Geometric function theory in several complex variables
Geometric function theory in several complex variables
复制标题
多复变量的几何函数论
DOI：
10.1007/s10690-022-09358-8
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发表时间：
1990
影响因子：
1.7
通讯作者：
落合 卓四郎
中科院分区：
文献类型：
--
作者：
野口 潤次郎;落合 卓四郎
管理包含多种资产的大规模投资组合是金融领域最具挑战性的任务之一。部分原因是当资产数量超过观察数量n时，资产收益的协方差或精度矩阵的估计往往不稳定甚至不可行。为此，以往关于投资组合管理的研究大多集中在案例上。为了处理这种情况，我们建议使用基于自适应图形 LASSO 的新贝叶斯框架来估计大规模投资组合中资产回报的精度矩阵。与文献中之前关于图形LASSO的研究不同，我们的方法利用Oya和Nakatsuma（Japan J Stat Data Sci，2022）提出的精度矩阵的贝叶斯估计方法，因此始终保证精度矩阵的正定性。作为实证应用，我们使用所提出的方法以及非贝叶斯图形LASSO方法构建了不同n值的全局最小方差投资组合，并将它们的样本外性能与等权投资组合作为基准进行比较。我们还将它们与 Torri 等人使用的基于随机矩阵理论过滤和 Ledoit-Wolf 收缩估计的投资组合进行比较。 （计算管理科学 16：375–400，2019 年）。在此比较中，即使比非贝叶斯方法和其他比较方法小得多，所提出的方法在夏普比率、投资组合构成和周转率方面也能产生更稳定的结果。
Managing a large-scale portfolio with many assets is one of the most challenging tasks in the field of finance. It is partly because estimation of either covariance or precision matrix of asset returns tends to be unstable or even infeasible when the number of assetspexceeds the number of observationsn. For this reason, most of the previous studies on portfolio management have focused on the case of. To deal with the case of, we propose to use a new Bayesian framework based on adaptive graphical LASSO for estimating the precision matrix of asset returns in a large-scale portfolio. Unlike the previous studies on graphical LASSO in the literature, our approach utilizes a Bayesian estimation method for the precision matrix proposed by Oya and Nakatsuma (Japanese J Stat Data Sci, 2022.) so that the positive definiteness of the precision matrix should be always guaranteed. As an empirical application, we construct the global minimum variance portfolio offor various values ofnwith the proposed approach as well as the non-Bayesian graphical LASSO approach, and compare their out-of-sample performance with the equal weight portfolio as the benchmark. We also compare them with portfolios based on random matrix theory filtering and Ledoit-Wolf shrinkage estimation which were used by Torri et al. (Comput Manage Sci 16:375–400, 2019). In this comparison, the proposed approach produces more stable results than the non-Bayesian approach and the other comparative approaches in terms of Sharpe ratio, portfolio composition and turnover even ifnis much smaller thanp.