A Dynamic AutoRegressive Expectile for Time-Invariant Portfolio Protection Strategies

Among the most popular techniques for portfolio insurance strategies that are used nowadays, the so-called \Constant Proportion Portfolio In- surance" (CPPI) allocation simply consists in reallocating the risky part of a portfolio according to the market conditions. This general method crucially depends upon a parameter - called the multiple - guaranteeing a predetermined oor whatever the plausible market evolutions. However, the unconditional multiple is dened once and for all in the traditional CPPI setting; we propose in this article an alternative to the standard CPPI method, based on the determination of a conditional multiple. In this time-varying framework, the multiple is conditionally determined in order the risk exposure to remain constant, but depending on market con- ditions. We thus propose to dene the multiple as a function of Expected Shortfall. After brie y recalling the portfolio insurance principles, the CPPI framework and the main properties of the conditional or unconditional multiples, we present a Dynamic AutoRegressive Expectile (DARE) class of models for the conditional multiple in a time-varying strategy whose aim is to adapt the current exposition to market conditions following a traditional risk management philosophy. We illustrate this approach in a Time-Invariant Portfolio Protection (TIPP) strategy, as introduced by Estep and Kritzman (1988), which aims to increase the protected oor according to the insured portfolio performance. Finally, we use an option valuation approach for measuring the gap risk in both conditional and unconditional approaches.