Dynamic Portfolio Insurance Strategies: Risk Management under Johnson Distributions

The purpose of this paper is to analyze the gap risk of dynamic portfo- lio insurance strategies which generalize the "Constant Proportion Port- folio 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 dy- namics 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.