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Portfolio Construction as Linearly Constrained Separable Optimization

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Listed:
  • Nicholas Moehle
  • Jack Gindi
  • Stephen Boyd
  • Mykel Kochenderfer

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.

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  • Nicholas Moehle & Jack Gindi & Stephen Boyd & Mykel Kochenderfer, 2021. "Portfolio Construction as Linearly Constrained Separable Optimization," Papers 2103.05455, arXiv.org, revised Jul 2022.
    • Handle: RePEc:arx:papers:2103.05455
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    References listed on IDEAS

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    1. William F. Sharpe, 1963. "A Simplified Model for Portfolio Analysis," Management Science, INFORMS, vol. 9(2), pages 277-293, January.
    2. Nicholas Moehle & Mykel J. Kochenderfer & Stephen Boyd & Andrew Ang, 2021. "Tax-Aware Portfolio Construction via Convex Optimization," Journal of Optimization Theory and Applications, Springer, vol. 189(2), pages 364-383, May.
    3. Nicholas Moehle & Mykel J. Kochenderfer & Stephen Boyd & Andrew Ang, 2020. "Tax-Aware Portfolio Construction via Convex Optimization," Papers 2008.04985, arXiv.org, revised Feb 2021.
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    Cited by:

    1. Stephen Boyd & Kasper Johansson & Ronald Kahn & Philipp Schiele & Thomas Schmelzer, 2024. "Markowitz Portfolio Construction at Seventy," Papers 2401.05080, arXiv.org.

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