摘要翻译：
本文得到了复Wishart矩阵的逆的期望的一个性质，它是由复Wishart矩阵的正交不变性引起的。利用这一性质和随机矩阵理论(RMT)的结果，我们得到了估计协方差矩阵所引起的噪声对最优投资组合风险计算的渐近影响。这进而使我们不仅在独立观测情况下，而且在相关观测情况下，得到最优投资组合风险的渐近无偏估计。这种改进提供了一种基于指数加权移动平均股票收益估计的协方差矩阵估计投资组合风险的新方法。
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英文标题：
《Compound Wishart Matrices and Noisy Covariance Matrices: Risk
Underestimation》
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作者：
Beno\\^it Collins, David McDonald and Nadia Saad
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最新提交年份：
2013
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分类信息：

一级分类：Quantitative Finance 数量金融学
二级分类：Risk Management 风险管理
分类描述：Measurement and management of financial risks in trading, banking, insurance, corporate and other applications
衡量和管理贸易、银行、保险、企业和其他应用中的金融风险
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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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英文摘要：
In this paper, we obtain a property of the expectation of the inverse of compound Wishart matrices which results from their orthogonal invariance. Using this property as well as results from random matrix theory (RMT), we derive the asymptotic effect of the noise induced by estimating the covariance matrix on computing the risk of the optimal portfolio. This in turn enables us to get an asymptotically unbiased estimator of the risk of the optimal portfolio not only for the case of independent observations but also in the case of correlated observations. This improvement provides a new approach to estimate the risk of a portfolio based on covariance matrices estimated from exponentially weighted moving averages of stock returns.
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