论文标题
用于投资组合优化的T-Student分布的广义精度矩阵
A generalized precision matrix for t-Student distributions in portfolio optimization
论文作者
论文摘要
Markowitz模型仍然是现代投资组合理论的基石。特别是，当关注最小变量投资组合时，协方差矩阵或更高的逆向，即所谓的精度矩阵，是所需的唯一输入。到目前为止，大多数学者都致力于改善输入的估计，但是在捕获非高斯环境中捕获依赖性结构时，几乎没有关注逆协方差矩阵的局限性。虽然精度矩阵允许在高斯设置中正确理解随机向量的条件依赖性结构，但当高斯失败时，协方差矩阵的倒数可能不一定会导致可靠的信息来源。在本文中，提供了局部依赖函数，提供了为一般分布类别的广义精度矩阵（GPM）的不同定义。特别是，我们专注于多元t-student分布，并指出随机向量中的相互作用不仅取决于协方差矩阵的倒数，而且还取决于其他元素。我们通过考虑S \＆P 100以及FAMA和法国行业数据，使用最小差异投资组合设置来测试拟议的GPM的性能。我们表明，依赖GPM的投资组合通常比出艺术最新方法产生统计学上显着的样本外差异。
The Markowitz model is still the cornerstone of modern portfolio theory. In particular, when focusing on the minimum-variance portfolio, the covariance matrix or better its inverse, the so-called precision matrix, is the only input required. So far, most scholars worked on improving the estimation of the input, however little attention has been given to the limitations of the inverse covariance matrix when capturing the dependence structure in a non-Gaussian setting. While the precision matrix allows to correctly understand the conditional dependence structure of random vectors in a Gaussian setting, the inverse of the covariance matrix might not necessarily result in a reliable source of information when Gaussianity fails. In this paper, exploiting the local dependence function, different definitions of the generalized precision matrix (GPM), which holds for a general class of distributions, are provided. In particular, we focus on the multivariate t-Student distribution and point out that the interaction in random vectors does not depend only on the inverse of the covariance matrix, but also on additional elements. We test the performance of the proposed GPM using a minimum-variance portfolio set-up by considering S\&P 100 and Fama and French industry data. We show that portfolios relying on the GPM often generate statistically significant lower out-of-sample variances than state-of-art methods.
