On Path–dependency ofConstant Proportion Portfolio Insurance strategies

This paper evaluates the path–dependency/independency of most widespread PortfolioInsurance strategies. In particular, we look at Constant Proportion Portfolio Insurance (CPPI)structures and compare them to both the classical Option Based Portfolio Insurance(OBPI)and naive strategies such as Stop-loss Portfolio Insurance (SLPI) or a CPPI with a multiplierof one. The paper is based uponconditional Monte Carlo simulations and we show that CPPI strategies with a multiplier higher than 1 are extremely path-dependent and that they can easilyget cash-locked, even in scenarios when the underlying at maturity can be worth much morethan initially. The likelihood of being cash-locked increases with the size of the multiplierand the maturity of the CPPI, as well as with properties of the risky underlying’s dynamics.To emphasize the path dependency of CPPIs,we show that even in scenarios where theinvestor correctly “guesses” a higher future value for the underlying, CPPIs can get cash-locked,losing the linkage to the risky asset.This cash-lock problem is specific of CPPIs, itgoes against its European-style nature of traded CPPIs, and it introduces into the strategy a risks not related to the underlying risky asset – a design risk.Design risk does not occur forpath-independent portfolio insurance strategies, like the classical case of OBPI strategies, norin naive strategies. This study contributes to reinforce the idea that CPPI strategies suffer froma serious design problem.