The use of the multi-cumulant tensor analysis for the algorithmic optimisation of investment portfolios

TL;DR

This paper introduces a novel cumulant tensor-based algorithm using the Alternating Least Squares method to optimize investment portfolios by minimizing higher-order cumulants, tested on stock data during a crash.

Contribution

The paper develops a new algorithm based on cumulant tensors up to the 6th order for portfolio optimization, a novel approach in financial data analysis.

Findings

Algorithm outperforms benchmarks during low Hurst exponent periods.

Effective in identifying low-variability portfolios during market crashes.

Potential applicability to other non-Gaussian data analysis.

Abstract

The cumulant analysis plays an important role in non Gaussian distributed data analysis. The shares' prices returns are good example of such data. The purpose of this research is to develop the cumulant based algorithm and use it to determine eigenvectors that represent investment portfolios with low variability. Such algorithm is based on the Alternating Least Square method and involves the simultaneous minimisation 2'nd -- 6'th cumulants of the multidimensional random variable (percentage shares' returns of many companies). Then the algorithm was tested during the recent crash on the Warsaw Stock Exchange. To determine incoming crash and provide enter and exit signal for the investment strategy the Hurst exponent was calculated using the local DFA. It was shown that introduced algorithm is on average better that benchmark and other portfolio determination methods, but only within examination window determined by low values of the Hurst exponent. Remark that the algorithm of is based on cumulant tensors up to the 6'th order calculated for a multidimensional random variable, what is the novel idea. It can be expected that the algorithm would be useful in the financial data analysis on the world wide scale as well as in the analysis of other types of non Gaussian distributed data.