Constrained Max Drawdown: a Fast and Robust Portfolio Optimization Approach

TL;DR

The paper addresses robust and scalable portfolio optimization by proposing a linear Maximum Drawdown (MD) framework as an alternative to the classical Markowitz quadratic model. It develops a sequence of models, from a standard MD LP to a constrained MILP variant that enforces minimum allocations, and demonstrates dramatic speedups (up to ~200x) over the traditional QP, with competitive risk-return profiles. Using COVID-era data for ~400 US stocks, the authors show MD approaches reduce maximum drawdown and, in out-of-sample tests, yield strong returns relative to Markowitz baselines, while the MILP version offers noticeably improved robustness to parameter perturbations. The work highlights practical benefits for real-time or large-universe portfolio optimization and suggests future extensions to multi-period or stochastic settings to further enhance robustness and performance.

Abstract

We propose an alternative linearization to the classical Markowitz quadratic portfolio optimization model, based on maximum drawdown. This model, which minimizes maximum portfolio drawdown, is particularly appealing during times of financial distress, like during the COVID-19 pandemic. In addition, we will present a Mixed-Integer Linear Programming variation of our new model that, based on our out-of-sample results and sensitivity analysis, delivers a more profitable and robust solution with a 200 times faster solving time compared to the standard Markowitz quadratic formulation.