基于最小扰动相关去噪法股票投资组合风险优化

发布时间：2018-03-24 19:09

本文选题：金融相关噪声　切入点：随机矩阵理论　出处：《系统工程理论与实践》2013年10期

【摘要】：金融相关矩阵的计算是构建金融投资组合的基础.为解决金融相关矩阵的"维数灾祸"问题,进而促进金融投资组合风险的优化,受基于随机矩阵理论(RMT)和特征向量的Krzanowski稳定性的KR去噪法的启发,对收益相关矩阵特征值增大时的特征向量最小扰动进行了数学推导,并将以该扰动衡量的特征向量的Krzanowski稳定性引入到RMT去噪法中,进而建立对金融收益相关矩阵去噪的KRMIN方法.KRMIN法对KR法的算法进行了两方面的优化.一方面,KRMIN法对KR法的特征值设定方法进行了扩展;另一方面,KRMIN法采用模拟退火算法计算特征值.理论研究表明,由于在收益相关矩阵特征向量的稳定性和特征值算法准确性上的优势,KRMIN方法将获得比KR法更好的组合风险优化效果.通过bootstrap方法,开展了将LCPB法、PG+法、KR法和KRMIN法用于不同数量股票的投资组合优化的实证研究.结果表明:LCPB法、PG+法、KR法和KRMIN法都能通过股票收益相关矩阵去噪而带来投资组合风险的优化;基于收益相关矩阵特征向量的Krzanowski稳定性的KR法和KRMIN法的组合风险比其他两种方法更低;由KRMIN法得到的收益相关矩阵的特征向量稳定性和组合风险优化效果好于KR法.
[Abstract]:The calculation of financial correlation matrix is the basis of constructing financial portfolio. In order to solve the problem of "dimension disaster" of financial correlation matrix and promote the optimization of financial portfolio risk, Inspired by the KR denoising method based on the stochastic matrix theory and the Krzanowski stability of the eigenvector, the minimum perturbation of the eigenvector is derived when the eigenvalue of the income correlation matrix increases. The Krzanowski stability of the eigenvector measured by the disturbance is introduced into the RMT denoising method. Then the KRMIN method of financial income correlation matrix denoising is established. The KRMIN method optimizes the KR algorithm in two aspects. On the one hand, the KRMIN method extends the eigenvalue setting method of the KR method. On the other hand, the KRMIN method uses simulated annealing algorithm to calculate the eigenvalues. Because of the advantage of KRMIN method in the stability of the eigenvector and the accuracy of eigenvalue algorithm, the KRMIN method will achieve better combinatorial risk optimization effect than KR method. An empirical study on portfolio optimization of different stocks using LCPB / PG / KR and KRMIN methods is carried out. The results show that both the KR method and KRMIN method can bring about portfolio risk optimization through stock return correlation matrix de-noising. The combination risk of KR method and KRMIN method based on the eigenvector of the income correlation matrix is lower than that of the other two methods, and the eigenvector stability and portfolio risk optimization of the return correlation matrix obtained by the KRMIN method are better than that of the KR method.
【作者单位】：哈尔滨工业大学经济与管理学院;东北大学秦皇岛分校数学与统计学院;
【基金】：国家自然科学基金(70773028,71173060,71031003)
【分类号】：O224;F830.91

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