Rotationally invariant estimators on portfolio optimization to unveil financial risk’s states

Abstract

Rotationally Invariant Estimators (RIE) are a new family of covariance matrix estimators based on random matrix theory and free probability. The family RIE has been proposed to improve the performance of an investment portfolio in the Markowitz model’s framework. Here, we apply state-of-the-art RIE techniques to improve the estimation of financial states via the correlation matrix. The Synthesized Clustering (SYNCLUS) and a dynamic programming algorithm for optimal one-dimensional clustering were employed to that aim. We found that the RIE estimations of the minimum portfolio risk increase the Active Information Storage (AIS) in the American and European markets. AIS’s local dynamic also mimics financial states’ behavior when estimating under the one-dimensional clustering algorithm. Our results suggest that in times of financial turbulence, RIE estimates can be of great advantage in minimizing risk exposure.