Traditionally, the measure of risk used in portfolio optimisation models is the variance. However, alternative measures of risk have many theoretical and practical advantages and it is peculiar therefore that they are not used more frequently. This may be because of the difficulty in deciding which measure of risk is best and any attempt to compare different risk measures may be a futile exercise until a common risk measure can be identified. To overcome this, another approach is considered, comparing the portfolio holdings produced by different risk measures, rather than the risk return trade‐off. In this way we can see whether the risk measures used produce asset allocations that are essentially the same or very different. The results indicate that the portfolio compositions produced by different risk measures vary quite markedly from measure to measure. These findings have a practical consequence for the investor or fund manager because they suggest that the choice of model depends very much on the individual's attitude to risk rather than any theoretical and/or practical advantages of one model over another.

Different Risk Measures: Different Portfolio Compositions?

For multi-attribute decision-making problems with interval numbers whose attribute weights are completely unknown, it is difficult to compare the value of interval numbers. So this paper proposes a method based on TOPSIS and the weighted parameter to deal with it. Firstly, this paper transforms the interval number matrix into two exact number matrices which reduces sorting complexity. Secondly, a parameter is given when determining the weights with entropy weight in order to reflect all the information of the interval numbers. Then TOPSIS is used to determine the order of each scheme. In addition, the average value of the ranking number is used to reflect the actual situation better. Finally, the analysis of the car purchase case shows the proposed method is feasible and practical. And the comparative analysis with the other method based on practical application dataset demonstrates the proposed method is stable and effective. 

Interval number multi-attribute decision-making method based on TOPSIS

For multi-attribute decision-making problems with interval numbers whose attribute weights are completely unknown, it is difficult to compare the value of interval numbers. So this paper proposes a method based on TOPSIS and the weighted parameter to deal with it. Firstly, this paper transforms the interval number matrix into two exact number matrices which reduces sorting complexity. Secondly, a parameter is given when determining the weights with entropy weight in order to reflect all the information of the interval numbers. Then TOPSIS is used to determine the order of each scheme. In addition, the average value of the ranking number is used to reflect the actual situation better. Finally, the analysis of the car purchase case shows the proposed method is feasible and practical. And the comparative analysis with the other method based on practical application dataset demonstrates the proposed method is stable and effective.

In recent years, fuzzy set theory and possibility theory have been widely used to deal with an uncertain decision environment characterized by vagueness and ambiguity in the financial market. Considering that the expected return rate of investors may not be a fixed real number but can be an interval number, this paper establishes an interval-valued possibilistic mean-variance portfolio selection model. In this model, the return rate of assets is regarded as a fuzzy number, and the expected return rate of assets is measured by the interval-valued possibilistic mean of fuzzy numbers. Therefore, the possibilistic portfolio selection model is transformed into an interval-valued optimization model. The optimal solution of the model is obtained by using the order relations of interval numbers. Finally, a numerical example is given. Through the numerical example, it is shown that, when compared with the traditional possibilistic model, the proposed model has more constraints and can better reflect investor psychology. It is an extension of the traditional possibilistic model and offers greater flexibility in reflecting investor expectations.

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A Mean-Variance Portfolio Selection Model with Interval-Valued Possibility Measures

Synergy between Stock Prices and Investor Sentiment in Social Media

Investor sentiment is a hot topic in behavioral finance. How to measure investor sentiment? Is the influence of investor sentiment on the stock market symmetrical? That is all we need to think about. Therefore, this paper firstly selects five emotional proxy variables and constructs an investor sentiment composite index by principal component analysis. Secondly, the MS-VAR model is employed to study the dynamic relationship among investor sentiment, stock market returns, and volatility. Using the model MSIH (2)-VAR (2), we found that the relationship among the investor sentiment, stock returns, and volatility is different in different regimes. The results of orthogonal cumulative impulse response analysis showed that the shock to investor sentiment has a significant impact on stock market returns, and this impact in the bullish stock market is significantly higher than in the bearish stock market. The impact of the shock to stock market returns on investor sentiment and stock market volatility is relatively significant. The shock to stock market volatility has significant effects on the stock market returns. Overall, the influence of investor sentiment on the stock market is asymmetric; that is, in different regimes of the stock market, the impact of investor sentiment on the stock market is different. Realizing this, investors can better understand and grasp the market, guiding their own investment behavior. Other researchers can also further study the measurement of investor sentiment on this basis to better guide investors’ behavior.

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The Measurement Method of Investor Sentiment and Its Relationship with Stock Market

Investors are concerned about the reliability and safety of their capital, especially its liquidity, when investing. This paper sets up a possibilistic portfolio selection model with liquidity constraint. In this model, the asset return and liquidity are fuzzy variables which follow the normal possibility distributions. Liquidity is measured as the turnover rate of the asset. On the basis of possibility theory, we transform the model into a quadratic programming problem to obtain its solution. We illustrate that, in the process of investment, investors can make better use of capital by choosing their investment portfolios according to their expected return and asset liquidity.

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A Possibilistic Portfolio Model with Fuzzy Liquidity Constraint

Traditional portfolio theory uses probability theory to analyze the uncertainty of financial market. The assets’ return in a portfolio is regarded as a random variable which follows a certain probability distribution. However, it is difficult to estimate the assets return in the real financial market, so the interval distribution of asset return can be estimated according to the relevant suggestions of experts and decision makers, that is, the interval number is used to describe the distribution of asset return. Therefore, this paper establishes a portfolio selection model based on the interval number. In this model, the semiabsolute deviation risk function is used to measure the portfolio’s risk, and the solution of the model is obtained by using the order relation of the interval number. At the same time, a satisfactory solution of the model is obtained by using the concept of acceptability of the interval number. Finally, an example is given to illustrate the practicability of the model.

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Fang Ma

Papers

The Measurement Method of Investor Sentiment and Its Relationship with Stock Market

A Possibilistic Portfolio Model with Fuzzy Liquidity Constraint

A Mean-Variance Portfolio Selection Model with Interval-Valued Possibility Measures

A Portfolio Selection Model Based on the Interval Number