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Robust Growth-Optimal Portfolios

Author

Listed:
  • Napat Rujeerapaiboon

    (Risk Analytics and Optimization Chair, École Polytechnique Fédérale de Lausanne, CH-1015 Lausanne, Switzerland)

  • Daniel Kuhn

    (Risk Analytics and Optimization Chair, École Polytechnique Fédérale de Lausanne, CH-1015 Lausanne, Switzerland)

  • Wolfram Wiesemann

    (Imperial College Business School, Imperial College London, London SW7 2AZ, United Kingdom)

Abstract

The growth-optimal portfolio is designed to have maximum expected log return over the next rebalancing period. Thus, it can be computed with relative ease by solving a static optimization problem. The growth-optimal portfolio has sparked fascination among finance professionals and researchers because it can be shown to outperform any other portfolio with probability 1 in the long run. In the short run, however, it is notoriously volatile. Moreover, its computation requires precise knowledge of the asset return distribution, which is not directly observable but must be inferred from sparse data. By using methods from distributionally robust optimization, we design fixed-mix strategies that offer similar performance guarantees as the growth-optimal portfolio but for a finite investment horizon and for a whole family of distributions that share the same first- and second-order moments. We demonstrate that the resulting robust growth-optimal portfolios can be computed efficiently by solving a tractable conic program whose size is independent of the length of the investment horizon. Simulated and empirical backtests show that the robust growth-optimal portfolios are competitive with the classical growth-optimal portfolio across most realistic investment horizons and for an overwhelming majority of contaminated return distributions. This paper was accepted by Yinyu Ye, optimization .

Suggested Citation

  • Napat Rujeerapaiboon & Daniel Kuhn & Wolfram Wiesemann, 2016. "Robust Growth-Optimal Portfolios," Management Science, INFORMS, vol. 62(7), pages 2090-2109, July.
    • Handle: RePEc:inm:ormnsc:v:62:y:2016:i:7:p:2090-2109
    DOI: 10.1287/mnsc.2015.2228
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    References listed on IDEAS

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    4. Alireza Ghahtarani & Ahmed Saif & Alireza Ghasemi, 2022. "Robust portfolio selection problems: a comprehensive review," Operational Research, Springer, vol. 22(4), pages 3203-3264, September.
    5. Pätäri, Eero & Ahmed, Sheraz & Luukka, Pasi & Yeomans, Julian Scott, 2023. "Can monthly-return rank order reveal a hidden dimension of momentum? The post-cost evidence from the U.S. stock markets," The North American Journal of Economics and Finance, Elsevier, vol. 65(C).
    6. Ling, Aifan & Sun, Jie & Wang, Meihua, 2020. "Robust multi-period portfolio selection based on downside risk with asymmetrically distributed uncertainty set," European Journal of Operational Research, Elsevier, vol. 285(1), pages 81-95.
    7. Chung-Han Hsieh, 2021. "On Asymptotic Log-Optimal Buy-and-Hold Strategy," Papers 2103.04898, arXiv.org.
    8. Ariel Neufeld & Matthew Ng Cheng En & Ying Zhang, 2024. "Robust SGLD algorithm for solving non-convex distributionally robust optimisation problems," Papers 2403.09532, arXiv.org.
    9. Ariel Neufeld & Julian Sester, 2024. "Non-concave distributionally robust stochastic control in a discrete time finite horizon setting," Papers 2404.05230, arXiv.org.
    10. Ling, Aifan & Li, Junxue & Wen, Limin & Zhang, Yi, 2023. "When trackers are aware of ESG: Do ESG ratings matter to tracking error portfolio performance?," Economic Modelling, Elsevier, vol. 125(C).
    11. Ashrafi, Hedieh & Thiele, Aurélie C., 2021. "A study of robust portfolio optimization with European options using polyhedral uncertainty sets," Operations Research Perspectives, Elsevier, vol. 8(C).
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    14. Napat Rujeerapaiboon & Daniel Kuhn & Wolfram Wiesemann, 2018. "Chebyshev Inequalities for Products of Random Variables," Mathematics of Operations Research, INFORMS, vol. 43(3), pages 887-918, August.

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