稳定分布下基于不同风险度量的投资组合研究

发布时间：2018-07-07 08:29

本文选题：稳定分布 + 投资组合　；参考：《郑州大学》2015年硕士论文

【摘要】：投资组合问题作为现代金融学的一个核心课题,主要研究在不确定情况下对资产进行最优配置与选择,从而实现收益率最大化与风险最小化间的均衡。1952年,美国经济学家Markowitz[1]首次用资产收益率的方差度量风险,并提出了均值-方差投资组合模型,被认为开创了现代投资组合理论的先河,奠定了定量研究金融投资问题的基础。但是,Markowitz的均值-方差投资组合模型必须依赖于资产的收益率服从正态分布且方差存在,而大量的实证研究证明,无论是收益率的正态假设还是方差的存在性都是值得怀疑的。基于Markowitz理论框架下的投资组合模型,对输入的参数要求严格,但是,对未来资产的回报做精准的预测非常困难,并且在不同的经济环境中,各资产之间的相关性是变化的,很难预测未来资产之间的相关性。针对上述问题,本文运用不同的风险度量并引入具有尖峰厚尾特征的稳定分布来研究投资组合理论。稳定分布具有四个参数,但是没有解析的密度函数和分布函数的表达式,为此文章研究高效快速的数值算法来解决稳定分布给模型带来的计算量和复杂性。文章通过实证研究部分,对各个模型进行对比分析,发现基于稳定分布的均值-绝对离差模型和均值-半绝对离差模型与正态分布下对应的模型相比,有效前沿向左上方移动,且计算出的最优比例的投资效果更佳。本文介绍了风险平价理论,并对该理论下的模型进行修正改进,求出模型的最优比例。
[Abstract]:As a core subject of modern finance, portfolio problem is mainly concerned with the optimal allocation and selection of assets under uncertain conditions, so as to achieve the equilibrium between maximization of return rate and minimization of risk. The American economist Markowitz [1] measures the risk with the variance of the return on assets for the first time, and puts forward the mean-variance portfolio model, which is regarded as the pioneer of the modern portfolio theory and lays the foundation for the quantitative study of the financial investment problem. However, Markowitz's mean-variance portfolio model must depend on the return of assets from the normal distribution and the existence of variance, and a large number of empirical studies prove that the existence of both the normal assumption of return and variance is doubtful. The portfolio model based on Markowitz theory requires strict input parameters, but it is very difficult to predict the return of future assets accurately, and the correlation between assets varies in different economic environments. It is difficult to predict the correlation between future assets. In order to solve the above problems, this paper uses different risk measures and introduces a stable distribution with peak and thick tail to study portfolio theory. The stable distribution has four parameters, but there is no analytic density function and distribution function expression. In this paper, an efficient and fast numerical algorithm is studied to solve the computational complexity and complexity brought by the stable distribution to the model. In the part of empirical research, we find that the mean-absolute deviation model and the mean-semi-absolute deviation model based on stable distribution move to the upper left of the model compared with the corresponding model under normal distribution. And the optimal proportion of the calculated investment effect is better. In this paper, the theory of risk parity is introduced, and the model under the theory is modified and improved to find the optimal proportion of the model.
【学位授予单位】：郑州大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：F830.59;F224

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