复合Wishart矩阵与噪声协方差矩阵：风险低估
Compound Wishart Matrices and Noisy Covariance Matrices: Risk Underestimation
摘要：
本文利用复合Wishart矩阵的正交不变性，得到了复合Wishart矩阵逆的期望的一个性质。利用这一性质以及随机矩阵理论（RMT）的结果，我们推导出估计协方差矩阵对计算最优投资组合风险的噪声的渐近效应。这反过来又使我们能够得到一个渐近无偏估计的最优投资组合的风险，不仅在独立的情况下，而且在相关的观察。这种改进提供了一种新的方法来估计投资组合的风险的基础上估计的协方差矩阵的指数加权移动平均的股票收益。
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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