熵视角下投资组合风险度量模型的研究
发布时间：2018-07-20 17:35
【摘要】：投资市场是一个有人参与的复杂动态系统,投资环境中充斥着众多影响投资收益的不确定因素,包括市场随机因素和投资者认知模糊因素。而风险就是这些不确定性因素引进的。几何平均产出比同时存在随机不确定性和模糊不确定性的特点,在经典的投资组合理论中,大都只考虑了单一的不确定性,本文综合考虑了两种不确定性统一作用下的总风险,引入混合熵测度作为度量投资风险的指标。混合熵弥补了方差和Va R度量指标的部分缺陷,可比较准确地度量总的不确定性,而且增值熵能够反映资产的增值速度。本文在度量几何平均产出比的模糊不确定性时,将其视为一个三角函数,利用马尔可夫链方法预测,并利用混合熵和增值熵分别作为风险和收益的度量指标,构建了最小混合熵-最大增值熵投资组合模型,同时考虑了市场摩擦因素中的交易费用,通过模糊决策理论和优化方法对模型进行求解。另外,为了反映不同风险偏好特性水平的投资者对风险的态度,又提出了一种加入风险权重系数的新投资组合模型,扩大了模型的适用范围。作为理论检验,随机选取了最具代表性的沪深300指数中50支股票进行了实证研究。实证结果表明,对于风险保守型投资者,本文提出的最小混合熵-最大增值熵投资组合模型能够给出令人满意的投资效果,具有一定的理论价值和现实意义;对于风险进取型和中庸型投资者,按加入风险权重系数后的最优投资比例构建投资组合,投资结果也十分令人满意,但是对于保守型投资者,该模型给出的结果却不够理想,有待进一步改进。
[Abstract]:The investment market is a complex dynamic system in which the investment environment is full of many uncertain factors which affect the investment returns, including market random factors and investors' cognitive ambiguity. And risk is the introduction of these uncertainties. The geometric mean output ratio has the characteristics of both random uncertainty and fuzzy uncertainty. In the classical portfolio theory, only a single uncertainty is considered. In this paper, the total risk under the unified action of the two kinds of uncertainties is considered comprehensively. The mixed entropy measure is introduced as an index to measure investment risk. The mixed entropy makes up for some defects of variance and VaR, and can measure the total uncertainty more accurately, and the increment entropy can reflect the appreciation rate of assets. In this paper, when we measure the fuzzy uncertainty of geometric mean output ratio, we regard it as a trigonometric function and use Markov chain method to predict it. A portfolio model of minimum mixed entropy and maximum increment entropy is constructed, and the transaction cost in the market friction factor is considered. The model is solved by fuzzy decision theory and optimization method. In addition, in order to reflect the attitude of investors with different risk preference characteristics to risk, a new portfolio model with risk weighting coefficient is proposed, which expands the scope of application of the model. As a theoretical test, 50 stocks in the most representative CSI 300 index were randomly selected for empirical research. The empirical results show that the minimum mixed Entropy and maximum Value-Entropy portfolio model proposed in this paper can give satisfactory investment effect for risk conservative investors, which has certain theoretical value and practical significance. For venture enterprising and moderate investors, the investment portfolio is constructed according to the optimal investment proportion after adding risk weight coefficient, and the result is very satisfactory, but for conservative investors, the result is not satisfactory. Further improvement is needed.
【学位授予单位】：宁波大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：F830.59
本文编号：2134247
[Abstract]:The investment market is a complex dynamic system in which the investment environment is full of many uncertain factors which affect the investment returns, including market random factors and investors' cognitive ambiguity. And risk is the introduction of these uncertainties. The geometric mean output ratio has the characteristics of both random uncertainty and fuzzy uncertainty. In the classical portfolio theory, only a single uncertainty is considered. In this paper, the total risk under the unified action of the two kinds of uncertainties is considered comprehensively. The mixed entropy measure is introduced as an index to measure investment risk. The mixed entropy makes up for some defects of variance and VaR, and can measure the total uncertainty more accurately, and the increment entropy can reflect the appreciation rate of assets. In this paper, when we measure the fuzzy uncertainty of geometric mean output ratio, we regard it as a trigonometric function and use Markov chain method to predict it. A portfolio model of minimum mixed entropy and maximum increment entropy is constructed, and the transaction cost in the market friction factor is considered. The model is solved by fuzzy decision theory and optimization method. In addition, in order to reflect the attitude of investors with different risk preference characteristics to risk, a new portfolio model with risk weighting coefficient is proposed, which expands the scope of application of the model. As a theoretical test, 50 stocks in the most representative CSI 300 index were randomly selected for empirical research. The empirical results show that the minimum mixed Entropy and maximum Value-Entropy portfolio model proposed in this paper can give satisfactory investment effect for risk conservative investors, which has certain theoretical value and practical significance. For venture enterprising and moderate investors, the investment portfolio is constructed according to the optimal investment proportion after adding risk weight coefficient, and the result is very satisfactory, but for conservative investors, the result is not satisfactory. Further improvement is needed.
【学位授予单位】：宁波大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：F830.59
【参考文献】
相关期刊论文 前2条
1 尚修刚,蒋慰孙;关于混合熵的讨论[J];控制理论与应用;1999年01期
2 顾昌耀,邱菀华;复熵及其在Bayes决策中的应用[J];控制与决策;1991年04期
，本文编号：2134247
本文链接：https://www.wllwen.com/jingjilunwen/zbyz/2134247.html
