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A Dynamic AutoRegressive Expectile for Time-Invariant Portfolio Protection Strategies

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  • Benjamin HAMIDI
  • Bertrand MAILLET
  • Jean-Luc PRIGENT

Abstract

"Constant proportion portfolio insurance" is a popular technique among portfolio insurance strategies: the risky part of a portfolio is reallocated with respect to market conditions, via a fixed parameter (the multiple), guaranteeing a predetermined floor. We propose here to use a conditional time-varying multiple as an alternative. We provide the main properties of the conditional multiples for some mainstream cases, including discrete-time rebalancing and an underlying risk asset driven by the Lévy process, while evaluating conditional and unconditional gap risks. Finally, we evaluate the use of a dynamic autoregressive expectile model for estimating the conditional multiple in such a context.
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  • Benjamin HAMIDI & Bertrand MAILLET & Jean-Luc PRIGENT, 2013. "A Dynamic AutoRegressive Expectile for Time-Invariant Portfolio Protection Strategies," LEO Working Papers / DR LEO 164, Orleans Economics Laboratory / Laboratoire d'Economie d'Orleans (LEO), University of Orleans.
    • Handle: RePEc:leo:wpaper:164
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    1. Caporin, Massimiliano & Costola, Michele & Jannin, Gregory & Maillet, Bertrand, 2018. "“On the (Ab)use of Omega?”," Journal of Empirical Finance, Elsevier, vol. 46(C), pages 11-33.
    2. Nieto, María Rosa, 2008. "Measuring financial risk : comparison of alternative procedures to estimate VaR and ES," DES - Working Papers. Statistics and Econometrics. WS ws087326, Universidad Carlos III de Madrid. Departamento de Estadística.
    3. James W. Taylor, 2008. "Using Exponentially Weighted Quantile Regression to Estimate Value at Risk and Expected Shortfall," Journal of Financial Econometrics, Oxford University Press, vol. 6(3), pages 382-406, Summer.
    4. Kuan, Chung-Ming & Yeh, Jin-Huei & Hsu, Yu-Chin, 2009. "Assessing value at risk with CARE, the Conditional Autoregressive Expectile models," Journal of Econometrics, Elsevier, vol. 150(2), pages 261-270, June.
    5. S. G. Kou, 2002. "A Jump-Diffusion Model for Option Pricing," Management Science, INFORMS, vol. 48(8), pages 1086-1101, August.
    6. Robert F. Engle & Jose Gonzalo Rangel, 2008. "The Spline-GARCH Model for Low-Frequency Volatility and Its Global Macroeconomic Causes," The Review of Financial Studies, Society for Financial Studies, vol. 21(3), pages 1187-1222, May.
    7. Campbell, Rachel & Huisman, Ronald & Koedijk, Kees, 2001. "Optimal portfolio selection in a Value-at-Risk framework," Journal of Banking & Finance, Elsevier, vol. 25(9), pages 1789-1804, September.
    8. Brennan, Michael J & Schwartz, Eduardo S, 1989. "Portfolio Insurance and Financial Market Equilibrium," The Journal of Business, University of Chicago Press, vol. 62(4), pages 455-472, October.
    9. Keith Kuester & Stefan Mittnik & Marc S. Paolella, 2006. "Value-at-Risk Prediction: A Comparison of Alternative Strategies," Journal of Financial Econometrics, Oxford University Press, vol. 4(1), pages 53-89.
    10. Leland, Hayne E, 1980. "Who Should Buy Portfolio Insurance?," Journal of Finance, American Finance Association, vol. 35(2), pages 581-594, May.
    11. Benjamin Hamidi & Bertrand Maillet & Jean-Luc Prigent, 2009. "A Risk Management Approach for Portfolio Insurance Strategies," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00389789, HAL.
    12. Kingston, Geoffrey, 1989. "Theoretical foundations of constant-proportion portfolio insurance," Economics Letters, Elsevier, vol. 29(4), pages 345-347.
    13. Brandouy, Olivier & Briec, Walter & Kerstens, Kristiaan & Van de Woestyne, Ignace, 2010. "Portfolio performance gauging in discrete time using a Luenberger productivity indicator," Journal of Banking & Finance, Elsevier, vol. 34(8), pages 1899-1910, August.
    14. Robert F. Engle & Simone Manganelli, 2004. "CAViaR: Conditional Autoregressive Value at Risk by Regression Quantiles," Journal of Business & Economic Statistics, American Statistical Association, vol. 22, pages 367-381, October.
    15. 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.
    16. Rama Cont & Peter Tankov, 2009. "Constant Proportion Portfolio Insurance In The Presence Of Jumps In Asset Prices," Mathematical Finance, Wiley Blackwell, vol. 19(3), pages 379-401, July.
    17. Koenker,Roger, 2005. "Quantile Regression," Cambridge Books, Cambridge University Press, number 9780521845731, September.
    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. P. Bertrand & J.L. Prigent, 2000. "Portfolio Insurance : The extreme Value of the CCPI Method," THEMA Working Papers 2000-49, THEMA (THéorie Economique, Modélisation et Applications), Université de Cergy-Pontoise.
    20. Massimiliano Caporin & Grégory M. Jannin & Francesco Lisi & Bertrand B. Maillet, 2014. "A Survey On The Four Families Of Performance Measures," Journal of Economic Surveys, Wiley Blackwell, vol. 28(5), pages 917-942, December.
