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Portfolio insurance: Gap risk under conditional multiples

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  • Ben Ameur, H.
  • Prigent, J.L.

Abstract

The research on financial portfolio optimization has been originally developed by Markowitz (1952). It has been further extended in many directions, among them the portfolio insurance theory introduced by Leland and Rubinstein (1976) for the “Option Based Portfolio Insurance” (OBPI) and Perold (1986) for the “Constant Proportion Portfolio Insurance” method (CPPI). The recent financial crisis has dramatically emphasized the interest of such portfolio strategies. This paper examines the CPPI method when the multiple is allowed to vary over time. To control the risk of such portfolio management, a quantile approach is introduced together with expected shortfall criteria. In this framework, we provide explicit upper bounds on the multiple as function of past asset returns and volatilities. These values can be statistically estimated from financial data, using for example ARCH type models. We show how the multiple can be chosen in order to satisfy the guarantee condition, at a given level of probability and for various financial market conditions.

Suggested Citation

  • 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.
  • Handle: RePEc:eee:ejores:v:236:y:2014:i:1:p:238-253
    DOI: 10.1016/j.ejor.2013.11.027
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    1. Yu, Jing-Rung & Lee, Wen-Yi, 2011. "Portfolio rebalancing model using multiple criteria," European Journal of Operational Research, Elsevier, vol. 209(2), pages 166-175, March.
    2. Heynen, Ronald & Kemna, Angelien & Vorst, Ton, 1994. "Analysis of the Term Structure of Implied Volatilities," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 29(1), pages 31-56, March.
    3. Nelson, Daniel B., 1990. "ARCH models as diffusion approximations," Journal of Econometrics, Elsevier, vol. 45(1-2), pages 7-38.
    4. Brennan, M.J. & Solanki, R., 1981. "Optimal Portfolio Insurance," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 16(3), pages 279-300, September.
    5. Yi-Ting Chen & Chung-Ming Kuan, 2002. "Time irreversibility and EGARCH effects in US stock index returns," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 17(5), pages 565-578.
    6. 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.
    7. 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.
    8. Jérôme B. Detemple & Ren Garcia & Marcel Rindisbacher, 2003. "A Monte Carlo Method for Optimal Portfolios," Journal of Finance, American Finance Association, vol. 58(1), pages 401-446, February.
    9. Leland, Hayne E, 1980. "Who Should Buy Portfolio Insurance?," Journal of Finance, American Finance Association, vol. 35(2), pages 581-594, May.
    10. Yu, Bosco Wing-Tong & Pang, Wan Kai & Troutt, Marvin D. & Hou, Shui Hung, 2009. "Objective comparisons of the optimal portfolios corresponding to different utility functions," European Journal of Operational Research, Elsevier, vol. 199(2), pages 604-610, December.
    11. Awartani, Basel M.A. & Corradi, Valentina, 2005. "Predicting the volatility of the S&P-500 stock index via GARCH models: the role of asymmetries," International Journal of Forecasting, Elsevier, vol. 21(1), pages 167-183.
    12. 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.
    13. Christian S. Pedersen & Stephen E. Satchell, 1998. "An Extended Family of Financial-Risk Measures," The Geneva Risk and Insurance Review, Palgrave Macmillan;International Association for the Study of Insurance Economics (The Geneva Association), vol. 23(2), pages 89-117, December.
    14. 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.
    15. 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.
    16. Campbell, John Y. & Viceira, Luis M., 2002. "Strategic Asset Allocation: Portfolio Choice for Long-Term Investors," OUP Catalogue, Oxford University Press, number 9780198296942.
    17. 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.
    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. Engle, Robert F & Ng, Victor K, 1993. "Measuring and Testing the Impact of News on Volatility," Journal of Finance, American Finance Association, vol. 48(5), pages 1749-1778, December.
    20. Hans FÃllmer & Peter Leukert, 1999. "Quantile hedging," Finance and Stochastics, Springer, vol. 3(3), pages 251-273.
    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. 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.
    23. Rockafellar, R. Tyrrell & Uryasev, Stanislav, 2002. "Conditional value-at-risk for general loss distributions," Journal of Banking & Finance, Elsevier, vol. 26(7), pages 1443-1471, July.
    24. Engle, Robert F, 1982. "Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation," Econometrica, Econometric Society, vol. 50(4), pages 987-1007, July.
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    2. Xiu Xu & Andrija Mihoci & Wolfgang Karl Hardle, 2020. "lCARE -- localizing Conditional AutoRegressive Expectiles," Papers 2009.13215, arXiv.org.
    3. Hamidi, Benjamin & Maillet, Bertrand & Prigent, Jean-Luc, 2014. "A dynamic autoregressive expectile for time-invariant portfolio protection strategies," Journal of Economic Dynamics and Control, Elsevier, vol. 46(C), pages 1-29.
    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. Zagst, Rudi & Kraus, Julia & Bertrand, Philippe, 2019. "Option-Based performance participation," Journal of Banking & Finance, Elsevier, vol. 105(C), pages 44-61.
    6. 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.
    7. Tawil, Dima, 2018. "Risk-adjusted performance of portfolio insurance and investors’ preferences," Finance Research Letters, Elsevier, vol. 24(C), pages 10-18.
    8. Xu, Xiu & Mihoci, Andrija & Härdle, Wolfgang Karl, 2018. "lCARE - localizing conditional autoregressive expectiles," Journal of Empirical Finance, Elsevier, vol. 48(C), pages 198-220.
    9. 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.
    10. Marcos Escobar-Anel & Andreas Lichtenstern & Rudi Zagst, 2020. "Behavioral portfolio insurance strategies," Financial Markets and Portfolio Management, Springer;Swiss Society for Financial Market Research, vol. 34(4), pages 353-399, December.
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    12. 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.
    13. 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.

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