基于时变系数回归分析的动态组合投资决策及应用

发布时间：2018-10-17 14:20

【摘要】：Markowitz利用二次规划方法求解均值-方差模型,开创了现代组合投资理论的先河。传统的组合投资决策模型是静态的,没有考虑金融资产收益和风险的时变特征。此外,基于二次规划的均值-方差模型,一方面在模型求解方面效率较低下；另一方面只能解决方差风险组合投资问题。因此,本文将均值-方差模型和均值-VaR模型分别转换成均值回归和分位数回归问题,并运用时变系数回归分析构造动态组合投资决策模型,为投资者实时调整组合投资权重,获取更好的组合投资效果(更高收益或者更低风险)提供了基本工具。本文主要开展了以下两个方面的研究工作。(1)基于时变系数均值回归给出了动态组合投资决策模型一种新算法。该算法主要有两个显著特点：第一,将均值-方差组合投资决策中的优化问题转化为统计学中经典的均值回归分析问题；第二,采用可行性最小二乘方法进行模型求解,得到时变的组合投资权重。选取上证综指及上海证券交易所挂牌的16支股票进行实证研究,通过滚动分析和返回测试,将基于时变系数均值回归的动态组合投资决策模型与传统的组合投资决策模型进行比较,结果表明前者在收益、风险和Sharpe比率方面都优于后者。(2)结合普通分位数回归的模型结构和可行性最小二乘方法的时变系数特征,在普通分位数回归模型的损失函数中引入动态误差设定,提出了一种新的时变系数分位数回归模型,并给出其模型表示和参数估计方法：可行性分位数回归方法。时变系数分位数回归模型能够适应更为广泛数据类型的建模需求,体现回归系数的时变特征,揭示解释变量对响应变量完整条件分布特征的影响,具有广阔的应用前景。将其应用于组合投资决策分析,构造出VaR风险动态组合投资方案,并与VaR风险静态组合投资方案、方差风险静态组合投资方案、方差风险动态组合投资方案等进行实证比较,实证结果表明：基于时变系数分位数回归模型的VaR风险动态组合投资方案所得投资效果在收益、方差、Sharpe比率和VaR数值等方面都显著优于其他三种方案。
[Abstract]:Markowitz uses quadratic programming method to solve mean-variance model and creates the first step of modern portfolio investment theory. The traditional portfolio decision model is static and does not take into account the time-varying characteristics of financial asset returns and risks. In addition, the mean-variance model based on quadratic programming is inefficient in solving the model on the one hand, and can only solve the problem of variance risk portfolio investment on the other hand. Therefore, the mean variance model and mean VaR model are transformed into mean regression and quantile regression respectively, and the dynamic portfolio decision model is constructed by time-varying coefficient regression analysis to adjust the portfolio weight for investors in real time. Achieving better portfolio outcomes (higher returns or lower risk) provides the basic tools. In this paper, the following two aspects of the research work are mainly carried out. (1) based on the mean regression of time-varying coefficients, a new algorithm for dynamic portfolio decision model is presented. The algorithm has two main characteristics: first, the optimization problem in the mean-variance portfolio investment decision is transformed into the classical mean regression problem in statistics; second, the feasibility least square method is used to solve the model. The time-varying weight of portfolio investment is obtained. Select the Shanghai Composite Index and Shanghai Stock Exchange listed 16 stocks for empirical research, through rolling analysis and return test, The dynamic portfolio decision model based on the mean regression of time-varying coefficients is compared with the traditional portfolio investment decision model. Both the risk and the Sharpe ratio are better than the latter. (2) combined with the model structure of the ordinary quantile regression and the characteristics of the feasible least square method, the dynamic error setting is introduced into the loss function of the ordinary quantile regression model. In this paper, a new quantile regression model with time-varying coefficients is proposed, and its model representation and parameter estimation method: feasible quantile regression method is given. The quantile regression model with time-varying coefficients can meet the needs of more extensive data types, reflect the time-varying characteristics of regression coefficients, and reveal the influence of explanatory variables on the complete conditional distribution of response variables, which has a broad application prospect. It is applied to portfolio investment decision analysis to construct VaR risk dynamic portfolio investment scheme, and to compare it with VaR risk static portfolio scheme, variance risk dynamic portfolio investment scheme and so on. The empirical results show that the VaR risk dynamic portfolio investment scheme based on time-varying coefficient quantile regression model is superior to the other three schemes in terms of return, variance, Sharpe ratio and VaR value.
【学位授予单位】：合肥工业大学
【学位级别】：硕士
【学位授予年份】：2016
【分类号】：F224;F832.51

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