IDEAS home Printed from https://ideas.repec.org/a/spr/mathme/v93y2021i3d10.1007_s00186-021-00737-x.html
   My bibliography  Save this article

Relative utility bounds for empirically optimal portfolios

Author

Listed:
  • Dmitry B. Rokhlin

    (Southern Federal University)

Abstract

We consider a single-period portfolio selection problem for an investor, maximizing the expected ratio of the portfolio utility to the utility of a best asset taken in hindsight. The decision rules are based on the history of stock returns with unknown distribution. Assuming that the utility function is Lipschitz or Hölder continuous (the concavity is not required), we obtain high probability utility bounds under the sole assumption that the returns are independent and identically distributed. These bounds depend only on the utility function, the number of assets and the number of observations. For concave utilities similar bounds are obtained for the portfolios produced by the exponentiated gradient algorithm. Also we use statistical experiments to study risk and generalization properties of empirically optimal portfolios. Herein we consider a model with one risky asset and several datasets, containing real stock prices.

Suggested Citation

  • Dmitry B. Rokhlin, 2021. "Relative utility bounds for empirically optimal portfolios," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 93(3), pages 437-462, June.
    • Handle: RePEc:spr:mathme:v:93:y:2021:i:3:d:10.1007_s00186-021-00737-x
    DOI: 10.1007/s00186-021-00737-x
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s00186-021-00737-x
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s00186-021-00737-x?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Sujin Kim & Raghu Pasupathy & Shane G. Henderson, 2015. "A Guide to Sample Average Approximation," International Series in Operations Research & Management Science, in: Michael C Fu (ed.), Handbook of Simulation Optimization, edition 127, chapter 0, pages 207-243, Springer.
    2. Victor DeMiguel & Lorenzo Garlappi & Francisco J. Nogales & Raman Uppal, 2009. "A Generalized Approach to Portfolio Optimization: Improving Performance by Constraining Portfolio Norms," Management Science, INFORMS, vol. 55(5), pages 798-812, May.
    3. Wing-Keung Wong, 2020. "Review on behavioral economics and behavioral finance," Studies in Economics and Finance, Emerald Group Publishing Limited, vol. 37(4), pages 625-672, June.
    4. Daniel Kahneman & Amos Tversky, 2013. "Prospect Theory: An Analysis of Decision Under Risk," World Scientific Book Chapters, in: Leonard C MacLean & William T Ziemba (ed.), HANDBOOK OF THE FUNDAMENTALS OF FINANCIAL DECISION MAKING Part I, chapter 6, pages 99-127, World Scientific Publishing Co. Pte. Ltd..
    5. Jun-ya Gotoh & Akiko Takeda, 2011. "On the role of norm constraints in portfolio selection," Computational Management Science, Springer, vol. 8(4), pages 323-353, November.
    6. Ghosal,Subhashis & van der Vaart,Aad, 2017. "Fundamentals of Nonparametric Bayesian Inference," Cambridge Books, Cambridge University Press, number 9780521878265, January.
    7. Giorgio Consigli & Daniel Kuhn & Paolo Brandimarte, 2017. "Optimal Financial Decision Making Under Uncertainty," International Series in Operations Research & Management Science, in: Giorgio Consigli & Daniel Kuhn & Paolo Brandimarte (ed.), Optimal Financial Decision Making under Uncertainty, chapter 0, pages 255-290, Springer.
    8. Gabriel Frahm, 2020. "Statistical properties of estimators for the log-optimal portfolio," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 92(1), pages 1-32, August.
    9. Gonçalo Simões & Mark McDonald & Stacy Williams & Daniel Fenn & Raphael Hauser, 2018. "Relative Robust Portfolio Optimization with benchmark regret," Quantitative Finance, Taylor & Francis Journals, vol. 18(12), pages 1991-2003, December.
    10. Raphael Hauser & Vijay Krishnamurthy & Reha Tutuncu, 2013. "Relative Robust Portfolio Optimization," Papers 1305.0144, arXiv.org, revised May 2013.
    11. Dimitris Bertsimas & Nathan Kallus, 2020. "From Predictive to Prescriptive Analytics," Management Science, INFORMS, vol. 66(3), pages 1025-1044, March.
    12. James E. Smith & Robert L. Winkler, 2006. "The Optimizer's Curse: Skepticism and Postdecision Surprise in Decision Analysis," Management Science, INFORMS, vol. 52(3), pages 311-322, March.
