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Risk management strategies for finding universal portfolios

Author

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  • Esther Mohr

    (University of Mannheim)

  • Robert Dochow

    (Saarland University)

Abstract

We consider Cover’s universal portfolio and the problem of risk management in a distribution-free setting when learning from experts. We aim to find optimal portfolios without modelling the financial market at the outset. Although it exists, the price distribution of the constituent assets is neither known nor given as part of the input. We consider the portfolio selection problem from the perspective of online algorithms that process input piece-by-piece in a serial fashion. Under the minimax regret criterion, we propose two risk-adjusted algorithms that track the expert with the lowest maximum drawdown. We obtain upper bounds on the worst-case performance of our algorithms that equal the bounds obtained by Cover (Math Finance 1(1):1–29, 1991). We also present computational evidence using NYSE data over a 22-year period, which shows superior performance of investment strategies that take risk management into account.

Suggested Citation

  • Esther Mohr & Robert Dochow, 2017. "Risk management strategies for finding universal portfolios," Annals of Operations Research, Springer, vol. 256(1), pages 129-147, September.
    • Handle: RePEc:spr:annopr:v:256:y:2017:i:1:d:10.1007_s10479-016-2176-6
    DOI: 10.1007/s10479-016-2176-6
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    1. Xiaoqiang Cai & Kok-Lay Teo & Xiaoqi Yang & Xun Yu Zhou, 2000. "Portfolio Optimization Under a Minimax Rule," Management Science, INFORMS, vol. 46(7), pages 957-972, July.
    2. Mark Rubinstein, 2002. "Markowitz's “Portfolio Selection”: A Fifty‐Year Retrospective," Journal of Finance, American Finance Association, vol. 57(3), pages 1041-1045, June.
    3. Georgia Perakis & Guillaume Roels, 2008. "Regret in the Newsvendor Model with Partial Information," Operations Research, INFORMS, vol. 56(1), pages 188-203, February.
    4. Gulpinar, Nalan & Rustem, Berc, 2007. "Worst-case robust decisions for multi-period mean-variance portfolio optimization," European Journal of Operational Research, Elsevier, vol. 183(3), pages 981-1000, December.
    5. Gaivoronski, A & Stella, F, 2000. "Nonstationary Optimization Approach for Finding Universal Portfolios," MPRA Paper 21913, University Library of Munich, Germany.
    6. Iftikhar Ahmad & Esther Mohr & Günter Schmidt, 2014. "Competitive Ratio as Coherent Measure of Risk," Operations Research Proceedings, in: Stefan Helber & Michael Breitner & Daniel Rösch & Cornelia Schön & Johann-Matthias Graf von der Schu (ed.), Operations Research Proceedings 2012, edition 127, pages 63-69, Springer.
    7. Alexei Gaivoronski & Fabio Stella, 2000. "Stochastic Nonstationary Optimization for Finding Universal Portfolios," Annals of Operations Research, Springer, vol. 100(1), pages 165-188, December.
    8. K.L. Teo & X.Q. Yang, 2001. "Portfolio Selection Problem with Minimax Type Risk Function," Annals of Operations Research, Springer, vol. 101(1), pages 333-349, January.
    9. Martin R. Young, 1998. "A Minimax Portfolio Selection Rule with Linear Programming Solution," Management Science, INFORMS, vol. 44(5), pages 673-683, May.
    10. Stefan Helber & Michael Breitner & Daniel Rösch & Cornelia Schön & Johann-Matthias Graf von der Schu (ed.), 2014. "Operations Research Proceedings 2012," Operations Research Proceedings, Springer, edition 127, number 978-3-319-00795-3, March.
    11. Huang, Xiaoxia, 2008. "Portfolio selection with a new definition of risk," European Journal of Operational Research, Elsevier, vol. 186(1), pages 351-357, April.
    12. Sharpe, William F., 1971. "A Linear Programming Approximation for the General Portfolio Analysis Problem," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 6(5), pages 1263-1275, December.
    13. Deng, Xiao-Tie & Li, Zhong-Fei & Wang, Shou-Yang, 2005. "A minimax portfolio selection strategy with equilibrium," European Journal of Operational Research, Elsevier, vol. 166(1), pages 278-292, October.
    14. David P. Helmbold & Robert E. Schapire & Yoram Singer & Manfred K. Warmuth, 1998. "On‐Line Portfolio Selection Using Multiplicative Updates," Mathematical Finance, Wiley Blackwell, vol. 8(4), pages 325-347, October.
    15. Patrick O'Sullivan & David Edelman, 2015. "Adaptive universal portfolios," The European Journal of Finance, Taylor & Francis Journals, vol. 21(4), pages 337-351, March.
    16. Polak, George G. & Rogers, David F. & Sweeney, Dennis J., 2010. "Risk management strategies via minimax portfolio optimization," European Journal of Operational Research, Elsevier, vol. 207(1), pages 409-419, November.
    17. Robert Dochow & Esther Mohr & Günter Schmidt, 2014. "Risk-Adjusted On-line Portfolio Selection," Operations Research Proceedings, in: Dennis Huisman & Ilse Louwerse & Albert P.M. Wagelmans (ed.), Operations Research Proceedings 2013, edition 127, pages 113-119, Springer.
    18. Stone, Bernell K., 1973. "A Linear Programming Formulation of the General Portfolio Selection Problem†," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 8(4), pages 621-636, September.
    19. Michael J. Best & Robert R. Grauer, 1991. "Sensitivity Analysis for Mean-Variance Portfolio Problems," Management Science, INFORMS, vol. 37(8), pages 980-989, August.
    20. Michael O. Ball & Maurice Queyranne, 2009. "Toward Robust Revenue Management: Competitive Analysis of Online Booking," Operations Research, INFORMS, vol. 57(4), pages 950-963, August.
    21. Thomas M. Cover, 1991. "Universal Portfolios," Mathematical Finance, Wiley Blackwell, vol. 1(1), pages 1-29, January.
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