Unveil stock correlation via a new tensor-based decomposition method

TL;DR

This paper introduces a novel tensor-based decomposition method called Slice-Diagonal Tensor (SDT) for estimating stable correlation matrices in finance, independent of sample period, enhancing portfolio risk management.

Contribution

The paper proposes a new tensor decomposition technique, SDT, which is more parsimonious and flexible than existing methods, providing stable correlation matrices unaffected by sample period.

Findings

SDT outperforms Tucker and PARAFAC in stability and flexibility.

Correlation matrices derived from SDT show structural dependencies.

Method is robust across simulated and empirical data.

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 doesn't 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. Moreover, this methodology applied to both simulated and empirical data shows results which are robust to two non-parametric tests, namely Kruskal-Wallis and Kolmogorov-Smirnov tests. Since the resulting correlation matrix features stability and emerging structural dependency properties, it can be used as alternative to other correlation matrices type of measures, including the Person correlation.