情绪投资组合研究
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摘要
行为金融学主要通过分析金融市场主体在市场行为中的偏差和信念来寻求不同市场主体在不同环境下的经验理论及决策行为特征，力求建立一种能正确反映市场主体实际决策行为和市场运行状况的描述性模型。一方面，已有的行为金融研究大多基于投资者偏差，这些模型往往只关注各种市场异常现象的单独确认和异常解释，从而造成了现有模型的分散、无逻辑和内涵模糊问题。另一方面，通过分析投资者的信念来讨论行为金融模型构建的研究还较为少见。而作为投资者信念重要表征的投资者情绪可以综合体现多种心理、行为偏差，这为基于投资者情绪建立更为统一有效的行为金融理论提供了可能。但是，在投资组合领域，如何基于投资者情绪对投资组合进行分析仍是学术界尚未解决的难题。
本文基于投资者情绪分析投资组合的构建问题，利用数理推导、数值分析及实证研究，讨论不同条件下投资者情绪对投资者构建投资组合的影响，并进一步利用本文构建的模型从投资者情绪的角度对风险分散不足、本地偏好等多种市场异象进行有效解释。本文主要创新点包括如下三个方面：
第一，构建了不同资产、不同市场的投资者情绪指标。首先，基于个股交易高频数据计算了BSI变量，并结合换手率等其它个股情绪代理变量采用主成分分析的方法构建了个股情绪复合指标；同时，采用面板数据分析讨论了个股情绪对个股收益的影响；其次，基于高频交易数据构建了股指期货市场投资者情绪，并且进一步通过GJR-GARCH模型分析了股指期货市场投资者情绪对股指期货各合约影响的日内效应。通过本文构建的股票市场个股情绪及股指期货市场情绪表明，投资者对不同资产有着不同的情绪，并且该情绪是影响资产表现的系统性因素。这正是本文基于不同资产投资者情绪建立情绪影响矩阵并进一步构建投资组合模型的出发点，同时为从投资者情绪角度对投资组合理论探讨的可行性提供支持。
第二，基于投资者对不同资产有着不同的投资者情绪，讨论了投资者情绪影响下的投资组合构建问题。本文分别分析了投资者情绪对风险厌恶系数、认知收益和认知风险的影响，并由此探讨了投资者情绪对投资组合的影响。然后，本文更深入探讨了非对称风险度量下基于投资者情绪的投资组合构建问题，以及二元情绪(单一资产情绪与整体市场情绪)影响下的投资组合构建问题。表明了投资者情绪是影响投资组合构建的重要系统性因素：投资者情绪影响着投资者从候选资产中选择出拟投资资产，并且投资者投资于某资产的投资比例随着投资者对该资产的情绪高涨而增加；投资组合的有效边界随着投资者情绪的高涨而扩张；当不考虑资产相关性时，在非对称风险度量下的情绪投资组合是与平均分配原则(1/n法则)基本一致的。
第三，通过对基于情绪认知的投资组合进一步分析，建立了情绪资本资产定价模型。本文构建的情绪资本资产定价模型表明投资者情绪是资产定价的重要系统因子。但是，资产价格并不是投资者情绪的单调增函数，存在投资者情绪的两个临界值S BT和S LT(其中S BT大于S LT)，使得资产价格随投资者情绪的变化呈现出如下两种可能：(1)当投资者情绪大于临界值S BT时，投资者对资产的定价随着情绪的高涨反而下跌；当投资者情绪小于临界值S BT时，投资者对资产的定价随着情绪的高涨而上涨；(2)当投资者情绪大于临界值S BT时，投资者对资产的定价随着情绪的高涨反而下跌；当投资者情绪小于临界值S BT且大于临界值S LT时，投资者对资产的定价随着情绪的高涨而上升、随着情绪的低落而下跌；如果投资者情绪小于临界值S LT，投资者对资产的定价随着情绪的低落反而上涨。
Behavioral finance seeks the empirical theory and the decision-making behaviorcharacteristics of difference market entities in different environment by analysis the entities’biases and beliefs, and trys to construct descriptive models which can reflect the practicaldecision-making behavior and market operation condition of market entities. On the one hand,the existing behavioral finance models are mostly based on the biases of investors, and onlypay attention to the independent confirmation and interpretation of anomaly. All that causesthe existing models to become no logic and the indistinct connotation. On the other hand,there is few scholars study the building of behavioral finance model by analyzing the investorbelief. And investor sentiment as a characterization of belief can reflect multiple biases of theinvestor, which provides the possibility for building a useful behavioral finance theory. Inparticular, in the portfolio field of academia, it is the problem to be solved how to analyze theportfolio theory based on the investor sentiment.
