Toma Aida, Leoni-Aubin Samuela
Department of Applied Mathematics, Bucharest Academy of Economic Studies, Bucharest, Romania; "Gh. Mihoc-C. Iacob" Institute of Mathematical Statistics and Applied Mathematics, Romanian Academy, Bucharest, Romania.
INSA Lyon, ICJ, Villeurbanne Cedex, France.
PLoS One. 2015 Oct 15;10(10):e0140546. doi: 10.1371/journal.pone.0140546. eCollection 2015.
The presence of outliers in financial asset returns is a frequently occurring phenomenon which may lead to unreliable mean-variance optimized portfolios. This fact is due to the unbounded influence that outliers can have on the mean returns and covariance estimators that are inputs in the optimization procedure. In this paper we present robust estimators of mean and covariance matrix obtained by minimizing an empirical version of a pseudodistance between the assumed model and the true model underlying the data. We prove and discuss theoretical properties of these estimators, such as affine equivariance, B-robustness, asymptotic normality and asymptotic relative efficiency. These estimators can be easily used in place of the classical estimators, thereby providing robust optimized portfolios. A Monte Carlo simulation study and applications to real data show the advantages of the proposed approach. We study both in-sample and out-of-sample performance of the proposed robust portfolios comparing them with some other portfolios known in literature.
金融资产回报中异常值的存在是一种常见现象，这可能导致均值 - 方差优化投资组合不可靠。这一事实是由于异常值对作为优化过程输入的均值回报和协方差估计量可能产生无界影响。在本文中，我们提出了均值和协方差矩阵的稳健估计量，它们是通过最小化假设模型与数据背后真实模型之间伪距离的经验版本而获得的。我们证明并讨论了这些估计量的理论性质，如仿射同变性、B - 稳健性、渐近正态性和渐近相对效率。这些估计量可以很容易地替代经典估计量，从而提供稳健的优化投资组合。蒙特卡罗模拟研究以及对实际数据的应用展示了所提出方法的优势。我们研究了所提出的稳健投资组合的样本内和样本外表现，并将它们与文献中已知的其他一些投资组合进行比较。
