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Optimal Guaranteed Return Portfolios and the Casino Effect

Author

Listed:
  • Cees Dert

    (ABN-AMRO Asset Management, P.O. Box 283, 1000 AE Amsterdam, The Netherlands, and Free University of Amsterdam, Financial Sector Management, De Boelelaan 1105, 1081 HV Amsterdam, The Netherlands)

  • Bart Oldenkamp

    (ABN-AMRO Asset Management, P.O. Box 283, 1000 AE Amsterdam, The Netherlands, and Erasmus University Rotterdam, Econometric Institute, P.O. Box 1738, 3000 DR Rotterdam, The Netherlands)

Abstract

In this paper we address the problem of determining optimal portfolios that may include options in a framework of return maximization with risk constraints relative to a benchmark, as well as in terms of absolute returns. The model we propose allows for deterministic constraints as well as probabilistic constraints. We derive properties of optimal and feasible portfolios and present a linear programming model to solve the problem. The optimal portfolios have payoff functions that reflect a gambling policy. We show that optimal solutions to a large class of portfolio models that maximize expected return subject to downside risk constraints are driven by this casino effect and present tractable conditions under which it occurs in our model. We propose to control the casino effect by using chance constraints. Using results from financial theory, we formulate an LP model that maximizes expected return subject to worst-case return constraints and chance constraints on achieving prespecified levels of return. The results are illustrated with real-life data on the S&P 500 index.

Suggested Citation

  • Cees Dert & Bart Oldenkamp, 2000. "Optimal Guaranteed Return Portfolios and the Casino Effect," Operations Research, INFORMS, vol. 48(5), pages 768-775, October.
    • Handle: RePEc:inm:oropre:v:48:y:2000:i:5:p:768-775
    DOI: 10.1287/opre.48.5.768.12400
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    References listed on IDEAS

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    1. Philip H. Dybvig, 1988. "Inefficient Dynamic Portfolio Strategies or How to Throw Away a Million Dollars in the Stock Market," The Review of Financial Studies, Society for Financial Studies, vol. 1(1), pages 67-88.
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    Cited by:

    1. André Lucas & Arjen Siegmann, 2008. "The Effect of Shortfall as a Risk Measure for Portfolios with Hedge Funds," Journal of Business Finance & Accounting, Wiley Blackwell, vol. 35(1‐2), pages 200-226, January.
    2. Zhi Chen & Daniel Kuhn & Wolfram Wiesemann, 2024. "Technical Note—Data-Driven Chance Constrained Programs over Wasserstein Balls," Operations Research, INFORMS, vol. 72(1), pages 410-424, January.
    3. Zymler, Steve & Rustem, Berç & Kuhn, Daniel, 2011. "Robust portfolio optimization with derivative insurance guarantees," European Journal of Operational Research, Elsevier, vol. 210(2), pages 410-424, April.
    4. Arjen Siegmann & André Lucas, 2005. "Discrete-Time Financial Planning Models Under Loss-Averse Preferences," Operations Research, INFORMS, vol. 53(3), pages 403-414, June.
    5. Grani A. Hanasusanto & Vladimir Roitch & Daniel Kuhn & Wolfram Wiesemann, 2017. "Ambiguous Joint Chance Constraints Under Mean and Dispersion Information," Operations Research, INFORMS, vol. 65(3), pages 751-767, June.
    6. M. Schyns & Y. Crama & G. Hübner, 2010. "Optimal selection of a portfolio of options under Value-at-Risk constraints: a scenario approach," Annals of Operations Research, Springer, vol. 181(1), pages 683-708, December.
    7. Arjan Berkelaar & Cees Dert & Bart Oldenkamp & Shuzhong Zhang, 2002. "A Primal-Dual Decomposition-Based Interior Point Approach to Two-Stage Stochastic Linear Programming," Operations Research, INFORMS, vol. 50(5), pages 904-915, October.
    8. Valle, C.A. & Meade, N. & Beasley, J.E., 2014. "Absolute return portfolios," Omega, Elsevier, vol. 45(C), pages 20-41.

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