A SimILS-Based Methodology for a Portfolio Optimization Problem with Stochastic Returns

Abstract

Combinatorial optimization has been a workhorse of financial and risk management, and it has spawned a large number of real-life applications. Prominent in this body of research is the mean-variance efficient frontier (MVEF) that emanates from the portfolio optimization problem (POP), pioneered by Harry Markowitz. A textbook version of POP minimizes risk for a given expected return on a portfolio of assets by setting the proportions of those assets. Most authors deal with the variability of returns by employing expected values. In contrast, we propose a simILS-based methodology (i.e., one extending the Iterated Local Search metaheuristic by integrating simulation), in which returns are modeled as random variables following specific probability distributions. Underlying simILS is the notion that the best solution for a scenario with expected values may have poor performance in a dynamic world.