参数不确定性对均值—方差前沿组合的影响及解决办法研究

发布时间：2018-03-31 16:13

本文选题：资产配置　切入点：参数不确定性　出处：《西南财经大学》2013年硕士论文

【摘要】：随着国内资本市场的日益发展,市场上可投资的金融产品越来越多,而且机构投资者的日益壮大,所管理的产品规模越来越大,同时持有大量的证券头寸该是如何分布呢?在理论上,Markowitz(1952)提出的均值方差模型是关于资产配置“完美”的理论,原理是在一定风险控制下寻求收益率最大化的组合,或者是在一定收益率的要求下寻求风险最小化的组合。但是这个理论是“事后最优的”,即当风险资产的收益率已经实现了的时候去寻求的“事后”最优的资产配置。所以在实际应用中,若使用均值方差模型进行资产配置就需要对风险资产的参数进行估计了,估计误差就难以避免了。不幸的是,均值方差模型对估计误差极其敏感,所估计的参数发生微小变化将导致权重发生剧烈的变化,同时还存在非直觉性以及误差放大等缺陷,在没有卖空限制条件下模型得到的权重发生权重过度集中的情形,这本身就违背了使用资产组合理论进行资产配置的初衷——通过构建投资组合以分散非系统风险。所以,在实际投资应用中,甚少投资者使用均值方差模型。因此本文就立足于这样的一个具体问题,尝试给出一个有效的资产配置的量化方案。本文首先通过实证方法证明了参数存在时变问题,利用历史数据估计得到的参数并不能直接运用到传统的均值方差模型中,发现期望收益率的不确定性程度越高,对组合的效率影响越大,而协方差矩阵的不确定性对模型的影响则不存在这样的问题；若从夏普损失比率的角度来看,协方差矩阵的不确定对模型的影响要不收益率的要低。因此在实际应用中利用历史数据估计波动率是相对可靠的。其次,在以上的讨论的基础上,以均值-CVaR的框架下总结了以贝叶斯算法为核心的资产组合模型体系。通过利用蒙特卡洛模拟和压力测试的方式,从损失、偏误和有效性三个方面讨论参数的估计精度问题,发现贝叶斯算法为核心的模型皆能提高对收益率的估计精度,但未能提高对波动率的估计精度；然后从夏普损失率函数角度讨论了四种模型的效率问题,发现在同样的经验意见以及置信度的情况下,鲁棒法估计和全观点估计性能相当优越,非常适合实际投资需求。最后,重点对全观点模型进行回溯测试,利用“市场上涨时投资高β股票、市场下跌时投资低β股票”的投资逻辑,通过历史数据估计股票的β值,分别在对经验意见的不同置信度下和对投资组合的不同CVaR下进行组合的构建,发现全观点模型均能获得超额的收益。因此,贝叶斯算法下的资产组合模型能够在一定程度下避免参数不确定对资产组合的效率损失问题,能够成为在实际投资中资产配置的有力工具。
[Abstract]:With the development of the domestic capital market, there are more and more financial products that can be invested in the market. With the growing of institutional investors, the scale of the products managed is becoming larger and larger. At the same time, how should we distribute a large number of securities positions? In theory, the mean variance model proposed by Markowitz (1952) is about the theory of "perfect" asset allocation, and the principle is to seek the combination of maximization of return rate under certain risk control. Or seek a combination of risk minimization under a certain rate of return. But this theory is "ex post optimal", that is, when the return rate of risk assets has been achieved, the "afterwards" optimal asset allocation. So in practice, If the mean variance model is used for asset allocation, it is necessary to estimate the parameters of the risk asset, and the estimation error is unavoidable. Unfortunately, the mean variance model is extremely sensitive to the estimation error. Small changes in the estimated parameters will lead to drastic changes in weights, and there are also some defects such as non-intuitionism and error amplification, and the weight of the model will be overconcentrated under the condition of no short selling restriction. This in itself goes against the original intention of using portfolio theory to allocate assets by building a portfolio to spread non-systemic risk. Very few investors use mean-variance model, so this paper tries to give an effective quantitative scheme of asset allocation based on such a specific problem. In this paper, we first prove that the parameters are time-varying by empirical method. The parameters estimated by historical data can not be directly applied to the traditional mean variance model, and the higher the degree of uncertainty of the expected return is, the higher the degree of uncertainty is. The greater the effect on the efficiency of the combination, the less the uncertainty of the covariance matrix has on the model; if viewed from the perspective of Sharp's loss ratio, The influence of uncertainty of covariance matrix on the model is less than that of the yield, so it is relatively reliable to estimate volatility by using historical data in practical application. Secondly, on the basis of the above discussion, the paper summarizes the portfolio model system with Bayesian algorithm as the core under the framework of mean value-CVaR. The estimation accuracy of parameters is discussed in three aspects: error and validity. It is found that the model with Bayesian algorithm as the core can improve the accuracy of the estimation of the return rate, but it can not improve the estimation accuracy of the volatility. Then the efficiency problems of the four models are discussed from the perspective of Sharpe loss rate function. It is found that under the same empirical opinion and confidence degree, the performance of robust estimation and full view estimation is quite superior, which is very suitable for the actual investment demand. Finally, this paper focuses on the backtracking test of the full view model, using the logic of "investing in high 尾 stocks when the market rises and investing in low 尾 stocks when the market falls", and estimating the 尾 value of stocks through historical data. Under the different confidence degree of the experience opinion and the different CVaR of the investment portfolio, it is found that the whole view model can obtain excess income. Therefore, the portfolio model based on Bayesian algorithm can avoid the loss of portfolio efficiency caused by parameter uncertainty to a certain extent, and become a powerful tool for asset allocation in real investment.
【学位授予单位】：西南财经大学
【学位级别】：硕士
【学位授予年份】：2013
【分类号】：F832.5;F224

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