A Dynamic AutoRegressive Expectile for Time-Invariant Portfolio Protection Strategies
"Constant proportion portfolio insurance" (CPPI) is nowadays one of the most popular techniques for portfolio insurance strategies. It simply consists of reallocating the risky part of a portfolio with respect to market conditions, via a leverage parameter - called the multiple - guaranteeing a predetermined floor. We propose to introduce a conditional time-varying multiple as an alternative to the standard unconditional CPPI method, directly linked to actual risk management problematics. This "ex ante" approach for the conditional multiple aims to diversify the risk model associated, for example, with the expected shortfall (ES) or extreme risk measure estimations. First, we recall the portfolio insurance principles, and main properties of the CPPI strategy, including the time-invariant portfolio protection (TIPP) strategy, as introduced by Estep and Kritzman (1988). We emphasize the existence of an upper bound on the multiple, for example to hedge against sudden drops in the market. Then, we provide the main properties of the conditional multiples for well-known financial models including the discrete-time portfolio rebalancing case and Lévy processes to describe the risky asset dynamics. For this purpose, we precisely define and evaluate different gap risks, in both conditional and unconditional frameworks. As a by-product, the introduction of discrete or random time portfolio rebalancing allows us to determine and/or estimate the density of durations between rebalancements. Finally, from a more practical and statistical point of view due to trading restrictions, we present the class of Dynamic AutoRegressive Expectile (DARE) models for estimating the conditional multiple. This latter approach provides useful complementary information about the risk and performance associated with probabilistic approaches to the conditional multiple.
|Date of creation:||26 Jun 2014|
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Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Qiwei Yao & Howell Tong, 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.
- Benjamin Hamidi & Bertrand Maillet & Jean-Luc Prigent, 2009.
"A Risk Management Approach for Portfolio Insurance Strategies,"
Documents de travail du Centre d'Economie de la Sorbonne
09034, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
- 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.
- James W. Taylor, 2008. "Estimating Value at Risk and Expected Shortfall Using Expectiles," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 6(2), pages 231-252, Spring.
- Hayne E. Leland., 1979.
"Who Should Buy Portfolio Insurance?,"
Research Program in Finance Working Papers
95, University of California at Berkeley.
- 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.
- Engle, Robert F & Manganelli, Simone, 1999. "CAViaR: Conditional Autoregressive Value at Risk by Regression Quantiles," University of California at San Diego, Economics Working Paper Series qt06m3d6nv, Department of Economics, UC San Diego.
- Robert Engle & Simone Manganelli, 2000. "CAViaR: Conditional Autoregressive Value at Risk by Regression Quantiles," Econometric Society World Congress 2000 Contributed Papers 0841, Econometric Society.
- Ruiz, Esther & 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.
- Sanford J. Grossman & Zhongquan Zhou, 1993. "Optimal Investment Strategies For Controlling Drawdowns," Mathematical Finance, Wiley Blackwell, vol. 3(3), pages 241-276.
- 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.
- 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.
- 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 473-76, October.
- Carlo Acerbi & Dirk Tasche, 2001.
"On the coherence of Expected Shortfall,"
cond-mat/0104295, arXiv.org, revised May 2002.
- Olivier Brandouy & Walter Briec & Kristiaan Kerstens & Ignace Van de Woestyne, 2008.
"Portfolio Performance Gauging in Discrete Time Using a Luenberger Productivity Indicator,"
2008-ECO-12, IESEG School of Management, revised Oct 2009.
- 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.
- O. Brandouy & W. Briec & K. Kerstens & I. Van de Woestyne, 2010. "Portfolio performance gauging in discrete time using a luenberger productivity indicator," Post-Print halshs-00490032, HAL.
- Brandouy, Olivier & Briec, Walter & Kerstens, Kristiaan, 2008. "Portfolio performance gauging in discrete time using a Luenberger productivity indicator," Working Papers 2008/60, Hogeschool-Universiteit Brussel, Faculteit Economie en Management.
- 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.
- Kingston, Geoffrey, 1988.
"Theoretical Foundations of Constant-Proportion Portfolio Insurance,"
116, University of Sydney, School of Economics.
