两个投资组合模型及其优化算法

发布时间：2018-04-06 20:38

本文选题：资本资产定价模型　切入点：均值—绝对偏差模型　出处：《广西大学》2017年硕士论文

【摘要】：金融市场变幻莫测,风险具有不确定性,那么如何将期望收益和风险控制在一个相对合理的状态,是当前所要解决的一个重要问题.1952年Harry Markowitz提出了均值—方差投资组合模型,本文研究的资本资产定价模型(CAPM)和均值—绝对偏差模型都是在此模型基础上的改进和延伸.由于数学投资组合模型的求解与优化算法是分不开的,文中采用优化算法和投资组合模型相结合,并做了实证研究.针对CAPM,介绍了存在无风险资产和不存在无风险资产的投资组合,该模型表明证券的预期收益和风险之间的关系是线性的,β值的大小可以衡量证券投资中的系统性风险,再对模型的研究推导采用乘子法.依据众多研究者对上证所证券的研究,对CAPM模型以及其扩展模型Fama-French三因子模型和Fama-French五因子模型在创业板市场的实证进行分析.针对修正的均值—绝对偏差模型,介绍了原均值—绝对偏差模型下的风险度量.由于证券的收益率不同,风险度量也应该有所不同,对此引入权值系数对模型进行修正,再给出广义投影共轭梯度算法求解模型,并结合深证A股进行数值实验.
[Abstract]:The financial market is unpredictable and the risk is uncertain, so how to control the expected income and risk in a relatively reasonable state is an important problem to be solved. Harry Markowitz put forward the mean-variance portfolio model in 1952.The capital asset pricing model (CAPMM) and the mean-absolute deviation model studied in this paper are both the improvement and extension of this model.Because the solution of the mathematical portfolio model is inseparable from the optimization algorithm, this paper combines the optimization algorithm with the portfolio model, and makes an empirical study.In this paper, we introduce the portfolio with and without riskless assets for CAPM.The model shows that the relationship between expected return and risk of securities is linear, and the magnitude of 尾 value can measure the systemic risk in securities investment.Then the method of multiplier is used in the research and derivation of the model.According to many researchers' research on Shanghai Securities, this paper analyzes the CAPM model and its extended Fama-French three-factor model and Fama-French five-factor model in the gem market.For the modified mean-absolute deviation model, the risk measurement under the original mean-absolute deviation model is introduced.Because the yield of securities is different, the risk measurement should be different. This paper introduces the weight coefficient to modify the model, then gives the generalized projection conjugate gradient algorithm to solve the model, and carries on the numerical experiment combined with Shenzhen A share.
【学位授予单位】：广西大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：F224;F830.91

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