Annals of Operations Research

, Volume 262, Issue 2, pp 605–629 | Cite as

Dynamic portfolio insurance strategies: risk management under Johnson distributions

  • Naceur NaguezEmail author
S.I.: Financial Economics


The purpose of this paper is to analyze the gap risk of dynamic portfolio insurance strategies which generalize the “Constant Proportion Portfolio Insurance” (CPPI) method by allowing the multiple to vary. We illustrate our theoretical results for conditional CPPI strategies indexed on hedge funds. For this purpose, we provide accurate estimations of hedge funds returns by means of Johnson distributions. We introduce also an EGARCH type model with Johnson innovations to describe dynamics of risky logreturns. We use both VaR and Expected Shortfall as downside risk measures to control gap risk. We provide accurate upper bounds on the multiple in order to limit this gap risk. We illustrate our theoretical results on Credit Suisse Hedge Fund Index. The time period of the analysis lies between December 1994 and December 2013.


Portfolio insurance CPPI Hedge funds Johnson distribution Gap risk VaR CVaR 

JEL Classification

C6 G11 G24 L10 


  1. Ackerman, C., McEnally, R., & Ravenscraft, D. (1999). The performance of hedge funds: Risk, return and incentives. Journal of Finance, 54, 833–874.CrossRefGoogle Scholar
  2. Agarwal, V., & Naik, N. Y. (2004). Risks and portfolio decisions involving hedge funds. Review of Financial Studies, 17, 63–98.CrossRefGoogle Scholar
  3. Bacmann, J.-F., & Scholz, S. (2003). Alternative performance measures for hedge funds. AIMA Journal, 55, 1–3.Google Scholar
  4. Ben Ameur, H., & Prigent, J.-L. (2014). Portfolio Insurance: Gap risk under conditional multiples. European Journal of Operational Research, 236, 238–253.CrossRefGoogle Scholar
  5. Bertrand, P., & Prigent, J.-L. (2002). Portfolio insurance: The extreme value approach to the CPPI method. Finance, 23, 69–86.Google Scholar
  6. Bertrand, P., & Prigent, J.-L. (2011). Omega performance measure and portfolio insurance. Journal of Banking and Finance, 35, 1811–1823.CrossRefGoogle Scholar
  7. Black, F., & Jones, R. (1987). Simplifying portfolio insurance. Journal of Portfolio Management, 14, 48–51.CrossRefGoogle Scholar
  8. Black, F., & Perold, A. R. (1992). Theory of constant proportion portfolio insurance. The Journal of Economics, Dynamics and Control, 16, 403–426.CrossRefGoogle Scholar
  9. Black, F., & Rouhani, R. (1989). Constant proportion portfolio insurance and the synthetic put option: A comparison. In F. J. Fabozzi (Ed.), Investment Management. Cambridge, Massachusetts: Ballinger.Google Scholar
  10. Brooks, C., & Kat, H. M. (2001). The statistical properties of Hedge fund index returns and their implications for investors. Working Paper, ISMA Centre Discussion Papers In Finance.Google Scholar
  11. Brown, S. J., Goetzmann, W. N., & Ibbotson, R. G. (1999). Offshore hedge funds: Survival and performance: 1989–1995. Journal of Business, 72, 91–119.CrossRefGoogle Scholar
  12. Caglayan, M., & Edwards, F. (2001). Hedge fund performance and manager skill. Journal of Futures Markets, 21, 1003–1028.Google Scholar
  13. Engle, R., & Manganelli, S. (2004). CAViaR: Conditional autoregressive value at risk by regression quantiles. Journal of Business and Economic Statistics, 22, 367–381.Google Scholar
  14. Ested, T., & Kritzman, M. (1988). TIPP: Insurance without complexity. Journal of Portfolio Management, 14, 38–42.CrossRefGoogle Scholar
  15. Föllmer, H., & Leukert, P. (1999). Quantile hedging. Finance and Stochastics, 3, 251–273.CrossRefGoogle Scholar
  16. Fung, W., & Hsieh, D. (1997). Empirical characteristics of dynamic trading strategies: The case of hedge funds. Review of Financial Studies, 10, 275–302.CrossRefGoogle Scholar
  17. Hamidi, B., Jurczenko, E., & Maillet, B. (2009a). D’un multiple conditionnel en assurance de portefeuille: CaViaR pour les gestionnaires? University of Paris 1. Working paper CES 2009.33.Google Scholar
  18. Hamidi, B., Jurczenko, E., & Maillet, B. (2009b) A CAViaR time-varying proportion portfolio insurance. Bankers, Markets and Investors 102, September–October, 4–21.Google Scholar
  19. Hamidi, B., Maillet, B., & Prigent, J. L. (2014). Dynamic autoregressive expectile for time-invariant portfolio protection strategies. Journal of Economic Dynamics and Control, 46, 1–29.CrossRefGoogle Scholar
  20. Hill, I. D., Hill, R., & Holder, R. L. (1976). Fitting Johnson curves by moments. Applied Statistics, AS99.Google Scholar
  21. Johnson, N. L. (1949). Systems of frequency curves generated by methods of translation. Biometrica, 58, 547–558.Google Scholar
  22. Longin, F. (1997). The treshold effect in expected volatility: A model based on asymmetric. Information Review of Financial Studies, 10, 837–869.CrossRefGoogle Scholar
  23. Naguez, N., & Prigent, J. L. (2014). Optimal portfolio positioning within Johnson distribution. THEMA, University of Cergy-Pontoise, Working Paper.Google Scholar
  24. Perold, A. R. (1986). Constant Proportion portfolio insurance. Harvard Business School, Working paper.Google Scholar
  25. Perold, A. R., & Sharpe, W. (1988). Dynamic strategies for asset allocations. Financial Analysts Journal, 44, 16–27.CrossRefGoogle Scholar
  26. Poncet, P., & Portait, R. (1997). Assurance de Portefeuille. In Y. Simon (Ed.), Encyclopédie des Marchés Financiers, Economica, pp. 140–141.Google Scholar
  27. Prigent, J. L. (2001). Assurance du portefeuille: analyse et extension de la méthode du coussin. Banque et Marchés, 51, 33–39.Google Scholar
  28. Roman, E., Kopprash, R., & Hakanoglu, E. (1989). Constant Proportion Portfolio Insurance for fixed-income investment. Journal of Portfolio Management, 15, 58–66.CrossRefGoogle Scholar
  29. Slifker, J. F., & Shapiro, S. S. (1980). The Johnson system: Selection and parameter estimation. Technometrics, 22, 239–246.CrossRefGoogle Scholar
  30. Wheeler, R. E. (1980). Quantile estimators of Johnson curve parameters. Biometrika, 67, 725–728.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  1. 1.University of Cergy-PontoiseCergy-PontoiseFrance

Personalised recommendations