- Kingston, Geoffrey, 1989. "Theoretical foundations of constant-proportion portfolio insurance," Economics Letters, Elsevier, vol. 29(4), pages 345-347.
- Acerbi Carlo & Simonetti Prospero, 2002. "Portfolio Optimization with Spectral Measures of Risk," Papers cond-mat/0203607, arXiv.org.
- Philippe Artzner & Freddy Delbaen & Jean-Marc Eber & David Heath, 1999. "Coherent Measures of Risk," Mathematical Finance, Wiley Blackwell, vol. 9(3), pages 203-228.
- Koenker, Roger W & Bassett, Gilbert, Jr, 1978. "Regression Quantiles," Econometrica, Econometric Society, vol. 46(1), pages 33-50, January.
- 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.
- Hans FÃllmer & Peter Leukert, 1999. "Quantile hedging," Finance and Stochastics, Springer, vol. 3(3), pages 251-273.
- Hélyette Geman & Marc Yor, 1993. "Bessel Processes, Asian Options, And Perpetuities," Mathematical Finance, Wiley Blackwell, vol. 3(4), pages 349-375.
- Gourieroux, C. & Jasiak, J., 2008.
"Dynamic quantile models,"
Journal of Econometrics,
Elsevier, vol. 147(1), pages 198-205, November.
- 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.
- 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.
- 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.
- Newey, Whitney K & Powell, James L, 1987. "Asymmetric Least Squares Estimation and Testing," Econometrica, Econometric Society, vol. 55(4), pages 819-47, July.
- Basak, Suleyman, 2002. "A comparative study of portfolio insurance," Journal of Economic Dynamics and Control, Elsevier, vol. 26(7-8), pages 1217-1241, July.
- Basak, Suleyman, 1995. "A General Equilibrium Model of Portfolio Insurance," Review of Financial Studies, Society for Financial Studies, vol. 8(4), pages 1059-90.
- 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.
- Rama Cont & Peter Tankov, 2007.
"Constant Proportion Portfolio Insurance in presence of Jumps in Asset Prices,"
- Rama Cont & Peter Tankov, 2009. "Constant proportion portfolio insurance in presence of jumps in asset prices," Post-Print hal-00445646, HAL.
- repec:hal:journl:halshs-00389789 is not listed on IDEAS
- Koenker,Roger, 2005.
Cambridge University Press, number 9780521845731, Junio.
- 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.
- Tepla, Lucie, 2001. "Optimal investment with minimum performance constraints," Journal of Economic Dynamics and Control, Elsevier, vol. 25(10), pages 1629-1645, October.
- 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.
- 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.
- Keith Kuester & Stefan Mittnik & Marc S. Paolella, 2006. "Value-at-Risk Prediction: A Comparison of Alternative Strategies," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 4(1), pages 53-89.
- S. G. Kou, 2002. "A Jump-Diffusion Model for Option Pricing," Management Science, INFORMS, vol. 48(8), pages 1086-1101, August.
- 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.
- Bertrand Maillet & Michele Costola & Massimiliano Caporin & Gregory Jannin, 2015. "On the (Ab)Use of Omega?," Working Papers 2015:02, Department of Economics, University of Venice "Ca' Foscari".
- Bertrand, Philippe & Prigent, Jean-luc, 2011. "Omega performance measure and portfolio insurance," Journal of Banking & Finance, Elsevier, vol. 35(7), pages 1811-1823, July.
- Robert F. Engle & Jose Gonzalo Rangel, 2008. "The Spline-GARCH Model for Low-Frequency Volatility and Its Global Macroeconomic Causes," Review of Financial Studies, Society for Financial Studies, vol. 21(3), pages 1187-1222, May.
- James W. Taylor, 2008. "Using Exponentially Weighted Quantile Regression to Estimate Value at Risk and Expected Shortfall," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 6(3), pages 382-406, Summer.
- 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.
- 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 455-72, October.
- Jones, M. C., 1994. "Expectiles and M-quantiles are quantiles," Statistics & Probability Letters, Elsevier, vol. 20(2), pages 149-153, May.
- 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.
- 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.
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