优证券投资组合模型的构建及风险分析 最初的投资者进行投资时仅仅要求获得更高的利益，并不注重市场的风险状况，但是当下投资风险情况越来越复杂，稍有不慎就可能倾家荡产，于是投资者就开始在规避风险的前提下获得更多的利益。而如何有效的规避风险也成了当下热议的话题。基于此，本文依照几类模型去讨论风险与收益的关系，建立适合中国市场的最优投资组合。由于中国市场限制卖空，而且人们投资时也会选择收益稳定的产品即无风险资产，这两种情况就作为本文的约束条件。因此本文以投资价值估值标准，随机选取20只股票，引入了均值-方差模型、均值-VAR模型，并在模型中加入两类条件，利用MATLAB编程解决二次规划问题，解出来每个模型所对应的最优权重。接着对各模型进行比较得出结论：利用时间加权历史模拟法的均值-VAR模型最优。随后在该方法下，建立最优证券投资组合。最后，讨论了投资组合中股票数目以及预期收益对组合的影响，得出结论：组合为17只股票时最优，且高收益高风险，预期收益与风险成正比。其他投资者则可以参考研究过程，根据自身的投资风格以及风险偏好，建立适合自己的投资组合。 关键词：均值-方差模型；均值-VAR模型；证券投资组合；二次规划 The construction and risk analysis of the optimal portfolio model of securities ABSTRACT At the beginning, investors only asked for higher profits and did not pay attention to the risk situation of the market. However, the current investment risk situation is becoming more and more complex, and a slight mistake may lead to ruin. Therefore, investors begin to gain more benefits on the premise of avoiding risks. And how to effectively avoid risk has become a hot topic at present. Based on this, this paper discusses the relationship between risk and return according to several types of models, and establishes the optimal investment portfolio suitable for the Chinese market. Since the Chinese market restricts short selling, and people tend to invest in products with stable returns, namely risk-free assets, these two conditions are the constraints of this paper. Therefore, based on the valuation criteria of investment value, this paper randomly selects 20 stocks, introduces mean-variance model and mean-VAR model, adds two kinds of conditions into the model, uses MATLAB programming to solve the quadratic programming problem, and works out the optimal weight corresponding to each model. Then we compare the models and conclude that the mean-VAR model using time-weighted historical simulation method is the best. Then, the optimal portfolio is established under this method. Finally, we discuss the influence of the number of stocks in the portfolio and the expected return on the portfolio, and draw the conclusion that the portfolio with 17 stocks is the best, and the high return and the high risk are proportional to the expected return and risk. Other investors can refer to the research process and build a portfolio that suits them according to their investment style and risk appetite. Keywords：Mean-variance model; Mean-VAR model; Portfolio of securities; Secondary planning 目 录 一、绪论 1 （一）研究背景及意义 1 （二）国内外研究现状 1 （三）本文的结构 1 二、确定证券投资价值 2 （一）选取证券投资价值评价指标 2 （二）选取证券样本 2 （三）对投资价值进行排序 3 三、各类收益-风险模型及比较 3 （一）马科维茨均值-方差模型 4 1．限制卖空 5 2．限制卖空且含有无风险资产 5 3．模型构建的最优投资组合 6 （二）标准历史模拟法下的均值-VaR模型 6 1．限制卖空 6 2．限制卖空且含有无风险资产 7 3．模型构建的最优投资组合 7 （三）时间加权历史模拟法下的均值-VaR模型 8 1．限制卖空 8 2．限制卖空且含有无风险资产 8 3．模型构建的最优投资组合 8 （四）VaR约束下的均值-方差模型 9 1．限制卖空 9 2．限制卖空且含有无风险资产型 10 3．模型构建的最优投资组合 10 （五）重要结论及模型比较 10 四、实证结果分析 11 （一）最优模型选择 11 1．检验股票收益率的正态性 11 2．比较模型业绩 12 （二）投资组合中股票数目与风险的关系 12 （三）投资组合中预期收益率与风险的关系 13 五、结论 13 参考文献 13
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