In this paper, the analyses based on investor sentiment are applied to construct portfoliomodel. Then the mathematical derivation, simulation analysis and empirical research are usedto discuss the impact of investor sentiment on the constructing of portfolio model. And theeffective interpretations of the market anomalies such as: lack of diversification and homebias, are given by our models.
The main innovations are listed in the following three aspects:
First, the indexes of investor sentiment about different markets and different assets areconstructed. On the one hand, we calculate the BSI by using the high frequency trading dataof the individual stock, and then combine with other stock variables such as turnover to builda composite index of individual stock by principal component analysis. And we also discussthe individual stock sentiment impact on individual stock return. On the other hand, weconstruct an index of investor sentiment of the stock index futures market based on highfrequency trading data. And we discuss the daily effects of investor sentiment with the fourstock index futures contract further more. The indexes of investor sentiment in stock indexfutures market and individual stock which we constructed show that investor have thedifferent sentiments for different assets. This is exactly the starting point which we build portfolio model by different assets’ sentiment, and simultaneously support feasibility study ofportfolio theory from investor’s belief.
Second, we discuss portfolio selection problem under the influence of sentiment.Specifically speaking, the sentiment perceived coefficient of risk aversion, the sentimentperceived return and the sentiment perceived risk are discussed. And the portfolio selectionmodels are built after the discussion. Then under the asymmetric risk measurement, we yieldvaluable insights into the portfolio selection problem based on the investor sentiment. Afterthat, a new portfolio selection model is given about the dual sentiment which consists of thesentiment about sole asset and the sentiment about the whole market sentiment. The mainresults show that investor sentiment is a predominant influence in the portfolio constructionprocess. The selection process about the assets to be investing from the candidate assets isinfluenced by investor sentiment. And the investing of an asset is monotone increasing by thesentiment. When sentiment is high, the efficient frontier of the portfolio is expanded. Andwhen the correlations of the assets are ignored, the sentiment-based portfolio under theasymmetric risk measurement is the same as the1/n rule.
Third, we establish the sentiment-based capital asset pricing model by the intensive studyof the sentiment-based portfolio model. In the asset pricing model, we show that sentiment isthe key factor in the process of asset pricing. But the asset pricing isn’t themonotone-increasing function of the sentiment. There are two critical valuesS BTandS LT(whereS BTis greater thanS LT) which lead to the two kinds of cases as follows:(1) Whensentiment is greater thanS BT, the asset price is monotone decreasing of the sentiment. Andwhen sentiment is lesser thanS BT, the asset price is monotone increasing of the sentiment.(2)When sentiment is greater thanS BT, the asset price is monotone decreasing of the sentiment.When sentiment is lesser thanS BTand greater thanS LT, the asset price is monotoneincreasing of the sentiment. And when sentiment is lesser thanS LT, the asset price ismonotone decreasing of the sentiment.
本文基于投资者情绪分析投资组合的构建问题，利用数理推导、数值分析及实证研究，讨论不同条件下投资者情绪对投资者构建投资组合的影响，并进一步利用本文构建的模型从投资者情绪的角度对风险分散不足、本地偏好等多种市场异象进行有效解释。本文主要创新点包括如下三个方面：
第一，构建了不同资产、不同市场的投资者情绪指标。首先，基于个股交易高频数据计算了BSI变量，并结合换手率等其它个股情绪代理变量采用主成分分析的方法构建了个股情绪复合指标；同时，采用面板数据分析讨论了个股情绪对个股收益的影响；其次，基于高频交易数据构建了股指期货市场投资者情绪，并且进一步通过GJR-GARCH模型分析了股指期货市场投资者情绪对股指期货各合约影响的日内效应。通过本文构建的股票市场个股情绪及股指期货市场情绪表明，投资者对不同资产有着不同的情绪，并且该情绪是影响资产表现的系统性因素。这正是本文基于不同资产投资者情绪建立情绪影响矩阵并进一步构建投资组合模型的出发点，同时为从投资者情绪角度对投资组合理论探讨的可行性提供支持。
第二，基于投资者对不同资产有着不同的投资者情绪，讨论了投资者情绪影响下的投资组合构建问题。本文分别分析了投资者情绪对风险厌恶系数、认知收益和认知风险的影响，并由此探讨了投资者情绪对投资组合的影响。然后，本文更深入探讨了非对称风险度量下基于投资者情绪的投资组合构建问题，以及二元情绪(单一资产情绪与整体市场情绪)影响下的投资组合构建问题。表明了投资者情绪是影响投资组合构建的重要系统性因素：投资者情绪影响着投资者从候选资产中选择出拟投资资产，并且投资者投资于某资产的投资比例随着投资者对该资产的情绪高涨而增加；投资组合的有效边界随着投资者情绪的高涨而扩张；当不考虑资产相关性时，在非对称风险度量下的情绪投资组合是与平均分配原则(1/n法则)基本一致的。
第三，通过对基于情绪认知的投资组合进一步分析，建立了情绪资本资产定价模型。本文构建的情绪资本资产定价模型表明投资者情绪是资产定价的重要系统因子。但是，资产价格并不是投资者情绪的单调增函数，存在投资者情绪的两个临界值S BT和S LT(其中S BT大于S LT)，使得资产价格随投资者情绪的变化呈现出如下两种可能：(1)当投资者情绪大于临界值S BT时，投资者对资产的定价随着情绪的高涨反而下跌；当投资者情绪小于临界值S BT时，投资者对资产的定价随着情绪的高涨而上涨；(2)当投资者情绪大于临界值S BT时，投资者对资产的定价随着情绪的高涨反而下跌；当投资者情绪小于临界值S BT且大于临界值S LT时，投资者对资产的定价随着情绪的高涨而上升、随着情绪的低落而下跌；如果投资者情绪小于临界值S LT，投资者对资产的定价随着情绪的低落反而上涨。
