Sentiment-based Portfolio Theory

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.