英文标题：
《Estimation of the Global Minimum Variance Portfolio in High Dimensions》
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作者：
Taras Bodnar, Nestor Parolya and Wolfgang Schmid
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最新提交年份：
2015
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英文摘要：
We estimate the global minimum variance (GMV) portfolio in the high-dimensional case using results from random matrix theory. This approach leads to a shrinkage-type estimator which is distribution-free and it is optimal in the sense of minimizing the out-of-sample variance. Its asymptotic properties are investigated assuming that the number of assets $p$ depends on the sample size $n$ such that $\\frac{p}{n}\\rightarrow c\\in (0,+\\infty)$ as $n$ tends to infinity. The results are obtained under weak assumptions imposed on the distribution of the asset returns, namely it is only required the fourth moments existence. Furthermore, we make no assumption on the upper bound of the spectrum of the covariance matrix. As a result, the theoretical findings are also valid if the dependencies between the asset returns are described by a factor model which appears to be very popular in financial literature nowadays. This is also well-documented in a numerical study where the small- and large-sample behavior of the derived estimator are compared with existing estimators of the GMV portfolio. The resulting estimator shows significant improvements and it turns out to be robust to the deviations from normality.
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中文摘要：
我们使用随机矩阵理论的结果估计高维情况下的全局最小方差（GMV）投资组合。这种方法得到了一个无分布的收缩型估计量，它在最小化样本外方差的意义上是最优的。假设资产的数量$p$取决于样本量$n$，使得$\\frac{p}{n}\\rightarrow c\\in（0，+\\infty）$随着$n$趋于无穷大，研究了它的渐近性质。结果是在对资产收益率分布的弱假设下得到的，即只需要四阶矩存在。此外，我们对协方差矩阵的谱的上界不作任何假设。因此，如果资产收益之间的依赖关系由一个因子模型描述，那么理论结果也是有效的，这在当今的金融文献中似乎非常流行。这一点在一项数值研究中也得到了很好的证明，在该研究中，导出的估计量的小样本和大样本行为与GMV投资组合的现有估计量进行了比较。由此产生的估计量显示出显著的改进，并且对偏离正态性的情况具有鲁棒性。
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分类信息：

一级分类：Quantitative Finance 数量金融学
二级分类：Statistical Finance 统计金融
分类描述：Statistical, econometric and econophysics analyses with applications to financial markets and economic data
统计、计量经济学和经济物理学分析及其在金融市场和经济数据中的应用
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一级分类：Mathematics 数学
二级分类：Statistics Theory 统计理论
分类描述：Applied, computational and theoretical statistics: e.g. statistical inference, regression, time series, multivariate analysis, data analysis, Markov chain Monte Carlo, design of experiments, case studies
应用统计、计算统计和理论统计：例如统计推断、回归、时间序列、多元分析、数据分析、马尔可夫链蒙特卡罗、实验设计、案例研究
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一级分类：Quantitative Finance 数量金融学
二级分类：Portfolio Management 项目组合管理
分类描述：Security selection and optimization, capital allocation, investment strategies and performance measurement
证券选择与优化、资本配置、投资策略与绩效评价
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一级分类：Statistics 统计学
二级分类：Statistics Theory 统计理论
分类描述：stat.TH is an alias for math.ST. Asymptotics, Bayesian Inference, Decision Theory, Estimation, Foundations, Inference, Testing.
Stat.Th是Math.St的别名。渐近，贝叶斯推论，决策理论，估计，基础，推论，检验。
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