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OPTIMAL COVARIANCES IN RISK MODEL AGGREGATION

机译:风险模型聚集中的最优协方差

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摘要

Portfolio risk forecasts are often made by estimating an asset or factor covariance matrix. Practitioners commonly want to adjust a global covariance matrix encompassing several sub-markets by individually correcting the sub-market diagonal blocks. Since this is likely to result in the loss of positive semi-definiteness of the overall matrix, the off-diagonal blocks must then be adjusted to restore that property. Since there are many ways to do this adjustment, this leads to an optimization problem of Procrustes type. We discuss two solutions: a closed form solution using an adapted norm, and a fast majorization approach.
机译:投资组合风险预测通常是通过估算资产或因子协方差矩阵来做出的。从业者通常希望通过单独校正子市场对角线块来调整包含多个子市场的全局协方差矩阵。由于这很可能导致整个矩阵的正半确定性损失,因此必须调整非对角线块以恢复该属性。由于有许多方法可以进行此调整,因此会导致Procrustes类型的优化问题。我们讨论两种解决方案:使用适应性范式的封闭式解决方案和快速主化方法。

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