Unveil stock correlation via a new tensor-based decomposition method

Abstract

Portfolio allocation and risk management make use of correlation matrices and heavily rely on the choice of a proper correlation matrix to be used. In this regard, one important question is related to the choice of the proper sample period to be used to estimate a stable correlation matrix. This paper addresses this question and proposes a new methodology to estimate the correlation matrix which does not depend on the chosen sample period. This new methodology is based on tensor factorization techniques. In particular, combining and normalizing factor components, we build a correlation matrix which shows emerging structural dependency properties not affected by the sample period. To retrieve the factor components, we propose a new tensor decomposition (which we name Slice-Diagonal Tensor (SDT) factorization) and compare it to the two most used tensor decompositions, the Tucker and the PARAFAC. We have that the new factorization is more parsimonious than the Tucker decomposition and more flexible than the PARAFAC. We apply our methodology to simulated datasets using different simulation parameters. Results are robust to different simulation settings and confirm the stability of the correlation matrix generated for two independent samples. The proposed tool applied to two independent samples of empirical data shows that the correlation matrices generated have a block structure representing stock industries. Furthermore, in accordance to two non-parametric tests, namely Kruskal–Wallis and Kolmogorov–Smirnov tests, the correlation matrices are statistically time invariant and hence, stable. Since the resulting correlation matrix is characterized by stability and emerging structural dependency properties, it can be used as alternative to other correlation matrices type of measures, including the Pearson correlation.