Portfolio Construction as Linearly Constrained Separable Optimization

Nicholas Moehle, Jack Gindi, Stephen Boyd and Mykel Kochenderfer

Papers from arXiv.org

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.

Date: 2021-03, Revised 2022-07
New Economics Papers: this item is included in nep-cmp and nep-cwa
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