structure of ourcapital market explains that the starting point is excellent in the market reform of oursecurities market systems, but relevant imperfect supporting systems will formtortured micro-structure of market systematically, and lead to more chaotic marketwhich is effective irrationally. The conclusion of the study has an importantsignificance on the establishment of future systems of our capital market.
引文
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