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In portfolio risk management, a global covariance matrix forecast often needs to be adjusted by changing diagonal blocks corresponding to specific sub-markets. Unless certain constraints are obeyed, this can result in the loss of positive definiteness of the global matrix. Imposing the proper constraints while minimizing the disturbance of off-diagonal blocks leads to a non-convex optimization problem in numerical linear algebra called the Weighted Orthogonal Procrustes Problem. We analyze and compare two local minimizing algorithms and offer an algorithm for global minimization. Our methods are faster and more effective than current numerical methods for covariance matrix revision.