    13. Andrew E. B. Lim & J. George Shanthikumar & Gah-Yi Vahn, 2012. "Robust Portfolio Choice with Learning in the Framework of Regret: Single-Period Case," Management Science, INFORMS, vol. 58(9), pages 1732-1746, September.
    14. Thomas M. Cover, 1991. "Universal Portfolios," Mathematical Finance, Wiley Blackwell, vol. 1(1), pages 1-29, January.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Dmitry B. Rokhlin, 2020. "Relative utility bounds for empirically optimal portfolios," Papers 2006.05204, arXiv.org.
    2. Alireza Ghahtarani & Ahmed Saif & Alireza Ghasemi, 2021. "Robust Portfolio Selection Problems: A Comprehensive Review," Papers 2103.13806, arXiv.org, revised Jan 2022.
    3. Kobayashi, Ken & Takano, Yuichi & Nakata, Kazuhide, 2023. "Cardinality-constrained distributionally robust portfolio optimization," European Journal of Operational Research, Elsevier, vol. 309(3), pages 1173-1182.
    4. 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.
    5. Alireza Ghahtarani & Ahmed Saif & Alireza Ghasemi, 2022. "Robust portfolio selection problems: a comprehensive review," Operational Research, Springer, vol. 22(4), pages 3203-3264, September.
    6. Giovanni Bonaccolto & Massimiliano Caporin & Sandra Paterlini, 2018. "Asset allocation strategies based on penalized quantile regression," Computational Management Science, Springer, vol. 15(1), pages 1-32, January.
    7. Keliang Wang & Leonardo Lozano & Carlos Cardonha & David Bergman, 2023. "Optimizing over an Ensemble of Trained Neural Networks," INFORMS Journal on Computing, INFORMS, vol. 35(3), pages 652-674, May.
    8. Shunichi Ohmori, 2021. "A Predictive Prescription Using Minimum Volume k -Nearest Neighbor Enclosing Ellipsoid and Robust Optimization," Mathematics, MDPI, vol. 9(2), pages 1-16, January.
    9. Ken Kobayashi & Yuichi Takano & Kazuhide Nakata, 2021. "Bilevel cutting-plane algorithm for cardinality-constrained mean-CVaR portfolio optimization," Journal of Global Optimization, Springer, vol. 81(2), pages 493-528, October.
    10. Andrew Butler & Roy H. Kwon, 2021. "Data-driven integration of norm-penalized mean-variance portfolios," Papers 2112.07016, arXiv.org, revised Nov 2022.
    11. Jingnan Chen & Gengling Dai & Ning Zhang, 2020. "An application of sparse-group lasso regularization to equity portfolio optimization and sector selection," Annals of Operations Research, Springer, vol. 284(1), pages 243-262, January.
    12. Qifa Xu & Junqing Zuo & Cuixia Jiang & Yaoyao He, 2021. "A large constrained time‐varying portfolio selection model with DCC‐MIDAS: Evidence from Chinese stock market," International Journal of Finance & Economics, John Wiley & Sons, Ltd., vol. 26(3), pages 3417-3435, July.
    13. Charilaos Mertzanis, 2013. "Risk Management Challenges after the Financial Crisis," Economic Notes, Banca Monte dei Paschi di Siena SpA, vol. 42(3), pages 285-320, November.
    14. Georgia Perakis & Melvyn Sim & Qinshen Tang & Peng Xiong, 2023. "Robust Pricing and Production with Information Partitioning and Adaptation," Management Science, INFORMS, vol. 69(3), pages 1398-1419, March.
    15. Johannes Bock, 2018. "An updated review of (sub-)optimal diversification models," Papers 1811.08255, arXiv.org.
    16. Michael Senescall & Rand Kwong Yew Low, 2024. "Quantitative Portfolio Management: Review and Outlook," Mathematics, MDPI, vol. 12(18), pages 1-25, September.
    17. Jun-ya Gotoh & Akiko Takeda & Rei Yamamoto, 2014. "Interaction between financial risk measures and machine learning methods," Computational Management Science, Springer, vol. 11(4), pages 365-402, October.
    18. Yen, Yu-Min & Yen, Tso-Jung, 2014. "Solving norm constrained portfolio optimization via coordinate-wise descent algorithms," Computational Statistics & Data Analysis, Elsevier, vol. 76(C), pages 737-759.
    19. Bernardo K. Pagnoncelli & Domingo Ramírez & Hamed Rahimian & Arturo Cifuentes, 2023. "A Synthetic Data-Plus-Features Driven Approach for Portfolio Optimization," Computational Economics, Springer;Society for Computational Economics, vol. 62(1), pages 187-204, June.
    20. So Yeon Chun & Miguel A. Lejeune, 2020. "Risk-Based Loan Pricing: Portfolio Optimization Approach with Marginal Risk Contribution," Management Science, INFORMS, vol. 66(8), pages 3735-3753, August.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:mathme:v:93:y:2021:i:3:d:10.1007_s00186-021-00737-x. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.