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Optimal VPPI strategy under Omega ratio with stochastic benchmark

Author

Listed:
  • Guohui Guan
  • Lin He
  • Zongxia Liang
  • Litian Zhang

Abstract

This paper studies a variable proportion portfolio insurance (VPPI) strategy. The objective is to determine the risk multiplier by maximizing the extended Omega ratio of the investor's cushion, using a binary stochastic benchmark. When the stock index declines, investors aim to maintain the minimum guarantee. Conversely, when the stock index rises, investors seek to track some excess returns. The optimization problem involves the combination of a non-concave objective function with a stochastic benchmark, which is effectively solved based on the stochastic version of concavification technique. We derive semi-analytical solutions for the optimal risk multiplier, and the value functions are categorized into three distinct cases. Intriguingly, the classification criteria are determined by the relationship between the optimal risky multiplier in Zieling et al. (2014 and the value of 1. Simulation results confirm the effectiveness of the VPPI strategy when applied to real market data calibrations.

Suggested Citation

  • Guohui Guan & Lin He & Zongxia Liang & Litian Zhang, 2024. "Optimal VPPI strategy under Omega ratio with stochastic benchmark," Papers 2403.13388, arXiv.org.
  • Handle: RePEc:arx:papers:2403.13388
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    References listed on IDEAS

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    1. Olga Biedova & Victoria Steblovskaya, 2020. "Multiplier Optimization For Constant Proportion Portfolio Insurance (Cppi) Strategy," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 23(02), pages 1-22, March.
    2. Weng, Chengguo, 2013. "Constant proportion portfolio insurance under a regime switching exponential Lévy process," Insurance: Mathematics and Economics, Elsevier, vol. 52(3), pages 508-521.
    3. Hambardzumyan, Hayk & Korn, Ralf, 2019. "Dynamic hybrid products with guarantees—An optimal portfolio framework," Insurance: Mathematics and Economics, Elsevier, vol. 84(C), pages 54-66.
    4. Balder, Sven & Brandl, Michael & Mahayni, Antje, 2009. "Effectiveness of CPPI strategies under discrete-time trading," Journal of Economic Dynamics and Control, Elsevier, vol. 33(1), pages 204-220, January.
    5. Jennifer N. Carpenter, 2000. "Does Option Compensation Increase Managerial Risk Appetite?," Journal of Finance, American Finance Association, vol. 55(5), pages 2311-2331, October.
    6. David Happersberger & Harald Lohre & Ingmar Nolte, 2020. "Estimating portfolio risk for tail risk protection strategies," European Financial Management, European Financial Management Association, vol. 26(4), pages 1107-1146, September.
    7. Charles Sprenger, 2015. "An Endowment Effect for Risk: Experimental Tests of Stochastic Reference Points," Journal of Political Economy, University of Chicago Press, vol. 123(6), pages 1456-1499.
    8. Leland, Hayne E, 1980. "Who Should Buy Portfolio Insurance?," Journal of Finance, American Finance Association, vol. 35(2), pages 581-594, May.
    9. Ben Ameur, H. & Prigent, J.L., 2014. "Portfolio insurance: Gap risk under conditional multiples," European Journal of Operational Research, Elsevier, vol. 236(1), pages 238-253.
    10. Huai-I. Lee & Min-Hsien Chiang & Hsinan Hsu, 2008. "A new choice of dynamic asset management: the variable proportion portfolio insurance," Applied Economics, Taylor & Francis Journals, vol. 40(16), pages 2135-2146.
    11. Jean-Luc Prigent & Philippe Bertrand, 2011. "Omega performance measure and portfolio insurance," Post-Print hal-01833064, HAL.
    12. Kapsos, Michalis & Christofides, Nicos & Rustem, Berç, 2014. "Worst-case robust Omega ratio," European Journal of Operational Research, Elsevier, vol. 234(2), pages 499-507.
    13. Xue Dong He & Steven Kou, 2018. "Profit Sharing In Hedge Funds," Mathematical Finance, Wiley Blackwell, vol. 28(1), pages 50-81, January.
    14. Annaert, Jan & Osselaer, Sofieke Van & Verstraete, Bert, 2009. "Performance evaluation of portfolio insurance strategies using stochastic dominance criteria," Journal of Banking & Finance, Elsevier, vol. 33(2), pages 272-280, February.
    15. Cox, John C. & Huang, Chi-fu, 1989. "Optimal consumption and portfolio policies when asset prices follow a diffusion process," Journal of Economic Theory, Elsevier, vol. 49(1), pages 33-83, October.
    16. Branger, Nicole & Mahayni, Antje & Schneider, Judith C., 2010. "On the optimal design of insurance contracts with guarantees," Insurance: Mathematics and Economics, Elsevier, vol. 46(3), pages 485-492, June.
    17. Dichtl, Hubert & Drobetz, Wolfgang, 2011. "Portfolio insurance and prospect theory investors: Popularity and optimal design of capital protected financial products," Journal of Banking & Finance, Elsevier, vol. 35(7), pages 1683-1697, July.
    18. Bertrand, Philippe & Prigent, Jean-luc, 2011. "Omega performance measure and portfolio insurance," Journal of Banking & Finance, Elsevier, vol. 35(7), pages 1811-1823, July.
    19. Enrico G. De Giorgi & Thierry Post, 2011. "Loss Aversion with a State-Dependent Reference Point," Management Science, INFORMS, vol. 57(6), pages 1094-1110, June.
    20. Bernard, Carole & Vanduffel, Steven & Ye, Jiang, 2019. "Optimal strategies under Omega ratio," European Journal of Operational Research, Elsevier, vol. 275(2), pages 755-767.
    21. Cesari, Riccardo & Cremonini, David, 2003. "Benchmarking, portfolio insurance and technical analysis: a Monte Carlo comparison of dynamic strategies of asset allocation," Journal of Economic Dynamics and Control, Elsevier, vol. 27(6), pages 987-1011, April.
    22. Guastaroba, G. & Mansini, R. & Ogryczak, W. & Speranza, M.G., 2016. "Linear programming models based on Omega ratio for the Enhanced Index Tracking Problem," European Journal of Operational Research, Elsevier, vol. 251(3), pages 938-956.
    23. Hongcan Lin & David Saunders & Chengguo Weng, 2019. "Portfolio Optimization With Performance Ratios," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 22(05), pages 1-38, August.
    24. Werner Dinkelbach, 1967. "On Nonlinear Fractional Programming," Management Science, INFORMS, vol. 13(7), pages 492-498, March.
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