    21. Rudi Zagst & Julia Kraus, 2011. "Stochastic dominance of portfolio insurance strategies," Annals of Operations Research, Springer, vol. 185(1), pages 75-103, May.
    22. Acerbi Carlo & Simonetti Prospero, 2002. "Portfolio Optimization with Spectral Measures of Risk," Papers cond-mat/0203607, arXiv.org.
    23. Jiang, Chonghui & Ma, Yongkai & An, Yunbi, 2009. "The effectiveness of the VaR-based portfolio insurance strategy: An empirical analysis," International Review of Financial Analysis, Elsevier, vol. 18(4), pages 185-197, September.
    24. Yao, Qiwei & Tong, Howell, 1996. "Asymmetric least squares regression estimation: a nonparametric approach," LSE Research Online Documents on Economics 19423, London School of Economics and Political Science, LSE Library.
    25. Grossman, Sanford J & Vila, Jean-Luc, 1989. "Portfolio Insurance in Complete Markets: A Note," The Journal of Business, University of Chicago Press, vol. 62(4), pages 473-476, October.
    26. Koenker, Roger W & Bassett, Gilbert, Jr, 1978. "Regression Quantiles," Econometrica, Econometric Society, vol. 46(1), pages 33-50, January.
    27. Philippe Bertrand & Jean-Luc Prigent, 2005. "Portfolio Insurance Strategies: OBPI versus CPPI," Post-Print hal-01833077, HAL.
    28. 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.
    29. Hélyette Geman & Marc Yor, 1993. "Bessel Processes, Asian Options, And Perpetuities," Mathematical Finance, Wiley Blackwell, vol. 3(4), pages 349-375, October.
    30. Ser-Huang Poon & Clive W.J. Granger, 2003. "Forecasting Volatility in Financial Markets: A Review," Journal of Economic Literature, American Economic Association, vol. 41(2), pages 478-539, June.
    31. Acerbi, Carlo & Tasche, Dirk, 2002. "On the coherence of expected shortfall," Journal of Banking & Finance, Elsevier, vol. 26(7), pages 1487-1503, July.
    32. 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.
    33. Jean-Luc Prigent & Philippe Bertrand, 2011. "Omega performance measure and portfolio insurance," Post-Print hal-01833064, HAL.
    34. Gourieroux, C. & Jasiak, J., 2008. "Dynamic quantile models," Journal of Econometrics, Elsevier, vol. 147(1), pages 198-205, November.
    35. Tepla, Lucie, 2001. "Optimal investment with minimum performance constraints," Journal of Economic Dynamics and Control, Elsevier, vol. 25(10), pages 1629-1645, October.
    36. Sanford J. Grossman & Zhongquan Zhou, 1993. "Optimal Investment Strategies For Controlling Drawdowns," Mathematical Finance, Wiley Blackwell, vol. 3(3), pages 241-276, July.
    37. Philippe Artzner & Freddy Delbaen & Jean‐Marc Eber & David Heath, 1999. "Coherent Measures of Risk," Mathematical Finance, Wiley Blackwell, vol. 9(3), pages 203-228, July.
    38. Philippe Bertrand & Jean-Luc Prigent, 2003. "Portfolio Insurance Strategies: A Comparison of Standard Methods When the Volatility of the Stock is Stochastic," Post-Print hal-01833118, HAL.
    39. Belkacem Abdous & Bruno Remillard, 1995. "Relating quantiles and expectiles under weighted-symmetry," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 47(2), pages 371-384, June.
    40. 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.
    41. El Karoui, Nicole & Jeanblanc, Monique & Lacoste, Vincent, 2005. "Optimal portfolio management with American capital guarantee," Journal of Economic Dynamics and Control, Elsevier, vol. 29(3), pages 449-468, March.
    42. Basak, Suleyman, 2002. "A comparative study of portfolio insurance," Journal of Economic Dynamics and Control, Elsevier, vol. 26(7-8), pages 1217-1241, July.
    43. Tepla, Lucie, 2000. "Optimal portfolio policies with borrowing and shortsale constraints," Journal of Economic Dynamics and Control, Elsevier, vol. 24(11-12), pages 1623-1639, October.
    44. Jones, M. C., 1994. "Expectiles and M-quantiles are quantiles," Statistics & Probability Letters, Elsevier, vol. 20(2), pages 149-153, May.
    45. Hans FÃllmer & Peter Leukert, 1999. "Quantile hedging," Finance and Stochastics, Springer, vol. 3(3), pages 251-273.
    46. Eling, Martin & Schuhmacher, Frank, 2007. "Does the choice of performance measure influence the evaluation of hedge funds?," Journal of Banking & Finance, Elsevier, vol. 31(9), pages 2632-2647, September.
    47. Newey, Whitney K & Powell, James L, 1987. "Asymmetric Least Squares Estimation and Testing," Econometrica, Econometric Society, vol. 55(4), pages 819-847, July.
    48. James W. Taylor, 2008. "Estimating Value at Risk and Expected Shortfall Using Expectiles," Journal of Financial Econometrics, Oxford University Press, vol. 6(2), pages 231-252, Spring.
    49. Black, Fischer & Perold, AndreF., 1992. "Theory of constant proportion portfolio insurance," Journal of Economic Dynamics and Control, Elsevier, vol. 16(3-4), pages 403-426.
    50. Basak, Suleyman, 1995. "A General Equilibrium Model of Portfolio Insurance," The Review of Financial Studies, Society for Financial Studies, vol. 8(4), pages 1059-1090.
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    Cited by:

