Portfolio Construction as Linearly Constrained Separable Optimization

TL;DR

This paper introduces a fast heuristic algorithm based on ADMM for complex mean-variance portfolio optimization problems with nonconvex, separable terms, demonstrating efficiency and effectiveness in tax-aware portfolio construction.

Contribution

It presents a novel ADMM-based heuristic for nonconvex, separable portfolio optimization problems with performance bounds and practical implementation details.

Findings

Solve times in tens to hundreds of milliseconds for ~1000 securities

Effective in tax-aware portfolio construction

Provides bounds on achievable performance

Abstract

Mean-variance portfolio optimization problems often involve separable nonconvex terms, including penalties on capital gains, integer share constraints, and minimum position and trade sizes. We propose a heuristic algorithm for such problems based on the alternating direction method of multipliers (ADMM). This method allows for solve times in tens to hundreds of milliseconds with around 1000 securities and 100 risk factors. We also obtain a bound on the achievable performance. Our heuristic and bound are both derived from similar results for other optimization problems with a separable objective and affine equality constraints. We discuss a concrete implementation in the case where the separable terms in the objective are piecewise quadratic, and we empirically demonstrate its effectiveness for tax-aware portfolio construction.