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End-to-end, decision-based, cardinality-constrained portfolio optimization

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  • Anis, Hassan T.
  • Kwon, Roy H.

Abstract

Portfolios employing a (factor) risk model are usually constructed using a two step process: first, the risk model parameters are estimated, then the portfolio is constructed. Recent works have shown that this decoupled approach may be improved using an integrated framework that takes the downstream portfolio optimization into account during parameter estimation. In this work we implement an integrated, end-to-end, predict-&-optimize framework to the cardinality-constrained portfolio optimization problem. To the best of our knowledge, we are the first to implement the framework to a nonlinear mixed integer programming problem. Since the feasible region of the problem is discontinuous, we are unable to directly differentiate through it. Thus, we compare three different continuous relaxations of increasing tightness to the problem which are placed as an implicit layers in a neural network. The parameters of the factor model governing the problem’s covariance matrix structure are learned using a loss function that directly corresponds to the decision quality made based on the factor model’s predictions. Using real world financial data, our proposed end-to-end, decision based model is compared to two decoupled alternatives. Results show significant improvements over the traditional decoupled approaches across all cardinality sizes and model variations while highlighting the need of additional research into the interplay between experimental design, problem size and structure, and relaxation tightness in a combinatorial setting.

Suggested Citation

  • Anis, Hassan T. & Kwon, Roy H., 2025. "End-to-end, decision-based, cardinality-constrained portfolio optimization," European Journal of Operational Research, Elsevier, vol. 320(3), pages 739-753.
  • Handle: RePEc:eee:ejores:v:320:y:2025:i:3:p:739-753
    DOI: 10.1016/j.ejor.2024.08.030
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    References listed on IDEAS

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    1. Brendan O’Donoghue & Eric Chu & Neal Parikh & Stephen Boyd, 2016. "Conic Optimization via Operator Splitting and Homogeneous Self-Dual Embedding," Journal of Optimization Theory and Applications, Springer, vol. 169(3), pages 1042-1068, June.
    2. Anis, Hassan T. & Kwon, Roy H., 2022. "Cardinality-constrained risk parity portfolios," European Journal of Operational Research, Elsevier, vol. 302(1), pages 392-402.
    3. X. Cui & X. Zheng & S. Zhu & X. Sun, 2013. "Convex relaxations and MIQCQP reformulations for a class of cardinality-constrained portfolio selection problems," Journal of Global Optimization, Springer, vol. 56(4), pages 1409-1423, August.
    4. Fama, Eugene F. & French, Kenneth R., 2015. "A five-factor asset pricing model," Journal of Financial Economics, Elsevier, vol. 116(1), pages 1-22.
    5. Yongjae Lee & Min Jeong Kim & Jang Ho Kim & Ju Ri Jang & Woo Chang Kim, 2020. "Sparse and robust portfolio selection via semi-definite relaxation," Journal of the Operational Research Society, Taylor & Francis Journals, vol. 71(5), pages 687-699, May.
    6. Levi, Yaron & Welch, Ivo, 2017. "Best Practice for Cost-of-Capital Estimates," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 52(2), pages 427-463, April.
    7. Merton, Robert C., 1980. "On estimating the expected return on the market : An exploratory investigation," Journal of Financial Economics, Elsevier, vol. 8(4), pages 323-361, December.
    8. Angelika Wiegele & Shudian Zhao, 2022. "Tight SDP Relaxations for Cardinality-Constrained Problems," Lecture Notes in Operations Research, in: Norbert Trautmann & Mario Gnägi (ed.), Operations Research Proceedings 2021, pages 167-172, Springer.
    9. Xiaojin Zheng & Xiaoling Sun & Duan Li, 2014. "Improving the Performance of MIQP Solvers for Quadratic Programs with Cardinality and Minimum Threshold Constraints: A Semidefinite Program Approach," INFORMS Journal on Computing, INFORMS, vol. 26(4), pages 690-703, November.
    10. Best, Michael J & Grauer, Robert R, 1991. "On the Sensitivity of Mean-Variance-Efficient Portfolios to Changes in Asset Means: Some Analytical and Computational Results," The Review of Financial Studies, Society for Financial Studies, vol. 4(2), pages 315-342.
    11. Dimitris Bertsimas & Ryan Cory-Wright, 2022. "A Scalable Algorithm for Sparse Portfolio Selection," INFORMS Journal on Computing, INFORMS, vol. 34(3), pages 1489-1511, May.
    12. Antonio Frangioni & Fabio Furini & Claudio Gentile, 2016. "Approximated perspective relaxations: a project and lift approach," Computational Optimization and Applications, Springer, vol. 63(3), pages 705-735, April.
    13. Alwosheel, Ahmad & van Cranenburgh, Sander & Chorus, Caspar G., 2018. "Is your dataset big enough? Sample size requirements when using artificial neural networks for discrete choice analysis," Journal of choice modelling, Elsevier, vol. 28(C), pages 167-182.
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