Non-linear Activated Beetle Antennae Search: A novel technique for non-convex tax-aware portfolio optimization problem

Abstract

The non-convex tax-aware portfolio optimization problem is traditionally approximated as a convex problem, which compromises the quality of the solution and converges to a local-minima instead of global minima. In this paper, we proposed a non-deterministic meta-heuristic algorithm called Non-linear Activated Beetle Antennae Search (NABAS). NABAS explores the search space at the given gradient estimate measure until it is smaller than a threshold known as “Activation Threshold”, which increases its convergence rate and avoids local minima. To test the validity of NABAS, we formulated an optimization-based tax-aware portfolio problem. The objective is to maximize the profit and minimize the risk and tax liabilities and fulfill other constraints. We collected stock data of 20 companies from the NASDAQ stock market and performed a simulation using MATLAB. A comprehensive comparison is made with BAS, PSO, and GA algorithms. The results also showed that a better-optimized portfolio is achieved with a non-convex problem than a convex problem.