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Portfolio allocation and risk management make use of correlation matrices andheavily rely on the choice of a proper correlation matrix to be used. In thisregard, one important question is related to the choice of the proper sampleperiod to be used to estimate a stable correlation matrix. This paper addressesthis question and proposes a new methodology to estimate the correlation matrixwhich doesn't depend on the chosen sample period. This new methodology is basedon tensor factorization techniques. In particular, combining and normalizingfactor components, we build a correlation matrix which shows emergingstructural dependency properties not affected by the sample period. To retrievethe factor components, we propose a new tensor decomposition (which we nameSlice-Diagonal Tensor (SDT) factorization) and compare it to the two most usedtensor decompositions, the Tucker and the PARAFAC. We have that the newfactorization is more parsimonious than the Tucker decomposition and moreflexible than the PARAFAC. Moreover, this methodology applied to both simulatedand empirical data shows results which are robust to two non-parametric tests,namely Kruskal-Wallis and Kolmogorov-Smirnov tests. Since the resultingcorrelation matrix features stability and emerging structural dependencyproperties, it can be used as alternative to other correlation matrices type ofmeasures, including the Person correlation.

Unveil stock correlation via a new tensor-based decomposition method