多阶段跟踪误差投资组合模型及实证研究

发布时间：2018-06-10 20:58

本文选题：跟踪误差 + 多阶段　；参考：《华南理工大学》2016年硕士论文

【摘要】：Markowitz(1952)在《The Journal of Finance》上发表了“Portfolio selection”一文,第一次从数理经济学角度解释了如何通过分散投资降低风险以及如何利用投资组合的有效边界选择最优组合,开创了现代金融理论和投资分析理论的先河,继而奠定了现代投资理论的基石。作为均值-方差模型的一种改进,跟踪误差模型以相对收益和相对风险的形式,对投资管理者的业绩进行了更为科学的评价。但是从投资组合管理风险控制的角度来看,单纯的控制跟踪误差而追寻高的期望收益容易导致投资管理者的冒险投资行为,因此需要对投资组合的总风险进行控制。经典投资组合优化模型仅考虑了单阶段投资组合优化问题,而机构投资者在真实的金融市场中的投资往往是长期的,因此一个投资管理者必须不断根据市场环境适时地调整投资组合的头寸,这就需要对动态投资组合优化问题进行研究。本文将单阶段的跟踪误差投资组合模型拓展到多阶段并创建了如下三种多阶段跟踪误差投资组合模型:1.虽然有学者从方差约束的角度控制投资组合整体风险,但方差关于均值对称以及缺乏对资产收益损失的刻画限制了其应用。因此我们采用平均绝对偏差作为多阶段跟踪误差投资组合模型的总风险约束,建立了基于平均绝对偏差总风险约束的多阶段跟踪误差投资组合模型。2.传统的多阶段均值方差模型为了控制风险,同时舍弃了高收益和低收益,这在现实中往往是不符合投资者真实心理的。由于方差度量风险消除高低收益,牺牲了投资者获取高回报的可能。因此我们考虑将半方差约束加入跟踪误差模型,并拓展到多阶段跟踪误差投资组合模型中。3.传统的VaR(Value-at-Risk)是无法考察超过分位点的下方风险,不能满足次可加性和凸性,不符合一致性的风险度量。CVaR(Conditional Value-at-Risk)虽然弥补了以上缺陷,但是只适用于随机变量分布已知的情况。因此本文调整多期跟踪误差投资组合模型,改进传统目标函数,在分布信息不完全的情形下,建立了基于WCVaR总风险约束的多阶段跟踪误差投资组合模型。另外,考虑到在现实金融市场中存在以下情况:首先,交易费用对于投资活动而言是必不可少的,每一次交易投资者都得向交易所和经纪人交纳相应的费用,包括手续费、税收等。其次,投资者并非所有资产都用于投资风险资产,可能部分用于无风险资产。最后,投资者在实际投资操作中会对组合中风险资产数量和投资资金比例加以限制。因此本文的多阶段跟踪误差投资组合模型同时考虑了卖空限制、交易费用、无风险资产及基数约束等约束条件。本文利用中国证券市场上证50的成分股数据进行数值分析,采用matlab软件,运用SQP算法及遗传算法进行实证分析,结果表明本文所建立的投资组合模型在样本内外均能获取超越基准组合的收益及绩效。
[Abstract]:"portfolio selection", published in the Journal of Finance in 1952, explains for the first time from a mathematical economics perspective how to reduce risk through diversification and how to use the efficient boundaries of a portfolio to select the optimal portfolio. Founded the modern financial theory and investment analysis theory, and then laid the foundation of modern investment theory. As an improvement of the mean-variance model, the tracking error model evaluates the performance of investment managers more scientifically in the form of relative returns and relative risks. But from the point of view of portfolio management risk control, it is easy to control the tracking error and pursue the high expected return, so it is necessary to control the total risk of the portfolio. The classical portfolio optimization model only considers the single-stage portfolio optimization problem, while the institutional investors' investment in the real financial market is often long-term. Therefore, an investment manager must constantly adjust the portfolio position according to the market environment, which needs to study the dynamic portfolio optimization problem. In this paper, the single-stage tracking error portfolio model is extended to multi-stage and the following three kinds of multi-stage tracking error portfolio model: 1 are created. Although some scholars control the overall risk of portfolio from the perspective of variance constraints, its application is limited by the symmetry of the mean value of variance and the lack of characterization of asset income loss. Therefore, we use the average absolute deviation as the total risk constraint of the multi-stage tracking error portfolio model, and establish the multi-stage tracking error portfolio model based on the average absolute deviation total risk constraint. In order to control the risk, the traditional multi-stage mean variance model forgets the high and low returns, which is often not in line with the real psychology of investors in reality. Because the variance measures the risk eliminates the high and low income, has sacrificed the investor to obtain the high return possibility. Therefore, we consider adding the semi-variance constraint to the tracking error model and extend it to the multi-stage tracking error portfolio model. The traditional VaRN Value-at-Risk) is unable to examine the lower risk beyond the locus, can not satisfy the secondary additivity and convexity, and does not conform to the consistency of the risk measure. CVaRU conditional Value-at-Risk) makes up for the above defects, but it is only applicable to the situation where the distribution of random variables is known. Therefore, this paper adjusts the multi-period tracking error portfolio model, improves the traditional objective function, and establishes a multi-stage tracking error portfolio model based on the total risk constraint of WCVaR in the case of incomplete distributed information. In addition, considering the fact that in real financial markets, transaction costs are essential for investment activities, investors in each transaction have to pay a corresponding fee, including fees, to exchanges and brokers, Tax, etc. Second, not all of investors' assets are invested in risky assets, possibly partly in risk-free assets. Finally, investors will limit the number of risky assets and the proportion of investment funds in the actual investment operations. Therefore, the multi-stage tracking error portfolio model takes into account the constraints of short selling, transaction costs, risk-free assets and cardinality constraints at the same time. In this paper, we use the data of Shanghai Stock Exchange 50 to carry out numerical analysis, and use matlab software, sqp algorithm and genetic algorithm to carry out empirical analysis. The results show that the portfolio model established in this paper can obtain the income and performance beyond the benchmark portfolio both within and outside the sample.
【学位授予单位】：华南理工大学
【学位级别】：硕士
【学位授予年份】：2016
【分类号】：F830.48;F224

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