    1. Caporin, Massimiliano & Costola, Michele & Jannin, Gregory & Maillet, Bertrand, 2018. "“On the (Ab)use of Omega?”," Journal of Empirical Finance, Elsevier, vol. 46(C), pages 11-33.
    2. Xiu Xu & Andrija Mihoci & Wolfgang Karl Hardle, 2020. "lCARE -- localizing Conditional AutoRegressive Expectiles," Papers 2009.13215, arXiv.org.
    3. Ben Ameur, H. & Prigent, J.-L., 2018. "Risk management of time varying floors for dynamic portfolio insurance," European Journal of Operational Research, Elsevier, vol. 269(1), pages 363-381.
    4. Naceur Naguez, 2018. "Dynamic portfolio insurance strategies: risk management under Johnson distributions," Annals of Operations Research, Springer, vol. 262(2), pages 605-629, March.
    5. 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.
    6. Carole Bernard & Massimiliano Caporin & Bertrand Maillet & Xiang Zhang, 2023. "Omega Compatibility: A Meta-analysis," Computational Economics, Springer;Society for Computational Economics, vol. 62(2), pages 493-526, August.
    7. Naceur Naguez & Jean-Luc Prigent, 2014. "Dynamic Portfolio Insurance Strategies: Risk Management under Johnson Distributions," Working Papers 2014-329, Department of Research, Ipag Business School.
    8. Tawil, Dima, 2018. "Risk-adjusted performance of portfolio insurance and investors’ preferences," Finance Research Letters, Elsevier, vol. 24(C), pages 10-18.
    9. Xu, Xiu & Mihoci, Andrija & Härdle, Wolfgang Karl, 2018. "lCARE - localizing conditional autoregressive expectiles," Journal of Empirical Finance, Elsevier, vol. 48(C), pages 198-220.
    10. Wentao Hu & Cuixia Chen & Yufeng Shi & Ze Chen, 2022. "A Tail Measure With Variable Risk Tolerance: Application in Dynamic Portfolio Insurance Strategy," Methodology and Computing in Applied Probability, Springer, vol. 24(2), pages 831-874, June.
    11. Farooq, Muhammad & Steinwart, Ingo, 2017. "An SVM-like approach for expectile regression," Computational Statistics & Data Analysis, Elsevier, vol. 109(C), pages 159-181.
    12. repec:hum:wpaper:sfb649dp2015-052 is not listed on IDEAS
    13. repec:ipg:wpaper:2014-510 is not listed on IDEAS
    14. Branger, Nicole & Mahayni, Antje & Zieling, Daniel, 2015. "Robustness of stable volatility strategies," Journal of Economic Dynamics and Control, Elsevier, vol. 60(C), pages 134-151.
    15. repec:ipg:wpaper:2014-604 is not listed on IDEAS
    16. repec:ipg:wpaper:2014-511 is not listed on IDEAS
    17. Peyman Alipour & Ali Foroush Bastani, 2023. "Value-at-Risk-Based Portfolio Insurance: Performance Evaluation and Benchmarking Against CPPI in a Markov-Modulated Regime-Switching Market," Papers 2305.12539, arXiv.org.
    18. repec:ipg:wpaper:2014-509 is not listed on IDEAS
    19. repec:ipg:wpaper:2014-468 is not listed on IDEAS
    20. repec:ipg:wpaper:2014-531 is not listed on IDEAS
    21. Katia Colaneri & Daniele Mancinelli & Immacolata Oliva, 2024. "On the optimal design of a new class of proportional portfolio insurance strategies in a jump-diffusion framework," Papers 2407.21148, arXiv.org.
    22. Zieling, Daniel & Mahayni, Antje & Balder, Sven, 2014. "Performance evaluation of optimized portfolio insurance strategies," Journal of Banking & Finance, Elsevier, vol. 43(C), pages 212-225.

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    More about this item

    Keywords

    CPPI; VaR; Expected Shortfall; Expective; Quantile Regression; Dynamic Quantile Model;
    All these keywords.

    JEL classification:

    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
    • C6 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling
    • G24 - Financial Economics - - Financial Institutions and Services - - - Investment Banking; Venture Capital; Brokerage
    • L10 - Industrial Organization - - Market Structure, Firm Strategy, and Market Performance - - - General

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