Behavioral finance seeks the empirical theory and the decision-making behaviorcharacteristics of difference market entities in different environment by analysis the entities’biases and beliefs, and trys to construct descriptive models which can reflect the practicaldecision-making behavior and market operation condition of market entities. On the one hand,the existing behavioral finance models are mostly based on the biases of investors, and onlypay attention to the independent confirmation and interpretation of anomaly. All that causesthe existing models to become no logic and the indistinct connotation. On the other hand,there is few scholars study the building of behavioral finance model by analyzing the investorbelief. And investor sentiment as a characterization of belief can reflect multiple biases of theinvestor, which provides the possibility for building a useful behavioral finance theory. Inparticular, in the portfolio field of academia, it is the problem to be solved how to analyze theportfolio theory based on the investor sentiment.
In this paper, the analyses based on investor sentiment are applied to construct portfoliomodel. Then the mathematical derivation, simulation analysis and empirical research are usedto discuss the impact of investor sentiment on the constructing of portfolio model. And theeffective interpretations of the market anomalies such as: lack of diversification and homebias, are given by our models.
The main innovations are listed in the following three aspects:
First, the indexes of investor sentiment about different markets and different assets areconstructed. On the one hand, we calculate the BSI by using the high frequency trading dataof the individual stock, and then combine with other stock variables such as turnover to builda composite index of individual stock by principal component analysis. And we also discussthe individual stock sentiment impact on individual stock return. On the other hand, weconstruct an index of investor sentiment of the stock index futures market based on highfrequency trading data. And we discuss the daily effects of investor sentiment with the fourstock index futures contract further more. The indexes of investor sentiment in stock indexfutures market and individual stock which we constructed show that investor have thedifferent sentiments for different assets. This is exactly the starting point which we build portfolio model by different assets’ sentiment, and simultaneously support feasibility study ofportfolio theory from investor’s belief.
Second, we discuss portfolio selection problem under the influence of sentiment.Specifically speaking, the sentiment perceived coefficient of risk aversion, the sentimentperceived return and the sentiment perceived risk are discussed. And the portfolio selectionmodels are built after the discussion. Then under the asymmetric risk measurement, we yieldvaluable insights into the portfolio selection problem based on the investor sentiment. Afterthat, a new portfolio selection model is given about the dual sentiment which consists of thesentiment about sole asset and the sentiment about the whole market sentiment. The mainresults show that investor sentiment is a predominant influence in the portfolio constructionprocess. The selection process about the assets to be investing from the candidate assets isinfluenced by investor sentiment. And the investing of an asset is monotone increasing by thesentiment. When sentiment is high, the efficient frontier of the portfolio is expanded. Andwhen the correlations of the assets are ignored, the sentiment-based portfolio under theasymmetric risk measurement is the same as the1/n rule.
Third, we establish the sentiment-based capital asset pricing model by the intensive studyof the sentiment-based portfolio model. In the asset pricing model, we show that sentiment isthe key factor in the process of asset pricing. But the asset pricing isn’t themonotone-increasing function of the sentiment. There are two critical valuesS BTandS LT(whereS BTis greater thanS LT) which lead to the two kinds of cases as follows:(1) Whensentiment is greater thanS BT, the asset price is monotone decreasing of the sentiment. Andwhen sentiment is lesser thanS BT, the asset price is monotone increasing of the sentiment.(2)When sentiment is greater thanS BT, the asset price is monotone decreasing of the sentiment.When sentiment is lesser thanS BTand greater thanS LT, the asset price is monotoneincreasing of the sentiment. And when sentiment is lesser thanS LT, the asset price ismonotone decreasing of the sentiment.
引文
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