基于两种协方差矩阵调整方法的投资组合构建与绩效分析

发布时间：2018-06-15 02:45

本文选题：投资组合 + 均值方差模型　；参考：《华东师范大学》2013年硕士论文

【摘要】：随着我国金融市场的日益完善,投资者尤其是机构投资者们越来越关注投资组合的风险管理,投资组合的理念被越来越多的投资者所熟知,对投资组合的研究也越来越深入。现代投资组合理论的先驱Markowitz提出了均值方差模型,但该模型在求解最优投资组合时却面临误差累计、模型不稳定等一系列问题。调整模型输入的协方差矩阵是解决这些问题的关键。本文介绍了解决这些问题的两种协方差矩阵调整方法。用传统方法得到的样本协方差矩阵往往倾向于低估最优投资组合的风险,本文定义了偏差统计量来刻画这种低估效应,猜测这种估计偏差很可能与协方差矩阵的特征因子有关,并通过数值模拟的方法准确而稳定地估计出这种偏差。在此基础上,我们用估计偏差对协方差矩阵作调整,得到特征调整的协方差矩阵。本文的研究结果表明,特征调整的协方差矩阵不仅克服了传统样本协方差矩阵在估计最优投资组合风险时的低估问题,还能够有效降低投资组合的样本外风险。在求解传统的均值方差模型时,对组合权重向量施加L1约束之后得到的最优投资组合具有稀疏性和稳定性。本文阐述了L1约束的理论基础,介绍了求解带约束的均值方差模型的算法,并用实际金融数据展示了组合的稀疏性和稳定性。最后,本文基于两种协方差矩阵调整方法用29个中信行业指数构建了5个投资组合。我们分析了5个投资组合自2005年6月至2013年6月的年化收益、风险和夏普比率,并与同一时期上证综指和深证成指的表现作比较,发现根据两种调整方法构建的投资组合在所考察的时间段内均取得了优于对照组合的业绩。
[Abstract]:With the improvement of China's financial market, investors, especially institutional investors, have paid more and more attention to the risk management of portfolio. The concept of portfolio is well known by more and more investors, and the research on portfolio is becoming more and more in-depth. The pioneer Markowitz of modern portfolio theory puts forward the mean variance model, but this model is a model. In solving the optimal portfolio, it is faced with a series of problems such as accumulative error and model instability. The key to solve these problems is to adjust the covariance matrix of the model input. In this paper, two covariance matrix adjustment methods for solving these problems are introduced.
The sample covariance matrix obtained by the traditional method tends to underestimate the risk of the optimal portfolio. This paper defines the deviation statistics to describe the undervaluation effect. It is guessed that the estimation deviation is likely to be related to the characteristic factor of the covariance matrix, and the deviation is estimated accurately and steadily by the numerical simulation method. On this basis, we use the estimated deviation to adjust the covariance matrix and get the covariance matrix of the characteristic adjustment. The results of this study show that the covariance matrix of the feature adjustment can not only overcome the underestimation of the traditional sample covariance matrix in the estimation of the optimal portfolio risk, but also can effectively reduce the external wind of the portfolio. Risk.
When the traditional mean variance model is solved, the optimal portfolio is sparsity and stability after applying the L1 constraint to the combined weight vector. This paper expounds the theoretical basis of the L1 constraint, introduces the algorithm for solving the mean variance model with constraints, and shows the sparsity and stability of the combination with the actual financial data.
Finally, based on two covariance matrix adjustment methods, 5 portfolios are constructed with 29 CITIC industry indices. We analyzed the annual income, risk and SHARP ratio of 5 portfolios from June 2005 to June 2013, and compared with the performance of the Shanghai Composite Index and Shenzhen stock index at the same time, and found that the two adjustment methods were constructed. The built portfolios achieved better performance than those in the control group during the period examined.
【学位授予单位】：华东师范大学
【学位级别】：硕士
【学位授予年份】：2013
【分类号】：F832.51;F224

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