Optimal Covariances in Risk Model Aggregation

A.N. Kercheval (USA)


covariance matrix, risk forecast, orthogonal procrustes, matrix optimization.


Abstract: Portfolio risk forecasts are often made by esti mating an asset or factor covariance matrix. Practitioners commonly want to adjust a global covariance matrix en compassing several sub-markets by individually correcting the sub-market diagonal blocks. Since this is likely to re sult in the loss of positive semi-deļ¬niteness of the over all 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 ap proach.

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