英文标题：
《Sampling Distributions of Optimal Portfolio Weights and Characteristics
in Low and Large Dimensions》
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作者：
Taras Bodnar, Holger Dette, Nestor Parolya and Erik Thors\\\'en
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最新提交年份：
2019
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英文摘要：
Optimal portfolio selection problems are determined by the (unknown) parameters of the data generating process. If an investor want to realise the position suggested by the optimal portfolios he/she needs to estimate the unknown parameters and to account the parameter uncertainty into the decision process. Most often, the parameters of interest are the population mean vector and the population covariance matrix of the asset return distribution. In this paper we characterise the exact sampling distribution of the estimated optimal portfolio weights and their characteristics by deriving their sampling distribution which is present in terms of a stochastic representation. This approach possesses several advantages, like (i) it determines the sampling distribution of the estimated optimal portfolio weights by expressions which could be used to draw samples from this distribution efficiently; (ii) the application of the derived stochastic representation provides an easy way to obtain the asymptotic approximation of the sampling distribution. The later property is used to show that the high-dimensional asymptotic distribution of optimal portfolio weights is a multivariate normal and to determine its parameters. Moreover, a consistent estimator of optimal portfolio weights and their characteristics is derived under the high-dimensional settings. Via an extensive simulation study, we investigate the finite-sample performance of the derived asymptotic approximation and study its robustness to the violation of the model assumptions used in the derivation of the theoretical results.
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中文摘要：
最优投资组合选择问题由数据生成过程的（未知）参数决定。如果投资者想要实现最优投资组合所建议的头寸，他/她需要估计未知参数，并在决策过程中考虑参数的不确定性。通常，相关参数是资产回报分布的总体平均向量和总体协方差矩阵。在本文中，我们通过导出估计最优投资组合权重的抽样分布（以随机表示形式表示），来描述其精确抽样分布及其特征。该方法具有以下优点：（i）通过表达式确定估计的最优投资组合权重的抽样分布，可以有效地从该分布中抽取样本；（ii）导出的随机表示的应用提供了一种获得采样分布渐近近似值的简单方法。后一个性质用于证明最优投资组合权重的高维渐近分布是多元正态分布，并确定其参数。此外，在高维环境下，得到了最优投资组合权重及其特征的一致估计。通过广泛的模拟研究，我们研究了导出的渐近近似的有限样本性能，并研究了其对违反理论结果推导中使用的模型假设的鲁棒性。
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分类信息：

一级分类：Quantitative Finance 数量金融学
二级分类：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：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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