基于熵改进的证券投资组合模型

发布时间：2018-01-21 11:49

本文关键词： 投资组合均值方差模型单指数模型熵　出处：《天津财经大学》2012年硕士论文　论文类型：学位论文

【摘要】：经济全球化和金融一体化给各国的投资市场带来前所未有的机遇的同时,投资风险也在随之悄然增长。在这种复杂的金融背景下,如何增强自身抵御市场波动的能力,获取较稳定的收益,其根源在于使用合理的方式捕捉市场波动的规律,准确的度量投资中的风险。近年来迅速发展的墒理论,凭借其无需对分布做任何假设和可以表达变量多阶矩的独特性质,在众多的投资组合风险度量方法中,受到越来越多的关注和应用。本文在马柯维茨均值——方差模型上,借鉴威廉夏普的单指数模型对风险分解的思想,将熵理论引入投资组合模型。依据熵的性质将其分解为互信息熵和条件信息熵,分别用单个股票的互信息熵代表系统风险,单个股票的条件信息熵代表非系统风险。利用单指数模型中β系数的内涵,对互信息墒进行加权,使单个股票之间的熵具有可加性进而构造投资组合的熵,作为投资组合的风险度量,建立了基于熵的投资组合模型,给投资者提供一种新的决策方式。在此基础上,本文选取上证50中表现较好的股票作为分析样本,使用新模型来构筑投资组合,并对比熵和方差在度量风险上的异同,得出了这两种方式在衡量风险大小上具有基本一致性的结论。同时,对比了新模型与传统均值——方差模型的有效前沿和投资比例,以验证新模型的有效性。研究结果表明,在投资者期望收益率相同的情况下新模型的投资组合策略较之均值——方差模型更为简洁,新模型只需为投资者提供较少的证券投资数量,就可达到与传统均值——方差模型同样的效果,这不仅节约了过度分散化给投资者带来的交易费用和管理费用,而且也节省了信息资源,增强了投资者对信息的处理能力。
[Abstract]:Economic globalization and financial integration have brought unprecedented opportunities to the investment markets of various countries, while investment risks are also quietly increasing. In this complex financial background. How to enhance their ability to resist market fluctuations and obtain more stable returns is rooted in the use of a reasonable way to capture the laws of market volatility. In recent years, the theory of soil moisture, which has developed rapidly in recent years, has been widely used in portfolio risk measurement, because it does not need to make any assumptions about distribution and can express the unique properties of multi-order moments of variables. By more and more attention and application. Based on the Markowitz mean-variance model, this paper uses William Sharp's single-index model for risk decomposition. The entropy theory is introduced into the portfolio model, which is decomposed into mutual information entropy and conditional information entropy according to the properties of entropy, and the mutual information entropy of a single stock is used to represent the system risk. The conditional information entropy of a single stock represents the non-systematic risk. By using the connotation of 尾 coefficient in the single index model, the mutual information information is weighted to make the entropy of a single stock additive and then construct the entropy of the investment portfolio. As a measure of portfolio risk, a portfolio model based on entropy is established, which provides a new way for investors to make decisions. On this basis, this paper selects the better performance of Shanghai Stock Exchange 50 stock as the analysis sample, uses the new model to construct the portfolio, and compares the similarities and differences of entropy and variance in measuring risk. At the same time, the effective frontier and investment ratio of the new model and the traditional mean-variance model are compared. In order to verify the validity of the new model, the results show that the portfolio strategy of the new model is more concise than the mean-variance model when investors expect the same rate of return. The new model can achieve the same effect as the traditional mean-variance model by providing investors with a small amount of securities investment, which not only saves the transaction costs and management costs brought to investors by excessive decentralization. It also saves information resources and enhances the ability of investors to deal with information.
【学位授予单位】：天津财经大学
【学位级别】：硕士
【学位授予年份】：2012
【分类号】：F224;F830.91

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