| With the continuous development of the economy and the steady accumulation of people’s wealth, Investment has gradually become the main way to maintain and increase the value of assets, against inflation. For the majority of investors, how to ensure access to certain benefits at the level of less risk or higher-yielding at a certain level of risk has become a question that every investor needs to be carefully considering. Modern portfolio theory is mainly to help investors solve the problem how to choose the assets and configure the right to them.1952, Markowitz portfolio theory is established. He used mean to measure income and used variance to measure risk, which established the mean-variance model (MV model). Then scholars start to propose some new, alternative variance risk measurement indexes.1990s, J.P Morgan uses VaR (Value-at-Risk) index, showing the level of risk faced by the portfolio at a certain level of confidence. VaR has good statistical properties, but it does not meet the times of additive. As the improvement of VaR, Rockafellar and Uryasev proposed CVaR (Conditional Value-at-Risk) concept, and used it as a risk measure to establish optimization model of portfolio. Getting CVaR is extremely complex. Krokhmal et al transformed the CVaR portfolio model into a linear programming model through linearization, discretization operation, which is easy to solve. But it requires the future stock return in portfolio as the model input. Clustering is a process that takes a set of physical or abstract objects into a number of classes. Clusters generated by clustering are a set of data objects, which are similar to the objects in the same cluster, and are different from the objects in other clusters. Traditional simulation methods take each asset return scenario probability as equal, which is clearly inconsistent with the reality. Using the K-means clustering method to generate the future yield of each stock in the portfolio can get the probability of the occurrence of various scenarios. With the cross development of different disciplines, the concept of the entropy and generalized entropy in the physical heat have begun to appear in the portfolio model analysis. In physics, the greater the entropy, the greater the uncertainty, application in the portfolio can show the degree of correlation between the portfolio of assets, then entropy can be used as a measure of the degree of dispersion of the assets in the portfolio.This paper constructs the C VaR linear programming model of portfolio with the constraint of generalized entropy. Positive aspects, this paper selected eight Shenzhen stocks portfolio as empirical analysis, which from January 1st,1998 to December 31st,2013. Accordingly we calculate each stock’s logarithmic rate of return data. According to these data, we use SPSS software based on the idea of K-means clustering to generate the yield of the stock of the 250 scenarios, the corresponding yield matrix and the corresponding probability matrix. Substituting them into the model constructed in this paper and compared with MV model, we find that this model can not only reflect more decentralized investment principle, but also perform better in the future yields, which has strong practicability. |
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