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Wasserstein-Kelly Portfolios: A Robust Data-Driven Solution to Optimize Portfolio Growth

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  • Jonathan Yu-Meng Li

Abstract

We introduce a robust variant of the Kelly portfolio optimization model, called the Wasserstein-Kelly portfolio optimization. Our model, taking a Wasserstein distributionally robust optimization (DRO) formulation, addresses the fundamental issue of estimation error in Kelly portfolio optimization by defining a ``ball" of distributions close to the empirical return distribution using the Wasserstein metric and seeking a robust log-optimal portfolio against the worst-case distribution from the Wasserstein ball. Enhancing the Kelly portfolio using Wasserstein DRO is a natural step to take, given many successful applications of the latter in areas such as machine learning for generating robust data-driven solutions. However, naive application of Wasserstein DRO to the growth-optimal portfolio problem can lead to several issues, which we resolve through careful modelling. Our proposed model is both practically motivated and efficiently solvable as a convex program. Using empirical financial data, our numerical study demonstrates that the Wasserstein-Kelly portfolio can outperform the Kelly portfolio in out-of-sample testing across multiple performance metrics and exhibits greater stability.

Suggested Citation

  • Jonathan Yu-Meng Li, 2023. "Wasserstein-Kelly Portfolios: A Robust Data-Driven Solution to Optimize Portfolio Growth," Papers 2302.13979, arXiv.org.
    • Handle: RePEc:arx:papers:2302.13979
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    1. Henry Allen Latane, 1959. "Criteria for Choice Among Risky Ventures," Journal of Political Economy, University of Chicago Press, vol. 67(2), pages 144-144.
    2. Merton, Robert C. & Samuelson, Paul A., 1974. "Fallacy of the log-normal approximation to optimal portfolio decision-making over many periods," Journal of Financial Economics, Elsevier, vol. 1(1), pages 67-94, May.
    3. Chung-Han Hsieh, 2022. "On Solving Robust Log-Optimal Portfolio: A Supporting Hyperplane Approximation Approach," Papers 2202.03858, arXiv.org.
    4. 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.
    5. Erick Delage & Yinyu Ye, 2010. "Distributionally Robust Optimization Under Moment Uncertainty with Application to Data-Driven Problems," Operations Research, INFORMS, vol. 58(3), pages 595-612, June.
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    Cited by:

    1. Anton V. Proskurnikov & B. Ross Barmish, 2023. "On the Benefit of Nonlinear Control for Robust Logarithmic Growth: Coin Flipping Games as a Demonstration Case," Papers 2303.10417, arXiv.org, revised May 2023.
    2. Hsieh, Chung-Han, 2024. "On solving robust log-optimal portfolio: A supporting hyperplane approximation approach," European Journal of Operational Research, Elsevier, vol. 313(3), pages 1129-1139.

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