Data-Driven Robust and Sparse Solutions for Large-scale Fuzzy Portfolio Optimization

There has been a growing interest in combining randomness and fuzziness to solve portfolio optimization problems in finance. However, many proposed fuzzy methods remain difficult to use in practice and hence, there is a need for efficient and robust approaches to obtain the optimal weights of the fuzzy models for real data. This paper focuses on the large-scale no short-selling fuzzy portfolio selection by modelling the returns of assets as nonlinear adaptive fuzzy numbers including trapezoidal fuzzy numbers. Moreover, the data-driven algorithmic approach proposed in this paper provides optimal portfolio weights by focusing on the robustness and sparsity of the solution. The proposed algorithms include interior-point (IP) with global search, pattern search (PS) with multiple starts, genetic algorithm (GA), ordered random weights algorithm (ORWA), and particle swarm optimization (PSO). Using 150 most traded stock prices downloaded from Yahoo finance, experiments are carried out and the results are described. The main findings are that out of the five proposed algorithms the PS (PSO) algorithm outperforms the rest in terms of robustness and sparsity to construct the optimal fuzzy minimum variance (tangency) portfolios respectively.