Active extension portfolio optimization with non-convex risk measures using metaheuristics

TL;DR

This paper introduces a metaheuristic approach for optimizing active extension portfolios, effectively handling non-convex risk measures like Value-at-Risk, and demonstrates its stability and effectiveness through empirical data analysis.

Contribution

It presents a novel multi-start local search heuristic for portfolio optimization that addresses non-convex risk measures, outperforming traditional convex optimization methods in certain scenarios.

Findings

Stable solutions from the heuristic approach.

Effective minimization of Value-at-Risk.

Successful application to Dow Jones and DAX 30 data.

Abstract

We consider the optimization of active extension portfolios. For this purpose, the optimization problem is rewritten as a stochastic programming model and solved using a clever multi-start local search heuristic, which turns out to provide stable solutions. The heuristic solutions are compared to optimization results of convex optimization solvers where applicable. Furthermore, the approach is applied to solve problems with non-convex risk measures, most notably to minimize Value-at-Risk. Numerical results using data from both the Dow Jones Industrial Average as well as the DAX 30 are shown.