基于Fama-French三因素模型下的高维协方差矩阵估计法在中国股票投资组合中的实证研究

发布时间：2018-05-21 14:15

本文选题：三因素模型 + 高维协方差　；参考：《厦门大学》2014年硕士论文

【摘要】：股票投资组合策略长期以来一直是人们非常关注的话题,无论是理论界还是实践中,人们都对如何在众多股票中选择一个在既定风险下能给他们带来最高回报的资产组合抱有浓厚的兴趣。早在1952年马克维茨(Markowitz)就提出了一个震惊学术界的均值方差资产组合模型。这个模型在理论上确实是一个巨大的成功,Markowitz还因此获得了诺贝尔经济学奖。但是在实践中越来越多的人反应,用Markowitz这个模型选择的投资组合表现有时不尽如人意,极有可能会产生很大的误差。背后的原因可能是多方面的,但其中不可忽视的是,投资组合表现与能否准确刻画资产组合里面各资产的关联程度,尤其是能否有效地估计他们的协方差矩阵息息相关。当资产的个数较大时,所对应的协方差矩阵是高维的,如果用传统的样本估计法来估计协方差就会产生很大的误差,从而导致相应计算所得到的投资组合也会产生较大的误差。虽然由于信息科技的发达,获取更多的数据也变得越来越容易,但是我们不能一味地想通过扩大样本量来减少估计误差,因为在时间序列分析领域存在一个数据稳定性问题,如果样本量太大,时间跨度太长就会影响数据的稳定性,因此如何构建协方差矩阵,是理论界一大热点,该研究对实际数据分析,尤其在金融领域的应用有举足轻重的作用。目前学术界已经探讨出了很多在不同假设前提下的高维协方差估计方法,例如Fan, Fan and Lv (2008)[1],就引入三因素模型估计法。但是相比之下,较少有人将这些估计方法应用到国内数据的研究中。随着中国资本市场越来越完善,越来越多的投资者参与投资,一个更合理可靠的股票投资组合就显得尤为重要。所以本论文决定以中国沪深主板市场A股股票的交易数据为基础,来研究利用Fama-French三因素模型估计高维协方差矩阵较传统样本估计法的优越性,以及利用此方法研究中国股票投资组合是否具有良好的效果。
[Abstract]:The stock portfolio strategy has long been a topic of great concern. Both in theory and in practice, people have a strong interest in how to choose a portfolio of assets that can bring them the highest returns at a given risk. In 1952, Markowitz put forward an earthquake. Startled the academia of the mean variance portfolio model. This model was indeed a great success in theory. Markowitz also won the Nobel prize in economics.
But in practice, more and more people respond, the investment portfolio selected by the Markowitz model is sometimes unsatisfactory, and it is likely to produce great errors. The reasons behind it may be multifaceted, but what can not be ignored is whether the portfolio performance and the accuracy of the relationship between the assets in the portfolio can be accurately depicted. In particular, whether their covariance matrix can be effectively estimated is closely related. When the number of assets is larger, the corresponding covariance matrix is high dimension. If the covariance is estimated by the traditional sample estimation method, it will produce a large error, which leads to the larger error in the corresponding calculation.
Although it is more and more easy to obtain more data because of the development of information technology, we can not blindly reduce the estimation error by expanding the sample size, because there is a data stability problem in the domain of time series analysis. If the sample size is too large and the time span is too long, it will affect the stability of the data. How to construct the covariance matrix is a hot topic in the theoretical field. This research plays a decisive role in the actual data analysis, especially in the financial field.
At present, there have been many high dimensional covariance estimation methods under different assumptions, such as Fan, Fan and Lv (2008) [1], and the introduction of three factor model estimation. However, few people apply these estimation methods to domestic data research. As China's capital market is more and more perfect and more and more, more and more The investor participates in the investment, a more reasonable and reliable stock portfolio is particularly important. Therefore, based on the transaction data of A shares in the Shanghai and Shenzhen stock market, this paper studies the superiority of using the Fama-French three factor model to estimate the higher dimension covariance matrix than the traditional sample estimation method, and uses this method to make use of this method. Study whether China's stock portfolio has a good effect.
【学位授予单位】：厦门大学
【学位级别】：硕士
【学位授予年份】：2014
【分类号】：F224;F832.51

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